Abstract

Here, we focus on using composite pulses to realize high-robustness and high-fidelity coherent control in three-level quantum systems. We design the dynamic parameters (Rabi frequency and detuning) for three-level Hamiltonians for high-fidelity quantum state control using five well-known coherent control techniques including a composite adiabatic passage (CAP). Furthermore, we compare their performance against the Rabi frequency and systematic errors, and accordingly show that the CAP is the most robust against them. It features a broad range of high efficiencies above 99.9%. Thus, it provides an accurate approach for manipulating the evolution of quantum states in three-level quantum systems.

© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

Accurate initialization and manipulation of quantum states have generated extensive interest in the fields of quantum optics, quantum control, and quantum simulations [1,2]. In addition, they have widespread successful applications in atomic, molecular, and optical physics, chemistry, and many other aspects [35]. To achieve these targets, there are numerous control methods that can be employed, such as resonance excitation (RE) [6], adiabatic passages (APs), shortcuts to adiabaticity (STAs) [711], dynamical correction technique [12,13], reinforcement learning [1417], frequency tuning method [18], and composite schemes [1921]. RE uses $\pi$ or $\pi /2$ resonant pulses to realize rapid quantum state control. APs, including rapid adiabatic passages [22], piecewise adiabatic passages [23], and stimulated Raman adiabatic passages [24,25], can cause quantum systems to evolve adiabatically along an eigenstate of the Hamiltonian, leading to efficient and robust population transfer. STAs, including counter-diabatic (CD) shortcuts [2631] and Lewis-Riesenfeld invariants (LRIs) [3236], can accelerate a quantum adiabatic process to reproduce the same final population.

Composite pulses (CPs) are well-studied protocols for realizing specific coherent quantum control using a sequence of pulses. Their advantage is the control of the phases of pulses to produce desired results, instead of the control of the amplitudes of pulses. Two typical types of CPs are composite adiabatic passage (CAP) and universal composite pulses (UCPs). A CAP is a combination of an adiabatic scheme and a CP, which can eliminate experimental errors by appropriately selecting the phases of the pulse sequences; a UCP is a more general composite technology, without specific requirements for pulses. Both are regarded as powerful tools for precise quantum state manipulations in various quantum systems [3740]. For example, in 2011, Torosov et al. [37] proposed a CAP to optimize the defect that an AP cannot achieve complete population inversion in two-level systems. In 2014, Genov et al. [38] used a UCP to realize robust high-fidelity population inversion in two-state quantum systems, and experimentally demonstrated its effectiveness and universality in a $\rm {\Pr ^{3 +}}$:$\rm {Y_2}Si{O_5}$ crystal. In 2018, Torosov et al. [39] presented three classes of symmetric broadband CP sequences, which compensate the imperfections in the pulse area to an arbitrary high order. In 2021, Shi et al. [40] proposed a method to realize robust general single-qubit gates using CPs in a three-level system.

Imperfect experimental implementations and conditions generate experimental control errors and parameter fluctuations of the Hamiltonian. For example, atoms adopting different Rabi frequencies induced by different positions and fields [41] cause the original Hamiltonian elements to present small global shifts. In addition, atoms or ions in the nonuniform spatial distribution of an external laser, a microwave, or the radiofrequency field produce fluctuations of the Rabi frequency. These errors affect the accuracy and efficiency of quantum state control. A CAP is a useful method for suppressing these experimental errors, because it is insensitive to the pulse shape or pulse area. In 2013, Schraft et al. [42] experimentally demonstrated the robustness and efficiency advantages of a CAP even under weak adiabatic conditions. In 2018, Bruns et al. [43] experimentally demonstrated the improvement in the transfer efficiency and robustness of composite stimulated Raman adiabatic passages compared to those of conventional and repeated stimulated Raman adiabatic passages. In 2021, Torosov et al. [44] compared six well-known techniques for coherent control of two-state quantum systems with respect to various sources of errors, and showed that a CAP is more resilient to experimental errors than the other methods.

Here, we establish a method to use CPs to realize complete and robust coherent control in three-level quantum systems. The CPs change a quantum state using CP sequences, with the relative phases serving as the control parameters, without dependence on the specific shapes of the pulses. More importantly, we compare the performance of a CAP with RE, an AP, a CD, and an LRI with respect to common experimental errors, and find that the CAP is the most robust against these errors among all considered methods. Moreover, it can maintain the transition probability at ultrahigh efficiencies above $99.9\%$ over broad ranges of the error parameters. This offers an effective route for achieving high-fidelity coherent control of three-level quantum systems using CAPs.

2. Preliminaries

We consider here arrays of optical wells, where the dipole force of a red detuned laser field is used to store neutral atoms in each of the foci of a set of microlenses [45]. Three in-line dipole wells are modeled as three harmonic potentials, and we assume here that we can initially store no or one neutral atom per well. The Hamiltonian, in the basis of $\{\left |L\right \rangle,\left |C\right \rangle, \left |R\right \rangle \}$, is expressed as

$$\begin{aligned}{H_0}(t)= \left( {\begin{array}{*{20}{c}} K & { - \sqrt 2 J} & 0\\ { - \sqrt 2 J} & 0 & { - \sqrt 2 J}\\ 0 & { - \sqrt 2 J} & K \end{array}} \right), \end{aligned}$$
where $\left |L\right \rangle =\left (\begin {array}{c} 1 \\ 0 \\ 0 \end {array} \right )$, $\left |C\right \rangle =\left (\begin {array}{c} 0 \\ 1 \\ 0 \end {array} \right )$, and $\left |R\right \rangle =\left (\begin {array}{c} 0 \\ 0 \\ 1 \end {array} \right )$, and they represent the minimal channel basis for the left, central, and right wavefunctions in a triple well, respectively. $K$ plays the role of the bias of the outer wells with respect to the central one and $J$ is the coupling coefficient between adjacent wells [46]. The three-level Hamiltonian also describes other physical systems, e.g., two bosons in two wells [46,47], three coupled waveguides [48,49], and a three-level atom under appropriate laser interactions [50].

Here, our objective is to manipulate the evolution of an atom wavefunction from the central well to the external wells with the same probability amplitude, i.e., $\left |C\right \rangle \rightarrow 1/\sqrt {2}\left (\left |L\right \rangle +\left |R\right \rangle \right )$. This is similar to a crucial device of many optical experimental and measurement systems–a beam splitter–which can split a beam of light in two (see Fig. 1). For this purpose, we can rewrite the Hamiltonian, ${H_0}(t)$, in the basis of $\{\left |C\right \rangle,\left |\Phi _+\right \rangle, \left |\Phi _-\right \rangle \}$, as

$$\begin{aligned}{H_0}^{\prime} (t)= \frac{1}{2}\left( {\begin{array}{*{20}{c}} { - K} & { - 4J} & 0\\ { - 4J} & K & 0\\ 0 & 0 & K \end{array}} \right) \end{aligned}$$
where $\left |\Phi _\pm \right \rangle =1/\sqrt {2}\left (\left |L\right \rangle \pm \left |R\right \rangle \right )$, and the identity matrix, $\frac {1}{2}K$, is omitted. We can find that if the system starts in state $\left |\Phi _-\right \rangle$, the Hamiltonian ${H_0}^{\prime } (t)$ will drive the system to always stay in this state, and it never evolves into the state $\left |C\right \rangle$, $\left |\Phi _+\right \rangle$, or any superposition of them. Thus, in this case, state $\left |\Phi _-\right \rangle$ is decoupled from the subspace of $\left |C\right \rangle$ and $\left |\Phi _+\right \rangle$. Therefore, the Hamiltonian, in subspace $\{\left |C\right \rangle,\left |\Phi _+\right \rangle \}$, can be further reduced to
$$\begin{aligned} H(t) = \frac{1}{2}\left( {\begin{array}{*{20}{c}} { - \Delta } & \Omega \\ \Omega & \Delta \end{array}} \right), \end{aligned}$$
where $\Delta = K$ is the detuning and $\Omega = - 4J$ is the Rabi frequency in terms of the standard notation for two-level Hamiltonians in quantum optics. Thus, the objective is transformed into realizing population inversion in two-level quantum systems.

 figure: Fig. 1.

Fig. 1. Illustration of 1:2 beam splitter.

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3. Quantum state control using five coherent techniques

3.1 RE

First, we show how to achieve the above-mentioned aim using RE. RE requires that the frequency of the external drive field should be the same as the Bohr transition frequency, i.e., $\Delta = 0$. We can write analytically the time-dependent evolution of the transition probability as

$$P(t) = \frac{1}{2}\left[ {1 - \cos (A)} \right],$$
where $A(t) = \int _{{t_0}}^{t} {\Omega (t')dt'}$ is the pulse area. Understandably, when $A(t)$ is selected as an odd multiple of $\pi$ and $P=1$, complete population inversion can be achieved, regardless of the pulse shape. To explain, we take a Gaussian pulse [51] as an example, which is expressed as
$$\Omega (t) = \sqrt \pi {e^{ - {{(t/T)}^{2}}}}/T,$$
where $\sqrt \pi /T$ is the peak Rabi frequency and $T$ is the pulse width, which are plotted in Fig. 2(a). It satisfies $A=\int _{ - \infty }^{ + \infty } {\Omega (t')dt'} = \pi$. In practice, the pulse duration cannot be infinite; it is typically sufficient to choose the condition, $t \in [ -3T,3T]$, to realize population inversion, as shown in Fig. 2(b).

 figure: Fig. 2.

Fig. 2. Time dependence of parameters $\Omega$ and population $P(t)$ of state $\left | {{\Phi _ + }} \right \rangle$ of RE method: (a) $\Omega$ (blue, solid line), (b) Population $P(t)$ (red, solid line).

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3.2 AP

AP is an important method to realize population inversion of two-state systems. It requires that the parameters of Hamiltonian change slowly enough. If the system starts in an eigenstate of Hamiltonian, then the system will evolve adiabatically along this eigenstate. Specifically, if we take a linearly chirped Gaussian pulse,

$$\Delta = \alpha \frac{t}{T},\;\;\;\;{\rm{ }}\Omega = {\Omega _0}{e^{ - {{(t/T)}^{2}}}},$$
the adiabatic condition is [44]
$$\sqrt 2 {\Omega _0} > \alpha \gg \frac{2}{T},$$
where ${\Omega _0}$ is the peak Rabi frequency and $\alpha$ is the chirp rate. Here we adopt
$$\Delta = \frac{5}{T}\frac{t}{T},\;\;\;\;{\rm{ }}\Omega = \frac{5{\sqrt \pi }}{T}{e^{ - {{(t/T)}^{2}}}},$$
which are plotted in Fig. 3(a). The corresponding population of state $\left | {{\Phi _ + }} \right \rangle$ are depicted in Fig. 3(b).

 figure: Fig. 3.

Fig. 3. Time dependence of parameters $\Omega$ and population $P(t)$ of state $\left | {{\Phi _ + }} \right \rangle$ of AP method: (a) $\Delta$ (red, dashed line) and $\Omega$ (blue, solid line), (b) Population $P(t)$ (red, solid line).

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3.3 CD control

CD control is a method of adding a CD Hamiltonian $H_c$ to original Hamiltonian $H(t)$ for adiabatic evolution, allowing to control the system by perfectly following the instantaneous eigenstate of the original Hamiltonian. Based on the theory of Berry [27], the CD Hamiltonian is written as

$${H_c} = i\hbar \sum_ \pm {\left( {\left| {{\partial _t}{\phi _ \pm }} \right\rangle \left\langle {{\phi _ \pm }} \right| - \left\langle {{{\phi _ \pm }}} \mathrel{\left | {\vphantom {{{\phi _ \pm }} {{\partial _t}{\phi _ \pm }}}} \right. } {{{\partial _t}{\phi _ \pm }}} \right\rangle \left| {{\phi _ \pm }} \right\rangle \left\langle {{\phi _ \pm }} \right|} \right)} ,$$
where
$$\begin{aligned}\left| {{\phi _ + }} \right\rangle = \left( {\begin{array}{*{20}{c}} {\sin \gamma }\\ {\cos \gamma } \end{array}} \;\;\;{\rm{ }}\right),\left| {{\phi _ - }} \right\rangle = \left( {\begin{array}{*{20}{c}} {\cos \gamma }\\ { - \sin \gamma } \end{array}} \right) \end{aligned}$$
are the eigenstates of original Hamiltonian $H(t)$, with $\gamma = \frac {1}{2}\arctan \left ( \Omega /\Delta \right )$ being the mixing angle. Thus, we obtain
$$\begin{aligned}{H_c} = \frac{1}{2}\left( {\begin{array}{*{20}{c}} 0 & {i{\Omega _c}}\\ { - i{\Omega _c}} & 0 \end{array}} \right), \end{aligned}$$
where ${\Omega _c} = 2\dot \gamma$, in which the dot represents the derivative with respect to time. Here, we adopt a chirped Gaussian pulse,
$$\Delta = \frac{2}{T}\frac{t}{T},\;\;\;\;{\rm{ }}\Omega = \frac{{\sqrt \pi }}{T}{e^{ - {{(t/T)}^{2}}}},$$
based on which the CD term is calculated as
$${\Omega _c} ={-} 2\sqrt \pi {e^{{{(t/T)}^{2}}}}\left[ {2{{(t/T)}^{2}} + 1} \right]/\left[ {4{{(t/T)}^{2}}T{e^{{{(t/T)}^{2}}}} + \pi T} \right].$$

The time evolutions of the Rabi frequency, detuning, and CD term are plotted in Fig. 4(a). The time evolutions governed by Hamiltonian $H' = H + {H_c}$ can achieve accurate population transfer for this system, as shown in Fig. 4(b).

 figure: Fig. 4.

Fig. 4. Time dependence of parameters $\Delta$, $\Omega$, and population $P(t)$ of state $\left | {{\Phi _ + }} \right \rangle$ of CD method: (a) $\Delta$ (red, dashed line), $\Omega$ (blue, solid line), and CD term ${\Omega _c}$ (green, dashed-dotted line), (b) Population $P(t)$ (red, solid line).

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3.4 LRIs

We consider an LRI for comparison. Using the concept of invariants [32], first, the dynamics of the system can be designed, by choosing a time-dependent invariant, and subsequently the Hamiltonian elements are inversely obtained by inverting the time-dependent Schrödinger equation. Specifically, for Hamiltonian $H(t)$, there exists an invariant

$$\begin{aligned}I = \frac{1}{2}\left( {\begin{array}{*{20}{c}} {\cos \theta } & {\sin \theta {e^{ - i\beta }}}\\ {\sin \theta {e^{i\beta }}} & { - \cos \theta } \end{array}} \right) \end{aligned}$$
that satisfies the dynamical equation,
$$\frac{{dI}}{{dt}} = \frac{1}{{i\hbar }}\left[ {I,H} \right] + \frac{{\partial I}}{{\partial t}} = 0.$$

By solving this equation, the following constraint conditions are obtained:

$$\dot \theta ={-} \Omega \sin \beta ,\;\;\;\;{\rm{ }}\dot \beta {\rm{ = }} - \Omega \cot\theta \cos\beta - \Delta .$$

Using eigenstates ${\left | {{\varphi _n}(t)} \right \rangle }$ of this invariant, the solution of Schrödinger equation $i\hbar \partial \left | {\psi (t)} \right \rangle /\partial t=H(t)\left | {\psi (t)} \right \rangle$ and the propagator [32] can be written as

$$\begin{aligned}\begin{array}{l} \left| {\psi (t)} \right\rangle = \sum_ {j={\pm}} {{C_j}{e^{i{\eta _j}(t)}}\left| {{\varphi _j}(t)} \right\rangle } ,\\ U(t,{t_0}) = \sum_ {j={\pm}} {{e^{i{\eta _j}(t)}}\left| {{\varphi _j}(t)} \right\rangle \left\langle {{\varphi _j}({t_0})} \right|}, \end{array} \end{aligned}$$
where
$$\begin{aligned}&\left| {{\varphi _ + }(t)} \right\rangle = \left( {\begin{array}{c} {{e^{ - i\beta /2}}\cos \frac{\theta }{2}}\\ {{e^{i\beta /2}}\sin \frac{\theta }{2}} \end{array}} \right), \\&\left| {{\varphi _ - }(t)} \right\rangle = \left( {\begin{array}{c} { - {e^{ - i\beta /2}}\sin \frac{\theta }{2}}\\ {{e^{i\beta /2}}\cos \frac{\theta }{2}} \end{array}} \right), \end{aligned}$$
${{C_j}}$ are constants and ${\eta _j}(t)$ are the Lewis–Riesenfeld phases, where
$${{\dot \eta }_j}(t) = \frac{1}{\hbar }\left\langle {{\varphi _j}(t)} \right|i\hbar \frac{\partial }{{\partial t}} - H\left| {{\varphi _j}(t)} \right\rangle .$$

This yields

$${{\dot \eta }_ + }(t) ={-} {{\dot \eta }_ - }(t) = \frac{{\dot \theta \cos\beta }}{{2\sin \theta \sin \beta }}.$$

To realize population inversion along eigenstate $\left | {{\varphi _ + }(t)} \right \rangle$, $\theta (t)$ can be chosen as

$$\theta (t) = 3\pi {\left( {\frac{t}{{6T}} + \frac{1}{2}} \right)^{2}} - 2\pi {\left( {\frac{t}{{6T}} + \frac{1}{2}} \right)^{3}},$$
where $t \in [ - 3T,3T]$. Here, we use the simple Fourier series type of Ansatz,
$${\eta _ + }(t) ={-} \theta - n\sin [2\theta ],$$
where $n$ is a freely chosen parameter. Using Eq. (20), we obtain
$$\beta (t) ={-} {\rm{arccot}}[2(1 + 2n \cdot \cos 2\theta )\sin\theta ].$$

Once $\theta (t)$ and $\beta (t)$ are determined, Rabi frequency $\Omega$ and detuning $\Delta$ leading to rapid population inversion are found using Eq. (16). When an error representing a weak disturbance to the system occurs, the Hamiltonian becomes $H_\delta =H+\delta V$, where $\delta$ is an unknown time-independent parameter representing the error in the description of the model and $V$ is the error Hamiltonian. For example, when $V = \Omega {\sigma _x}/2$, it implies that the system deviates only at Rabi frequency $\Omega$, which is called the Rabi frequency error. In contrast, when $V = H$, it implies that the system deviates at detuning $\Delta$ and Rabi frequency $\Omega$ of the Hamiltonian simultaneously, which is called the systematic error. These errors decrease the accuracy and efficiency of the control of quantum states.

Therefore, we should design different robust schemes against various errors. To this end, we define the control error sensitivity as

$${q_s} ={-} \frac{{{\partial ^{2}}P({t_f})}}{2{\partial {\delta ^{2}}}}{|_{\delta = 0}},$$
where $P({t_f})$ is the transition probability at the final moment. When ${q_s} = 0$ is satisfied, the error sensitivity is zero, suggesting that the optimal LRI shortcuts are robust against such types of errors. The Rabi frequencies and detunings for the optimal LRI against the Rabi frequency error and the systematic error are plotted in Fig. 5(a), and the corresponding population of state, $\left |\Phi _+\right \rangle$, is shown in Fig. 5(b).

 figure: Fig. 5.

Fig. 5. Time dependence of parameters $\Delta$, $\Omega$, and population $P(t)$ of state $\left | {{\Phi _ + }} \right \rangle$ of LRI method. (a) n = $-$0.5, $\Delta$ (red, dashed line) and $\Omega$ (blue, solid line); n = 0.125, $\Delta$ (yellow, dashed line) and $\Omega$ (purple, solid line), (b) Population $P(t)$ (red, solid line). It is worth noting that for all n, time-dependent functions of populations are same, because n affects only phases.

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3.5 CAP

Finally, we explicitly explain how use a CAP to produce a specific coherent change in the quantum system. For this purpose, we take pulses with the same shapes, widths, and detunings of each pulses, but different phases. For Hamiltonian $H(t)$, its propagator $U$ can be expressed by Cayley–Klein parameters $a$ and $b$,

$$\begin{aligned}U = \left( {\begin{array}{*{20}{c}} a & b\\ { - {b^{*}}} & {{a^{*}}} \end{array}} \right), \end{aligned}$$
where ${\left | a \right |^{2}} + {\left | b \right |^{2}} = 1$. In particular, the transition probability from initial state $\left |C\right \rangle$ to target state $\left |\Phi _+\right \rangle$ is expressed as $P=|U_{21}|^{2}=|b|^{2}$, and vice versa. The remaining probability of the initial state is $|a|^{2}$, which should be a very small value at the end of the transfer process. When a constant phase $\phi$ is added in driving field $\Omega$ compared to Eq. (3) while the detuning remains unchanged, Hamiltonian $H(t)$ changes to
$$\begin{aligned}H(\phi ) = \frac{1}{2}\left( {\begin{array}{*{20}{c}} { - \Delta } & {\Omega {e^{ - i\phi }}}\\ {\Omega {e^{i\phi }}} & \Delta \end{array}} \right). \end{aligned}$$

Thus, the propagator $U$ is

$$\begin{aligned} U(\phi ) = \left( {\begin{array}{*{20}{c}} a & {b{e^{ - i\phi }}}\\ { - {b^{*}}{e^{i\phi }}} & {{a^{*}}} \end{array}} \right).\end{aligned}$$

For a composite sequence of $N$ identical pulses, the total propagator is expressed as

$${U^{(N)}} = U({\phi _N})U({\phi _{N - 1}}) \cdots U({\phi _2})U({\phi _1}),$$
where phases ${\phi _k}$ are arbitrary control parameters. For simplicity, the first phase is set as zero because the global phase can be removed. To further reduce the constraint equations, phase sequences having symmetric distributions are applied, i.e., ${\phi _{N + 1 - k}} = {\phi _k}$, where $N$ is the total number of pulses. If the following constraints act the time-dependent variation in Hamiltonian $H$:
$$\Delta (t) ={-} \Delta ( - t),\;\;\;\;{\rm{ }}\Omega (t) = \Omega ( - t),$$
parameter $a$ of propagator $U$ is real, i.e., $a \in R$. For a three-pulse sequence, only the phase of the second pulse needs to be adjusted. Here, we choose the sequence of phases as $(0,{\phi _2},0)$. From Eqs. (27) and (28), we obtain
$$U_{11}^{(3)} = {a^{3}} - {a\left| b \right|^{2}}(1+2\cos{\phi _2}).$$

To realize a high-fidelity population transfer, an appropriate condition should be set to minimize $U_{11}^{(3)}$. To this end, we should only choose the condition that ${\phi _2} = 2\pi /3$, to ensure that the second term on the right-hand side of Eq. (30) is zero, and ${a^{3}}$ is a three-order small quantity of $a$. In addition, even if the population transfer of a single pulse is not completely reached, i.e., ${U_{11}} \ne 0$, this deviation can be exponentially reduced by a composite technique to achieve perfect transfer. For a five-pulse sequence with phases $(0,{\phi _2},{\phi _3},{\phi _2},0)$, we can similarly obtain

$$\begin{aligned} \begin{array}{c} U_{11}^{(5)} = {a^{5}} + a{\left| b \right|^{4}}[2\cos({\phi _2} - {\phi _3}) + 2\cos(2{\phi _2} - {\phi _3}) + 1]\\ - 2{a^{3}}{\left| b \right|^{2}}[2\cos{\phi _2} + \cos ({\phi _2} - {\phi _3}) + \cos{\phi _3} + 1]. \end{array} \end{aligned}$$

Again, we choose ${\phi _2} = 4\pi /5,{\phi _3} = 2\pi /5$; therefore, $U_{11}^{(5)}$ is only left with the highest-order term of $a$, i.e., $U_{11}^{(5)} = {a^{5}}$. Similarly, we can obtain the phases corresponding to a seven-pulse sequence: ${\phi _2} = 6\pi /7,{\phi _3} = 4\pi /7,$ and ${\phi _4} = 8\pi /7$. In fact, for any CP sequence, there is a general formula for the selection of phases [37]. It is worth noting that the choices of phases are nonunique because the constrained equations are nonlinear functions of phases, from Eqs. (30) and (31). For any set of pulses, if $\{ {\phi _k}\} _2^{N - 1}$ is a solution, then $\{ 2\pi - {\phi _k}\} _2^{N - 1}$ is also a solution. In addition, for a CAP with numerous pulses, there are frequently more than two independent solutions $\{ {\phi _k}\} _2^{N - 1}$ and $\{ 2\pi - {\phi _k}\} _2^{N - 1}$, e.g., $(0,2\pi /5,6\pi /5,2\pi /5,0)$ is also a solution of a five-pulse sequence. For an $N$-pulse sequence, the transition probability can be written as

$$P = 1 - {a^{2N}}.$$

If $N$ is sufficiently large, the fidelity of the prepared quantum state is infinitely close to $1$. In fact, $N=5$ or $7$ may be sufficient for the requirements of fidelity in quantum information processing.

Here, to realize population inversion, an odd number of pulses must be satisfied. For simplicity, we take a five-pulse sequence as an example. For single pulse, the Rabi frequency and the detuning are a Gaussian pulse and a linear chirp, respectively, i.e.,

$$\Delta = \frac{2}{{T}}\frac{t}{T},\;\;\;\;{\rm{ }}\Omega = \frac{{\sqrt \pi }}{T}{e^{ - {{(t/T)}^{2}}}},$$
which are shown in Fig. 6(a). They satisfy the constraint conditions in Eq. (29), and $t \in [ - 3T,3T]$. As depicted in Fig. 6(b), single pulse cannot achieve complete population transfer, and its transition probability is 92.32%. The transition probability increases with the increase in the pulse sequence. The five-pulse sequence can achieve complete population transfer with a transition probability of 99.99%.

 figure: Fig. 6.

Fig. 6. Time dependence of parameters $\Delta$, $\Omega$, and population $P(t)$ of state $\left | {{\Phi _ + }} \right \rangle$ of CAP method. In protocol, we employ five-pulse sequence to construct CAP, in which all pulses have the same Rabi frequencies and detunings. $\Delta$ (red, dashed line) and $\Omega$ (blue, solid line) of single pulse are plotted in (a). (b) Population $P(t)$ of CAP with five-pulse sequence (red, solid line), where duration of each pulse is 6T.

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4. Robustness against different experimental errors

Here, we discuss how the effectiveness of population inversion is affected by the Rabi frequency error and the systematic error for the quantum control protocols discussed above.

First, the error originating from the Rabi frequency is considered. For RE, we can write the relationship between the transition probability and the error coefficient analytically as $P({t_f}) = \frac {1}{2}\left [ {1 + \cos (\delta \pi )} \right ]$. For a CD, the errors of both original Hamiltonian $H$ and additional Hamiltonian ${H_c}$ should be considered, i.e., $(\Omega + i{\Omega _c} ) \to (1 + \delta )(\Omega + i{\Omega _c})$. For an LRI, the choice of parameters can be further optimized. When $n=-0.5$, ${q_s} = 0$ is satisfied; thus, the Rabi frequency and detuning for the optimal LRI scheme with respect to the Rabi frequency error are obtained from Eq. (16) (see Fig. 5). In Fig. 7, we compare the accuracies of the five methods by plotting the transition probability as a function of error parameter $\delta$. We find that in the vivinity of $\delta =0$, the RE, CD, LRI and CAP techniques behave very well, with the transition probability being 1. However, as $|\delta |$ increases, their accuracies are affected. The CAP method outperforms the other techniques, followed by the LRI and then the CD method. The RE method is sensitive to the variations in the Rabi frequency. The AP method cannot achieve complete population transfer when $\delta =0$, but it improves as $\delta$ increases. The CAP method maintains the probability at ultrahigh efficiencies above $99.9\%$ over broad ranges of $\delta$, showing its ultrahigh robustness against the Rabi frequency error.

 figure: Fig. 7.

Fig. 7. Transition probability $P({t_f})$ versus Rabi frequency error parameter $\delta$ (dimensionless parameter): RE (black, dashed line), CD (yellow, solid line), LRI (blue, dashed line), AP (green, dashed-dotted line), and CAP (red, solid line).

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In the following, the effect of the systematic error on quantum state control is considered. The systematic error of RE is also the Rabi frequency error. The CD method considers both original Hamiltonian $H$ and the error of additional Hamiltonian ${H_c}$, i.e., $(H + {H_c}) \to (1 + \delta )(H + {H_c})$. The optimal LRI scheme with respect to the systematic error is obtained when $n=0.125$, and the Rabi frequency and detuning are also determined using Eq. (16) (see Fig. 5). In Fig. 8, we observe that the effect of the variation in the systematic error is similar to that of the Rabi frequency variation. The efficiencies of the LRI and CD methods show robustness against the systematic error. As prior, the CAP technique outperforms its competitors and features a broad range of high efficiencies.

 figure: Fig. 8.

Fig. 8. Transition probability $P({t_f})$ versus systematic error parameter $\delta$ (dimensionless parameter): RE (black, dashed line), CD (yellow, solid line), LRI (blue, dashed line), AP (green, dashed-dotted line), and CAP (red, solid line).

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5. Summary

In summary, we show that CPs can be used to achieve complete and robust quantum state engineering in three-level quantum systems. A CAP combines the robustness of AP with the high fidelity of RE using a sequence of pulses to cause a change in the quantum state. For coherent control, RE and CAP do not depend on specific shapes of pulses; however, RE is sensitive to the pulse area and detuning. Different from the CD and LRI methods, a CAP is constructed by controlling the phases of the pulse sequence; thus, it has more freedom in designing the Hamiltonian parameters. By comparing the sensitivities of the CAP, RE, AP, CD, and LRI techniques to the Rabi frequency and systematic errors, we find that the LRI method needs to be changed corresponding to the Rabi frequency and the detuning to achieve robustness against the different experimental errors. The CAP shows ultrahigh robustness against these errors with a broad range of high efficiencies over $99.9\%$, without the need for varying the Hamiltonian parameters. All these features make a CAP a promising alternative for coherent control of three-level quantum systems.

Funding

Natural Science Foundation of Anhui Province (2008085QA43); National Natural Science Foundation of China (12004006, 12075001, 12175001).

Disclosures

The authors declare no conflicts of interest.

Data availability

Data produced by numerical simulations in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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2. H. J. Kimble, “The quantum internet,” Nature 453(7198), 1023–1030 (2008). [CrossRef]  

3. K. Bergmann, H. Theuer, and B. W. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys. 70(3), 1003–1025 (1998). [CrossRef]  

4. N. V. Vitanov, T. Halfmann, B. W. Shore, and K. Bergmann, “Laser-induced population transfer by adiabatic passage techniques,” Annu. Rev. Phys. Chem. 52(1), 763–809 (2001). [CrossRef]  

5. M. Saffman, T. G. Walker, and K. Mølmer, “Quantum information with Rydberg atoms,” Rev. Mod. Phys. 82(3), 2313–2363 (2010). [CrossRef]  

6. G. R. Feng, G. F. Xu, and G. L. Long, “Experimental realization of nonadiabatic holonomic quantum computation,” Phys. Rev. Lett. 110(19), 190501 (2013). [CrossRef]  

7. A. Ruschhaupt, X. Chen, D. Alonso, and J. G. Muga, “Optimally robust shortcuts to population inversion in two-level quantum systems,” New J. Phys. 14(9), 093040 (2012). [CrossRef]  

8. Y.-H. Chen, Y. Xia, Q.-Q. Chen, and J. Song, “Ef?cient shortcuts to adiabatic passage for fast population transfer in multiparticle systems,” Phys. Rev. A 89(3), 033856 (2014). [CrossRef]  

9. X.-K. Song, H. Zhang, Q. Ai, J. Qiu, and F.-G. Deng, “Shortcuts to adiabatic holonomic quantum computation in decoherence-free subspace with transitionless quantum driving algorithm,” New J. Phys. 18(2), 023001 (2016). [CrossRef]  

10. J.-L. Wu, Y. Wang, J.-X. Han, C. Wang, S.-L. Su, Y. Xia, Y. Jiang, and J. Song, “Two-path interference for enantiomer-selective state transfer of chiral molecules,” Phys. Rev. Applied 13(4), 044021 (2020). [CrossRef]  

11. L. Q. Qiu, H. Li, Z. K. Han, W. Zheng, X. P. Yang, Y. Q. Dong, S. Q. Song, D. Lan, X. S. Tan, and Y. Yu, “Experimental realization of noncyclic geometric gates with shortcut to adiabaticity in a superconducting circuit,” Appl. Phys. Lett. 118(25), 254002 (2021). [CrossRef]  

12. Z.-C. He and Z.-Y. Xue, “Robust nonadiabatic holonomic quantum gates on decoherence-protected qubits,” Appl. Phys. Lett. 119(10), 104001 (2021). [CrossRef]  

13. S. Li and Z.-Y. Xue, “Dynamically corrected nonadiabatic holonomic quantum gates,” Phys. Rev. Applied 16(4), 044005 (2021). [CrossRef]  

14. E. Zahedinejad, J. Ghosh, and B. C. Sanders, “Designing high-fidelity single-shot three-qubit gates: A machine-learning approach,” Phys. Rev. Applied 6(5), 054005 (2016). [CrossRef]  

15. Y.-B. Sheng and L. Zhou, “Distributed secure quantum machine learning,” Sci. Bull. 62(14), 1025–1029 (2017). [CrossRef]  

16. M. Bukov, A. G. R. Day, D. Sels, P. Weinberg, A. Polkovnikov, and P. Mehta, “Reinforcement learning in different phases of quantum control,” Phys. Rev. X 8, 031086 (2018). [CrossRef]  

17. Z. T. Wang, Y. Ashida, and M. Ueda, “Deep reinforcement learning control of quantum cartpoles,” Phys. Rev. Lett. 125(10), 100401 (2020). [CrossRef]  

18. X.-S. Xu, H. Zhang, X.-Y. Kong, M. Wang, and G. L. Long, “Frequency-tuning-induced state transfer in optical microcavities,” Photon. Research 8(4), 490–496 (2020). [CrossRef]  

19. B. T. Torosov and N. V. Vitanov, “Smooth composite pulses for high-?delity quantum information processing,” Phys. Rev. A 83(5), 053420 (2011). [CrossRef]  

20. X. Wang, L. S. Bishop, J. P. Kestner, E. Barnes, K. Sun, and S. D. Sarma, “Composite pulses for robust universal control of singlet–triplet qubits,” Nature Commun. 3(1), 997 (2012). [CrossRef]  

21. G. T. Genov, D. Schraft, N. V. Vitanov, and T. Halfmann, “Arbitrarily accurate pulse sequences for robust dynamical decoupling,” Phys. Rev. Lett. 118(13), 133202 (2017). [CrossRef]  

22. A. A. Rangelov, N. V. Vitanov, L. P. Yatsenko, B. W. Shore, T. Halfmann, and K. Bergmann, “Stark-shift-chirped rapid-adiabatic-passage technique among three states,” Phys. Rev. A 72(5), 053403 (2005). [CrossRef]  

23. E. A. Shapiro, V. Milner, C. Menzel-Jones, and M. Shapiro, “Piecewise adiabatic passage with a series of femtosecond pulses,” Phys. Rev. Lett. 99(3), 033002 (2007). [CrossRef]  

24. N. V. Vitanov, A. A. Rangelov, B. W. Shore, and K. Bergmann, “Stimulated Raman adiabatic passage in physics, chemistry, and beyond,” Rev. Mod. Phys. 89(1), 015006 (2017). [CrossRef]  

25. D. Y. Li, W. Zheng, J. Chu, X. P. Yang, S. Q. Song, Z. K. Han, Y. Q. Dong, Z. M. Wang, X. M. Yu, D. Lan, J. Zhao, S. X. Li, X. S. Tan, and Y. Yu, “Coherent state transfer between superconducting qubits via stimulated Raman adiabatic passage,” Appl. Phys. Lett. 118(10), 104003 (2021). [CrossRef]  

26. M. Demirplak and S. A. Rice, “Adiabatic population transfer with control fields,” J. Phys. Chem. A 107(46), 9937–9945 (2003). [CrossRef]  

27. M. V. Berry, “Transitionless quantum driving,” J. Phys. A 42(36), 365303 (2009). [CrossRef]  

28. X. Chen, I. Lizuain, A. Ruschhaupt, D. Guéry-Odelin, and J. G. Muga, “Shortcut to adiabatic passage in two- and three-level atoms,” Phys. Rev. Lett. 105(12), 123003 (2010). [CrossRef]  

29. X.-K. Song, Q. Ai, J. Qiu, and F.-G. Deng, “Physically feasible three-level transitionless quantum driving with multiple Schrödinger dynamics,” Phys. Rev. A 93(5), 052324 (2016). [CrossRef]  

30. H. Zhang, X.-K. Song, Q. Ai, H. Wang, G.-J. Yang, and F.-G. Deng, “Fast and robust quantum control for multimode interactions using shortcuts to adiabaticity,” Opt. Express 27(5), 7384–7392 (2019). [CrossRef]  

31. Y.-H. Chen, W. Qin, X. Wang, A. Miranowicz, and F. Nori, “Shortcuts to adiabaticity for the quantum Rabi model: Efficient generation of giant entangled cat states via parametric amplification,” Phys. Rev. Lett. 126(2), 023602 (2021). [CrossRef]  

32. H. R. Lewis and W. B. Riesenfeld, “An exact quantum theory of the time-dependent harmonic oscillator and of a charged particle in a time-dependent electromagnetic field,” J. Math. Phys. 10(8), 1458–1473 (1969). [CrossRef]  

33. X. Chen, A. Ruschhaupt, S. Schmidt, A. del Campo, D. Guéry-Odelin, and J. G. Muga, “Fast optimal frictionless atom cooling in harmonic traps: Shortcut to adiabaticity,” Phys. Rev. Lett. 104(6), 063002 (2010). [CrossRef]  

34. X.-T. Yu, Q. Zhang, Y. Ban, and X. Chen, “Fast and robust control of two interacting spins,” Phys. Rev. A 97(6), 062317 (2018). [CrossRef]  

35. X.-K. Song, F. Meng, B.-J. Liu, D. Wang, L. Ye, and M.-H. Yung, “Robust stimulated Raman shortcut-to-adiabatic passage with invariant-based optimal control,” Opt. Express 29(6), 7998–8014 (2021). [CrossRef]  

36. Z. K. Han, Y. Q. Dong, X. P. Yang, S. Q. Song, L. Q. Qiu, W. Zheng, J. W. Xu, T. Q. Huang, Z. M. Wang, D. Lan, X. S. Tan, and Y. Yu, “Realization of invariant-based shortcuts to population inversion with a superconducting circuit,” Appl. Phys. Lett. 118(22), 224003 (2021). [CrossRef]  

37. B. T. Torosov, S. Guérin, and N. V. Vitanov, “High-fidelity adiabatic passage by composite sequences of chirped pulses,” Phys. Rev. Lett. 106(23), 233001 (2011). [CrossRef]  

38. G. T. Genov, D. Schraft, T. Halfmann, and N. V. Vitanov, “Correction of arbitrary field errors in population inversion of quantum systems by universal composite pulses,” Phys. Rev. Lett. 113(4), 043001 (2014). [CrossRef]  

39. B. T. Torosov and N. V. Vitanov, “Arbitrarily accurate twin composite π-pulse sequences,” Phys. Rev. A 97(4), 043408 (2018). [CrossRef]  

40. Z.-C. Shi, H.-N. Wu, L.-T. Shen, J. Song, Y. Xia, X. X. Yi, and S.-B. Zheng, “Robust single-qubit gates by composite pulses in three-level systems,” Phys. Rev. A 103(5), 052612 (2021). [CrossRef]  

41. Y.-X. Du, Z.-T. Liang, Y.-C. Li, X.-X. Yue, Q.-X. Lv, W. Huang, X. Chen, H. Yan, and S.-L. Zhu, “Experimental realization of stimulated Raman shortcut-to-adiabatic passage with cold atoms,” Nat. Commun. 7(1), 12479 (2016). [CrossRef]  

42. D. Schraft, T. Halfmann, G. T. Genov, and N. V. Vitanov, “Experimental demonstration of composite adiabatic passage,” Phys. Rev. A 88(6), 063406 (2013). [CrossRef]  

43. A. Bruns, G. T. Genov, M. Hain, N. V. Vitanov, and T. Halfmann, “Experimental demonstration of composite stimulated Raman adiabatic passage,” Phys. Rev. A 98(5), 053413 (2018). [CrossRef]  

44. B. T. Torosov, B. W. Shore, and N. V. Vitanov, “Coherent control techniques for two-state quantum systems: A comparative study,” Phys. Rev. A 103(3), 033110 (2021). [CrossRef]  

45. K. Eckert, M. Lewenstein, R. Corbalan, G. Birkl, W. Ertmer, and J. Mompart, “Three-level atom optics via the tunneling interaction,” Phys. Rev. A 70(2), 023606 (2004). [CrossRef]  

46. S. Martínez-Garaot, E. Torrontegui, X. Chen, and J. G. Muga, “Shortcuts to adiabaticity in three-level systems using Lie transforms,” Phys. Rev. A 89(5), 053408 (2014). [CrossRef]  

47. T. Opatrný and K. Mølmer, “Partial suppression of nonadiabatic transitions,” New J. Phys. 16(1), 015025 (2014). [CrossRef]  

48. A. A. Rangelov and N. V. Vitanov, “Achromatic multiple beam splitting by adiabatic passage in optical waveguides,” Phys. Rev. A 85(5), 055803 (2012). [CrossRef]  

49. K.-H. Chien, C.-S. Yeih, and S.-Y. Tseng, “Mode conversion/splitting in multimode waveguides based on invariant engineering,” J. Lightwave Technol. 31(21), 3387–3394 (2013). [CrossRef]  

50. M. Ornigotti, G. D. Valle, T. T. Fernandez, A. Coppa, V. Foglietti, P. Laporta, and S. Longhi, “Visualization of two-photon Rabi oscillations in evanescently coupled optical waveguides,” J. Phys. B: At., Mol. Opt. Phys. 41(8), 085402 (2008). [CrossRef]  

51. G. S. Vasilev and N. V. Vitanov, “Coherent excitation of a two-state system by a linearly chirped Gaussian pulse,” J. Chem. Phys. 123(17), 174106 (2005). [CrossRef]  

References

  • View by:

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    [Crossref]
  4. N. V. Vitanov, T. Halfmann, B. W. Shore, and K. Bergmann, “Laser-induced population transfer by adiabatic passage techniques,” Annu. Rev. Phys. Chem. 52(1), 763–809 (2001).
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  8. Y.-H. Chen, Y. Xia, Q.-Q. Chen, and J. Song, “Ef?cient shortcuts to adiabatic passage for fast population transfer in multiparticle systems,” Phys. Rev. A 89(3), 033856 (2014).
    [Crossref]
  9. X.-K. Song, H. Zhang, Q. Ai, J. Qiu, and F.-G. Deng, “Shortcuts to adiabatic holonomic quantum computation in decoherence-free subspace with transitionless quantum driving algorithm,” New J. Phys. 18(2), 023001 (2016).
    [Crossref]
  10. J.-L. Wu, Y. Wang, J.-X. Han, C. Wang, S.-L. Su, Y. Xia, Y. Jiang, and J. Song, “Two-path interference for enantiomer-selective state transfer of chiral molecules,” Phys. Rev. Applied 13(4), 044021 (2020).
    [Crossref]
  11. L. Q. Qiu, H. Li, Z. K. Han, W. Zheng, X. P. Yang, Y. Q. Dong, S. Q. Song, D. Lan, X. S. Tan, and Y. Yu, “Experimental realization of noncyclic geometric gates with shortcut to adiabaticity in a superconducting circuit,” Appl. Phys. Lett. 118(25), 254002 (2021).
    [Crossref]
  12. Z.-C. He and Z.-Y. Xue, “Robust nonadiabatic holonomic quantum gates on decoherence-protected qubits,” Appl. Phys. Lett. 119(10), 104001 (2021).
    [Crossref]
  13. S. Li and Z.-Y. Xue, “Dynamically corrected nonadiabatic holonomic quantum gates,” Phys. Rev. Applied 16(4), 044005 (2021).
    [Crossref]
  14. E. Zahedinejad, J. Ghosh, and B. C. Sanders, “Designing high-fidelity single-shot three-qubit gates: A machine-learning approach,” Phys. Rev. Applied 6(5), 054005 (2016).
    [Crossref]
  15. Y.-B. Sheng and L. Zhou, “Distributed secure quantum machine learning,” Sci. Bull. 62(14), 1025–1029 (2017).
    [Crossref]
  16. M. Bukov, A. G. R. Day, D. Sels, P. Weinberg, A. Polkovnikov, and P. Mehta, “Reinforcement learning in different phases of quantum control,” Phys. Rev. X 8, 031086 (2018).
    [Crossref]
  17. Z. T. Wang, Y. Ashida, and M. Ueda, “Deep reinforcement learning control of quantum cartpoles,” Phys. Rev. Lett. 125(10), 100401 (2020).
    [Crossref]
  18. X.-S. Xu, H. Zhang, X.-Y. Kong, M. Wang, and G. L. Long, “Frequency-tuning-induced state transfer in optical microcavities,” Photon. Research 8(4), 490–496 (2020).
    [Crossref]
  19. B. T. Torosov and N. V. Vitanov, “Smooth composite pulses for high-?delity quantum information processing,” Phys. Rev. A 83(5), 053420 (2011).
    [Crossref]
  20. X. Wang, L. S. Bishop, J. P. Kestner, E. Barnes, K. Sun, and S. D. Sarma, “Composite pulses for robust universal control of singlet–triplet qubits,” Nature Commun. 3(1), 997 (2012).
    [Crossref]
  21. G. T. Genov, D. Schraft, N. V. Vitanov, and T. Halfmann, “Arbitrarily accurate pulse sequences for robust dynamical decoupling,” Phys. Rev. Lett. 118(13), 133202 (2017).
    [Crossref]
  22. A. A. Rangelov, N. V. Vitanov, L. P. Yatsenko, B. W. Shore, T. Halfmann, and K. Bergmann, “Stark-shift-chirped rapid-adiabatic-passage technique among three states,” Phys. Rev. A 72(5), 053403 (2005).
    [Crossref]
  23. E. A. Shapiro, V. Milner, C. Menzel-Jones, and M. Shapiro, “Piecewise adiabatic passage with a series of femtosecond pulses,” Phys. Rev. Lett. 99(3), 033002 (2007).
    [Crossref]
  24. N. V. Vitanov, A. A. Rangelov, B. W. Shore, and K. Bergmann, “Stimulated Raman adiabatic passage in physics, chemistry, and beyond,” Rev. Mod. Phys. 89(1), 015006 (2017).
    [Crossref]
  25. D. Y. Li, W. Zheng, J. Chu, X. P. Yang, S. Q. Song, Z. K. Han, Y. Q. Dong, Z. M. Wang, X. M. Yu, D. Lan, J. Zhao, S. X. Li, X. S. Tan, and Y. Yu, “Coherent state transfer between superconducting qubits via stimulated Raman adiabatic passage,” Appl. Phys. Lett. 118(10), 104003 (2021).
    [Crossref]
  26. M. Demirplak and S. A. Rice, “Adiabatic population transfer with control fields,” J. Phys. Chem. A 107(46), 9937–9945 (2003).
    [Crossref]
  27. M. V. Berry, “Transitionless quantum driving,” J. Phys. A 42(36), 365303 (2009).
    [Crossref]
  28. X. Chen, I. Lizuain, A. Ruschhaupt, D. Guéry-Odelin, and J. G. Muga, “Shortcut to adiabatic passage in two- and three-level atoms,” Phys. Rev. Lett. 105(12), 123003 (2010).
    [Crossref]
  29. X.-K. Song, Q. Ai, J. Qiu, and F.-G. Deng, “Physically feasible three-level transitionless quantum driving with multiple Schrödinger dynamics,” Phys. Rev. A 93(5), 052324 (2016).
    [Crossref]
  30. H. Zhang, X.-K. Song, Q. Ai, H. Wang, G.-J. Yang, and F.-G. Deng, “Fast and robust quantum control for multimode interactions using shortcuts to adiabaticity,” Opt. Express 27(5), 7384–7392 (2019).
    [Crossref]
  31. Y.-H. Chen, W. Qin, X. Wang, A. Miranowicz, and F. Nori, “Shortcuts to adiabaticity for the quantum Rabi model: Efficient generation of giant entangled cat states via parametric amplification,” Phys. Rev. Lett. 126(2), 023602 (2021).
    [Crossref]
  32. H. R. Lewis and W. B. Riesenfeld, “An exact quantum theory of the time-dependent harmonic oscillator and of a charged particle in a time-dependent electromagnetic field,” J. Math. Phys. 10(8), 1458–1473 (1969).
    [Crossref]
  33. X. Chen, A. Ruschhaupt, S. Schmidt, A. del Campo, D. Guéry-Odelin, and J. G. Muga, “Fast optimal frictionless atom cooling in harmonic traps: Shortcut to adiabaticity,” Phys. Rev. Lett. 104(6), 063002 (2010).
    [Crossref]
  34. X.-T. Yu, Q. Zhang, Y. Ban, and X. Chen, “Fast and robust control of two interacting spins,” Phys. Rev. A 97(6), 062317 (2018).
    [Crossref]
  35. X.-K. Song, F. Meng, B.-J. Liu, D. Wang, L. Ye, and M.-H. Yung, “Robust stimulated Raman shortcut-to-adiabatic passage with invariant-based optimal control,” Opt. Express 29(6), 7998–8014 (2021).
    [Crossref]
  36. Z. K. Han, Y. Q. Dong, X. P. Yang, S. Q. Song, L. Q. Qiu, W. Zheng, J. W. Xu, T. Q. Huang, Z. M. Wang, D. Lan, X. S. Tan, and Y. Yu, “Realization of invariant-based shortcuts to population inversion with a superconducting circuit,” Appl. Phys. Lett. 118(22), 224003 (2021).
    [Crossref]
  37. B. T. Torosov, S. Guérin, and N. V. Vitanov, “High-fidelity adiabatic passage by composite sequences of chirped pulses,” Phys. Rev. Lett. 106(23), 233001 (2011).
    [Crossref]
  38. G. T. Genov, D. Schraft, T. Halfmann, and N. V. Vitanov, “Correction of arbitrary field errors in population inversion of quantum systems by universal composite pulses,” Phys. Rev. Lett. 113(4), 043001 (2014).
    [Crossref]
  39. B. T. Torosov and N. V. Vitanov, “Arbitrarily accurate twin composite π-pulse sequences,” Phys. Rev. A 97(4), 043408 (2018).
    [Crossref]
  40. Z.-C. Shi, H.-N. Wu, L.-T. Shen, J. Song, Y. Xia, X. X. Yi, and S.-B. Zheng, “Robust single-qubit gates by composite pulses in three-level systems,” Phys. Rev. A 103(5), 052612 (2021).
    [Crossref]
  41. Y.-X. Du, Z.-T. Liang, Y.-C. Li, X.-X. Yue, Q.-X. Lv, W. Huang, X. Chen, H. Yan, and S.-L. Zhu, “Experimental realization of stimulated Raman shortcut-to-adiabatic passage with cold atoms,” Nat. Commun. 7(1), 12479 (2016).
    [Crossref]
  42. D. Schraft, T. Halfmann, G. T. Genov, and N. V. Vitanov, “Experimental demonstration of composite adiabatic passage,” Phys. Rev. A 88(6), 063406 (2013).
    [Crossref]
  43. A. Bruns, G. T. Genov, M. Hain, N. V. Vitanov, and T. Halfmann, “Experimental demonstration of composite stimulated Raman adiabatic passage,” Phys. Rev. A 98(5), 053413 (2018).
    [Crossref]
  44. B. T. Torosov, B. W. Shore, and N. V. Vitanov, “Coherent control techniques for two-state quantum systems: A comparative study,” Phys. Rev. A 103(3), 033110 (2021).
    [Crossref]
  45. K. Eckert, M. Lewenstein, R. Corbalan, G. Birkl, W. Ertmer, and J. Mompart, “Three-level atom optics via the tunneling interaction,” Phys. Rev. A 70(2), 023606 (2004).
    [Crossref]
  46. S. Martínez-Garaot, E. Torrontegui, X. Chen, and J. G. Muga, “Shortcuts to adiabaticity in three-level systems using Lie transforms,” Phys. Rev. A 89(5), 053408 (2014).
    [Crossref]
  47. T. Opatrný and K. Mølmer, “Partial suppression of nonadiabatic transitions,” New J. Phys. 16(1), 015025 (2014).
    [Crossref]
  48. A. A. Rangelov and N. V. Vitanov, “Achromatic multiple beam splitting by adiabatic passage in optical waveguides,” Phys. Rev. A 85(5), 055803 (2012).
    [Crossref]
  49. K.-H. Chien, C.-S. Yeih, and S.-Y. Tseng, “Mode conversion/splitting in multimode waveguides based on invariant engineering,” J. Lightwave Technol. 31(21), 3387–3394 (2013).
    [Crossref]
  50. M. Ornigotti, G. D. Valle, T. T. Fernandez, A. Coppa, V. Foglietti, P. Laporta, and S. Longhi, “Visualization of two-photon Rabi oscillations in evanescently coupled optical waveguides,” J. Phys. B: At., Mol. Opt. Phys. 41(8), 085402 (2008).
    [Crossref]
  51. G. S. Vasilev and N. V. Vitanov, “Coherent excitation of a two-state system by a linearly chirped Gaussian pulse,” J. Chem. Phys. 123(17), 174106 (2005).
    [Crossref]

2021 (9)

L. Q. Qiu, H. Li, Z. K. Han, W. Zheng, X. P. Yang, Y. Q. Dong, S. Q. Song, D. Lan, X. S. Tan, and Y. Yu, “Experimental realization of noncyclic geometric gates with shortcut to adiabaticity in a superconducting circuit,” Appl. Phys. Lett. 118(25), 254002 (2021).
[Crossref]

Z.-C. He and Z.-Y. Xue, “Robust nonadiabatic holonomic quantum gates on decoherence-protected qubits,” Appl. Phys. Lett. 119(10), 104001 (2021).
[Crossref]

S. Li and Z.-Y. Xue, “Dynamically corrected nonadiabatic holonomic quantum gates,” Phys. Rev. Applied 16(4), 044005 (2021).
[Crossref]

D. Y. Li, W. Zheng, J. Chu, X. P. Yang, S. Q. Song, Z. K. Han, Y. Q. Dong, Z. M. Wang, X. M. Yu, D. Lan, J. Zhao, S. X. Li, X. S. Tan, and Y. Yu, “Coherent state transfer between superconducting qubits via stimulated Raman adiabatic passage,” Appl. Phys. Lett. 118(10), 104003 (2021).
[Crossref]

Y.-H. Chen, W. Qin, X. Wang, A. Miranowicz, and F. Nori, “Shortcuts to adiabaticity for the quantum Rabi model: Efficient generation of giant entangled cat states via parametric amplification,” Phys. Rev. Lett. 126(2), 023602 (2021).
[Crossref]

X.-K. Song, F. Meng, B.-J. Liu, D. Wang, L. Ye, and M.-H. Yung, “Robust stimulated Raman shortcut-to-adiabatic passage with invariant-based optimal control,” Opt. Express 29(6), 7998–8014 (2021).
[Crossref]

Z. K. Han, Y. Q. Dong, X. P. Yang, S. Q. Song, L. Q. Qiu, W. Zheng, J. W. Xu, T. Q. Huang, Z. M. Wang, D. Lan, X. S. Tan, and Y. Yu, “Realization of invariant-based shortcuts to population inversion with a superconducting circuit,” Appl. Phys. Lett. 118(22), 224003 (2021).
[Crossref]

Z.-C. Shi, H.-N. Wu, L.-T. Shen, J. Song, Y. Xia, X. X. Yi, and S.-B. Zheng, “Robust single-qubit gates by composite pulses in three-level systems,” Phys. Rev. A 103(5), 052612 (2021).
[Crossref]

B. T. Torosov, B. W. Shore, and N. V. Vitanov, “Coherent control techniques for two-state quantum systems: A comparative study,” Phys. Rev. A 103(3), 033110 (2021).
[Crossref]

2020 (3)

Z. T. Wang, Y. Ashida, and M. Ueda, “Deep reinforcement learning control of quantum cartpoles,” Phys. Rev. Lett. 125(10), 100401 (2020).
[Crossref]

X.-S. Xu, H. Zhang, X.-Y. Kong, M. Wang, and G. L. Long, “Frequency-tuning-induced state transfer in optical microcavities,” Photon. Research 8(4), 490–496 (2020).
[Crossref]

J.-L. Wu, Y. Wang, J.-X. Han, C. Wang, S.-L. Su, Y. Xia, Y. Jiang, and J. Song, “Two-path interference for enantiomer-selective state transfer of chiral molecules,” Phys. Rev. Applied 13(4), 044021 (2020).
[Crossref]

2019 (1)

2018 (4)

M. Bukov, A. G. R. Day, D. Sels, P. Weinberg, A. Polkovnikov, and P. Mehta, “Reinforcement learning in different phases of quantum control,” Phys. Rev. X 8, 031086 (2018).
[Crossref]

B. T. Torosov and N. V. Vitanov, “Arbitrarily accurate twin composite π-pulse sequences,” Phys. Rev. A 97(4), 043408 (2018).
[Crossref]

A. Bruns, G. T. Genov, M. Hain, N. V. Vitanov, and T. Halfmann, “Experimental demonstration of composite stimulated Raman adiabatic passage,” Phys. Rev. A 98(5), 053413 (2018).
[Crossref]

X.-T. Yu, Q. Zhang, Y. Ban, and X. Chen, “Fast and robust control of two interacting spins,” Phys. Rev. A 97(6), 062317 (2018).
[Crossref]

2017 (3)

Y.-B. Sheng and L. Zhou, “Distributed secure quantum machine learning,” Sci. Bull. 62(14), 1025–1029 (2017).
[Crossref]

N. V. Vitanov, A. A. Rangelov, B. W. Shore, and K. Bergmann, “Stimulated Raman adiabatic passage in physics, chemistry, and beyond,” Rev. Mod. Phys. 89(1), 015006 (2017).
[Crossref]

G. T. Genov, D. Schraft, N. V. Vitanov, and T. Halfmann, “Arbitrarily accurate pulse sequences for robust dynamical decoupling,” Phys. Rev. Lett. 118(13), 133202 (2017).
[Crossref]

2016 (4)

X.-K. Song, Q. Ai, J. Qiu, and F.-G. Deng, “Physically feasible three-level transitionless quantum driving with multiple Schrödinger dynamics,” Phys. Rev. A 93(5), 052324 (2016).
[Crossref]

X.-K. Song, H. Zhang, Q. Ai, J. Qiu, and F.-G. Deng, “Shortcuts to adiabatic holonomic quantum computation in decoherence-free subspace with transitionless quantum driving algorithm,” New J. Phys. 18(2), 023001 (2016).
[Crossref]

E. Zahedinejad, J. Ghosh, and B. C. Sanders, “Designing high-fidelity single-shot three-qubit gates: A machine-learning approach,” Phys. Rev. Applied 6(5), 054005 (2016).
[Crossref]

Y.-X. Du, Z.-T. Liang, Y.-C. Li, X.-X. Yue, Q.-X. Lv, W. Huang, X. Chen, H. Yan, and S.-L. Zhu, “Experimental realization of stimulated Raman shortcut-to-adiabatic passage with cold atoms,” Nat. Commun. 7(1), 12479 (2016).
[Crossref]

2014 (4)

G. T. Genov, D. Schraft, T. Halfmann, and N. V. Vitanov, “Correction of arbitrary field errors in population inversion of quantum systems by universal composite pulses,” Phys. Rev. Lett. 113(4), 043001 (2014).
[Crossref]

S. Martínez-Garaot, E. Torrontegui, X. Chen, and J. G. Muga, “Shortcuts to adiabaticity in three-level systems using Lie transforms,” Phys. Rev. A 89(5), 053408 (2014).
[Crossref]

T. Opatrný and K. Mølmer, “Partial suppression of nonadiabatic transitions,” New J. Phys. 16(1), 015025 (2014).
[Crossref]

Y.-H. Chen, Y. Xia, Q.-Q. Chen, and J. Song, “Ef?cient shortcuts to adiabatic passage for fast population transfer in multiparticle systems,” Phys. Rev. A 89(3), 033856 (2014).
[Crossref]

2013 (3)

G. R. Feng, G. F. Xu, and G. L. Long, “Experimental realization of nonadiabatic holonomic quantum computation,” Phys. Rev. Lett. 110(19), 190501 (2013).
[Crossref]

K.-H. Chien, C.-S. Yeih, and S.-Y. Tseng, “Mode conversion/splitting in multimode waveguides based on invariant engineering,” J. Lightwave Technol. 31(21), 3387–3394 (2013).
[Crossref]

D. Schraft, T. Halfmann, G. T. Genov, and N. V. Vitanov, “Experimental demonstration of composite adiabatic passage,” Phys. Rev. A 88(6), 063406 (2013).
[Crossref]

2012 (3)

A. A. Rangelov and N. V. Vitanov, “Achromatic multiple beam splitting by adiabatic passage in optical waveguides,” Phys. Rev. A 85(5), 055803 (2012).
[Crossref]

A. Ruschhaupt, X. Chen, D. Alonso, and J. G. Muga, “Optimally robust shortcuts to population inversion in two-level quantum systems,” New J. Phys. 14(9), 093040 (2012).
[Crossref]

X. Wang, L. S. Bishop, J. P. Kestner, E. Barnes, K. Sun, and S. D. Sarma, “Composite pulses for robust universal control of singlet–triplet qubits,” Nature Commun. 3(1), 997 (2012).
[Crossref]

2011 (2)

B. T. Torosov and N. V. Vitanov, “Smooth composite pulses for high-?delity quantum information processing,” Phys. Rev. A 83(5), 053420 (2011).
[Crossref]

B. T. Torosov, S. Guérin, and N. V. Vitanov, “High-fidelity adiabatic passage by composite sequences of chirped pulses,” Phys. Rev. Lett. 106(23), 233001 (2011).
[Crossref]

2010 (3)

X. Chen, I. Lizuain, A. Ruschhaupt, D. Guéry-Odelin, and J. G. Muga, “Shortcut to adiabatic passage in two- and three-level atoms,” Phys. Rev. Lett. 105(12), 123003 (2010).
[Crossref]

X. Chen, A. Ruschhaupt, S. Schmidt, A. del Campo, D. Guéry-Odelin, and J. G. Muga, “Fast optimal frictionless atom cooling in harmonic traps: Shortcut to adiabaticity,” Phys. Rev. Lett. 104(6), 063002 (2010).
[Crossref]

M. Saffman, T. G. Walker, and K. Mølmer, “Quantum information with Rydberg atoms,” Rev. Mod. Phys. 82(3), 2313–2363 (2010).
[Crossref]

2009 (1)

M. V. Berry, “Transitionless quantum driving,” J. Phys. A 42(36), 365303 (2009).
[Crossref]

2008 (2)

H. J. Kimble, “The quantum internet,” Nature 453(7198), 1023–1030 (2008).
[Crossref]

M. Ornigotti, G. D. Valle, T. T. Fernandez, A. Coppa, V. Foglietti, P. Laporta, and S. Longhi, “Visualization of two-photon Rabi oscillations in evanescently coupled optical waveguides,” J. Phys. B: At., Mol. Opt. Phys. 41(8), 085402 (2008).
[Crossref]

2007 (2)

P. Král, I. Thanopulos, and M. Shapiro, “Colloquium: Coherently controlled adiabatic passage,” Rev. Mod. Phys. 79(1), 53–77 (2007).
[Crossref]

E. A. Shapiro, V. Milner, C. Menzel-Jones, and M. Shapiro, “Piecewise adiabatic passage with a series of femtosecond pulses,” Phys. Rev. Lett. 99(3), 033002 (2007).
[Crossref]

2005 (2)

A. A. Rangelov, N. V. Vitanov, L. P. Yatsenko, B. W. Shore, T. Halfmann, and K. Bergmann, “Stark-shift-chirped rapid-adiabatic-passage technique among three states,” Phys. Rev. A 72(5), 053403 (2005).
[Crossref]

G. S. Vasilev and N. V. Vitanov, “Coherent excitation of a two-state system by a linearly chirped Gaussian pulse,” J. Chem. Phys. 123(17), 174106 (2005).
[Crossref]

2004 (1)

K. Eckert, M. Lewenstein, R. Corbalan, G. Birkl, W. Ertmer, and J. Mompart, “Three-level atom optics via the tunneling interaction,” Phys. Rev. A 70(2), 023606 (2004).
[Crossref]

2003 (1)

M. Demirplak and S. A. Rice, “Adiabatic population transfer with control fields,” J. Phys. Chem. A 107(46), 9937–9945 (2003).
[Crossref]

2001 (1)

N. V. Vitanov, T. Halfmann, B. W. Shore, and K. Bergmann, “Laser-induced population transfer by adiabatic passage techniques,” Annu. Rev. Phys. Chem. 52(1), 763–809 (2001).
[Crossref]

1998 (1)

K. Bergmann, H. Theuer, and B. W. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys. 70(3), 1003–1025 (1998).
[Crossref]

1969 (1)

H. R. Lewis and W. B. Riesenfeld, “An exact quantum theory of the time-dependent harmonic oscillator and of a charged particle in a time-dependent electromagnetic field,” J. Math. Phys. 10(8), 1458–1473 (1969).
[Crossref]

Ai, Q.

H. Zhang, X.-K. Song, Q. Ai, H. Wang, G.-J. Yang, and F.-G. Deng, “Fast and robust quantum control for multimode interactions using shortcuts to adiabaticity,” Opt. Express 27(5), 7384–7392 (2019).
[Crossref]

X.-K. Song, Q. Ai, J. Qiu, and F.-G. Deng, “Physically feasible three-level transitionless quantum driving with multiple Schrödinger dynamics,” Phys. Rev. A 93(5), 052324 (2016).
[Crossref]

X.-K. Song, H. Zhang, Q. Ai, J. Qiu, and F.-G. Deng, “Shortcuts to adiabatic holonomic quantum computation in decoherence-free subspace with transitionless quantum driving algorithm,” New J. Phys. 18(2), 023001 (2016).
[Crossref]

Alonso, D.

A. Ruschhaupt, X. Chen, D. Alonso, and J. G. Muga, “Optimally robust shortcuts to population inversion in two-level quantum systems,” New J. Phys. 14(9), 093040 (2012).
[Crossref]

Ashida, Y.

Z. T. Wang, Y. Ashida, and M. Ueda, “Deep reinforcement learning control of quantum cartpoles,” Phys. Rev. Lett. 125(10), 100401 (2020).
[Crossref]

Ban, Y.

X.-T. Yu, Q. Zhang, Y. Ban, and X. Chen, “Fast and robust control of two interacting spins,” Phys. Rev. A 97(6), 062317 (2018).
[Crossref]

Barnes, E.

X. Wang, L. S. Bishop, J. P. Kestner, E. Barnes, K. Sun, and S. D. Sarma, “Composite pulses for robust universal control of singlet–triplet qubits,” Nature Commun. 3(1), 997 (2012).
[Crossref]

Bergmann, K.

N. V. Vitanov, A. A. Rangelov, B. W. Shore, and K. Bergmann, “Stimulated Raman adiabatic passage in physics, chemistry, and beyond,” Rev. Mod. Phys. 89(1), 015006 (2017).
[Crossref]

A. A. Rangelov, N. V. Vitanov, L. P. Yatsenko, B. W. Shore, T. Halfmann, and K. Bergmann, “Stark-shift-chirped rapid-adiabatic-passage technique among three states,” Phys. Rev. A 72(5), 053403 (2005).
[Crossref]

N. V. Vitanov, T. Halfmann, B. W. Shore, and K. Bergmann, “Laser-induced population transfer by adiabatic passage techniques,” Annu. Rev. Phys. Chem. 52(1), 763–809 (2001).
[Crossref]

K. Bergmann, H. Theuer, and B. W. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys. 70(3), 1003–1025 (1998).
[Crossref]

Berry, M. V.

M. V. Berry, “Transitionless quantum driving,” J. Phys. A 42(36), 365303 (2009).
[Crossref]

Birkl, G.

K. Eckert, M. Lewenstein, R. Corbalan, G. Birkl, W. Ertmer, and J. Mompart, “Three-level atom optics via the tunneling interaction,” Phys. Rev. A 70(2), 023606 (2004).
[Crossref]

Bishop, L. S.

X. Wang, L. S. Bishop, J. P. Kestner, E. Barnes, K. Sun, and S. D. Sarma, “Composite pulses for robust universal control of singlet–triplet qubits,” Nature Commun. 3(1), 997 (2012).
[Crossref]

Bruns, A.

A. Bruns, G. T. Genov, M. Hain, N. V. Vitanov, and T. Halfmann, “Experimental demonstration of composite stimulated Raman adiabatic passage,” Phys. Rev. A 98(5), 053413 (2018).
[Crossref]

Bukov, M.

M. Bukov, A. G. R. Day, D. Sels, P. Weinberg, A. Polkovnikov, and P. Mehta, “Reinforcement learning in different phases of quantum control,” Phys. Rev. X 8, 031086 (2018).
[Crossref]

Chen, Q.-Q.

Y.-H. Chen, Y. Xia, Q.-Q. Chen, and J. Song, “Ef?cient shortcuts to adiabatic passage for fast population transfer in multiparticle systems,” Phys. Rev. A 89(3), 033856 (2014).
[Crossref]

Chen, X.

X.-T. Yu, Q. Zhang, Y. Ban, and X. Chen, “Fast and robust control of two interacting spins,” Phys. Rev. A 97(6), 062317 (2018).
[Crossref]

Y.-X. Du, Z.-T. Liang, Y.-C. Li, X.-X. Yue, Q.-X. Lv, W. Huang, X. Chen, H. Yan, and S.-L. Zhu, “Experimental realization of stimulated Raman shortcut-to-adiabatic passage with cold atoms,” Nat. Commun. 7(1), 12479 (2016).
[Crossref]

S. Martínez-Garaot, E. Torrontegui, X. Chen, and J. G. Muga, “Shortcuts to adiabaticity in three-level systems using Lie transforms,” Phys. Rev. A 89(5), 053408 (2014).
[Crossref]

A. Ruschhaupt, X. Chen, D. Alonso, and J. G. Muga, “Optimally robust shortcuts to population inversion in two-level quantum systems,” New J. Phys. 14(9), 093040 (2012).
[Crossref]

X. Chen, I. Lizuain, A. Ruschhaupt, D. Guéry-Odelin, and J. G. Muga, “Shortcut to adiabatic passage in two- and three-level atoms,” Phys. Rev. Lett. 105(12), 123003 (2010).
[Crossref]

X. Chen, A. Ruschhaupt, S. Schmidt, A. del Campo, D. Guéry-Odelin, and J. G. Muga, “Fast optimal frictionless atom cooling in harmonic traps: Shortcut to adiabaticity,” Phys. Rev. Lett. 104(6), 063002 (2010).
[Crossref]

Chen, Y.-H.

Y.-H. Chen, W. Qin, X. Wang, A. Miranowicz, and F. Nori, “Shortcuts to adiabaticity for the quantum Rabi model: Efficient generation of giant entangled cat states via parametric amplification,” Phys. Rev. Lett. 126(2), 023602 (2021).
[Crossref]

Y.-H. Chen, Y. Xia, Q.-Q. Chen, and J. Song, “Ef?cient shortcuts to adiabatic passage for fast population transfer in multiparticle systems,” Phys. Rev. A 89(3), 033856 (2014).
[Crossref]

Chien, K.-H.

Chu, J.

D. Y. Li, W. Zheng, J. Chu, X. P. Yang, S. Q. Song, Z. K. Han, Y. Q. Dong, Z. M. Wang, X. M. Yu, D. Lan, J. Zhao, S. X. Li, X. S. Tan, and Y. Yu, “Coherent state transfer between superconducting qubits via stimulated Raman adiabatic passage,” Appl. Phys. Lett. 118(10), 104003 (2021).
[Crossref]

Coppa, A.

M. Ornigotti, G. D. Valle, T. T. Fernandez, A. Coppa, V. Foglietti, P. Laporta, and S. Longhi, “Visualization of two-photon Rabi oscillations in evanescently coupled optical waveguides,” J. Phys. B: At., Mol. Opt. Phys. 41(8), 085402 (2008).
[Crossref]

Corbalan, R.

K. Eckert, M. Lewenstein, R. Corbalan, G. Birkl, W. Ertmer, and J. Mompart, “Three-level atom optics via the tunneling interaction,” Phys. Rev. A 70(2), 023606 (2004).
[Crossref]

Day, A. G. R.

M. Bukov, A. G. R. Day, D. Sels, P. Weinberg, A. Polkovnikov, and P. Mehta, “Reinforcement learning in different phases of quantum control,” Phys. Rev. X 8, 031086 (2018).
[Crossref]

del Campo, A.

X. Chen, A. Ruschhaupt, S. Schmidt, A. del Campo, D. Guéry-Odelin, and J. G. Muga, “Fast optimal frictionless atom cooling in harmonic traps: Shortcut to adiabaticity,” Phys. Rev. Lett. 104(6), 063002 (2010).
[Crossref]

Demirplak, M.

M. Demirplak and S. A. Rice, “Adiabatic population transfer with control fields,” J. Phys. Chem. A 107(46), 9937–9945 (2003).
[Crossref]

Deng, F.-G.

H. Zhang, X.-K. Song, Q. Ai, H. Wang, G.-J. Yang, and F.-G. Deng, “Fast and robust quantum control for multimode interactions using shortcuts to adiabaticity,” Opt. Express 27(5), 7384–7392 (2019).
[Crossref]

X.-K. Song, Q. Ai, J. Qiu, and F.-G. Deng, “Physically feasible three-level transitionless quantum driving with multiple Schrödinger dynamics,” Phys. Rev. A 93(5), 052324 (2016).
[Crossref]

X.-K. Song, H. Zhang, Q. Ai, J. Qiu, and F.-G. Deng, “Shortcuts to adiabatic holonomic quantum computation in decoherence-free subspace with transitionless quantum driving algorithm,” New J. Phys. 18(2), 023001 (2016).
[Crossref]

Dong, Y. Q.

L. Q. Qiu, H. Li, Z. K. Han, W. Zheng, X. P. Yang, Y. Q. Dong, S. Q. Song, D. Lan, X. S. Tan, and Y. Yu, “Experimental realization of noncyclic geometric gates with shortcut to adiabaticity in a superconducting circuit,” Appl. Phys. Lett. 118(25), 254002 (2021).
[Crossref]

D. Y. Li, W. Zheng, J. Chu, X. P. Yang, S. Q. Song, Z. K. Han, Y. Q. Dong, Z. M. Wang, X. M. Yu, D. Lan, J. Zhao, S. X. Li, X. S. Tan, and Y. Yu, “Coherent state transfer between superconducting qubits via stimulated Raman adiabatic passage,” Appl. Phys. Lett. 118(10), 104003 (2021).
[Crossref]

Z. K. Han, Y. Q. Dong, X. P. Yang, S. Q. Song, L. Q. Qiu, W. Zheng, J. W. Xu, T. Q. Huang, Z. M. Wang, D. Lan, X. S. Tan, and Y. Yu, “Realization of invariant-based shortcuts to population inversion with a superconducting circuit,” Appl. Phys. Lett. 118(22), 224003 (2021).
[Crossref]

Du, Y.-X.

Y.-X. Du, Z.-T. Liang, Y.-C. Li, X.-X. Yue, Q.-X. Lv, W. Huang, X. Chen, H. Yan, and S.-L. Zhu, “Experimental realization of stimulated Raman shortcut-to-adiabatic passage with cold atoms,” Nat. Commun. 7(1), 12479 (2016).
[Crossref]

Eckert, K.

K. Eckert, M. Lewenstein, R. Corbalan, G. Birkl, W. Ertmer, and J. Mompart, “Three-level atom optics via the tunneling interaction,” Phys. Rev. A 70(2), 023606 (2004).
[Crossref]

Ertmer, W.

K. Eckert, M. Lewenstein, R. Corbalan, G. Birkl, W. Ertmer, and J. Mompart, “Three-level atom optics via the tunneling interaction,” Phys. Rev. A 70(2), 023606 (2004).
[Crossref]

Feng, G. R.

G. R. Feng, G. F. Xu, and G. L. Long, “Experimental realization of nonadiabatic holonomic quantum computation,” Phys. Rev. Lett. 110(19), 190501 (2013).
[Crossref]

Fernandez, T. T.

M. Ornigotti, G. D. Valle, T. T. Fernandez, A. Coppa, V. Foglietti, P. Laporta, and S. Longhi, “Visualization of two-photon Rabi oscillations in evanescently coupled optical waveguides,” J. Phys. B: At., Mol. Opt. Phys. 41(8), 085402 (2008).
[Crossref]

Foglietti, V.

M. Ornigotti, G. D. Valle, T. T. Fernandez, A. Coppa, V. Foglietti, P. Laporta, and S. Longhi, “Visualization of two-photon Rabi oscillations in evanescently coupled optical waveguides,” J. Phys. B: At., Mol. Opt. Phys. 41(8), 085402 (2008).
[Crossref]

Genov, G. T.

A. Bruns, G. T. Genov, M. Hain, N. V. Vitanov, and T. Halfmann, “Experimental demonstration of composite stimulated Raman adiabatic passage,” Phys. Rev. A 98(5), 053413 (2018).
[Crossref]

G. T. Genov, D. Schraft, N. V. Vitanov, and T. Halfmann, “Arbitrarily accurate pulse sequences for robust dynamical decoupling,” Phys. Rev. Lett. 118(13), 133202 (2017).
[Crossref]

G. T. Genov, D. Schraft, T. Halfmann, and N. V. Vitanov, “Correction of arbitrary field errors in population inversion of quantum systems by universal composite pulses,” Phys. Rev. Lett. 113(4), 043001 (2014).
[Crossref]

D. Schraft, T. Halfmann, G. T. Genov, and N. V. Vitanov, “Experimental demonstration of composite adiabatic passage,” Phys. Rev. A 88(6), 063406 (2013).
[Crossref]

Ghosh, J.

E. Zahedinejad, J. Ghosh, and B. C. Sanders, “Designing high-fidelity single-shot three-qubit gates: A machine-learning approach,” Phys. Rev. Applied 6(5), 054005 (2016).
[Crossref]

Guérin, S.

B. T. Torosov, S. Guérin, and N. V. Vitanov, “High-fidelity adiabatic passage by composite sequences of chirped pulses,” Phys. Rev. Lett. 106(23), 233001 (2011).
[Crossref]

Guéry-Odelin, D.

X. Chen, I. Lizuain, A. Ruschhaupt, D. Guéry-Odelin, and J. G. Muga, “Shortcut to adiabatic passage in two- and three-level atoms,” Phys. Rev. Lett. 105(12), 123003 (2010).
[Crossref]

X. Chen, A. Ruschhaupt, S. Schmidt, A. del Campo, D. Guéry-Odelin, and J. G. Muga, “Fast optimal frictionless atom cooling in harmonic traps: Shortcut to adiabaticity,” Phys. Rev. Lett. 104(6), 063002 (2010).
[Crossref]

Hain, M.

A. Bruns, G. T. Genov, M. Hain, N. V. Vitanov, and T. Halfmann, “Experimental demonstration of composite stimulated Raman adiabatic passage,” Phys. Rev. A 98(5), 053413 (2018).
[Crossref]

Halfmann, T.

A. Bruns, G. T. Genov, M. Hain, N. V. Vitanov, and T. Halfmann, “Experimental demonstration of composite stimulated Raman adiabatic passage,” Phys. Rev. A 98(5), 053413 (2018).
[Crossref]

G. T. Genov, D. Schraft, N. V. Vitanov, and T. Halfmann, “Arbitrarily accurate pulse sequences for robust dynamical decoupling,” Phys. Rev. Lett. 118(13), 133202 (2017).
[Crossref]

G. T. Genov, D. Schraft, T. Halfmann, and N. V. Vitanov, “Correction of arbitrary field errors in population inversion of quantum systems by universal composite pulses,” Phys. Rev. Lett. 113(4), 043001 (2014).
[Crossref]

D. Schraft, T. Halfmann, G. T. Genov, and N. V. Vitanov, “Experimental demonstration of composite adiabatic passage,” Phys. Rev. A 88(6), 063406 (2013).
[Crossref]

A. A. Rangelov, N. V. Vitanov, L. P. Yatsenko, B. W. Shore, T. Halfmann, and K. Bergmann, “Stark-shift-chirped rapid-adiabatic-passage technique among three states,” Phys. Rev. A 72(5), 053403 (2005).
[Crossref]

N. V. Vitanov, T. Halfmann, B. W. Shore, and K. Bergmann, “Laser-induced population transfer by adiabatic passage techniques,” Annu. Rev. Phys. Chem. 52(1), 763–809 (2001).
[Crossref]

Han, J.-X.

J.-L. Wu, Y. Wang, J.-X. Han, C. Wang, S.-L. Su, Y. Xia, Y. Jiang, and J. Song, “Two-path interference for enantiomer-selective state transfer of chiral molecules,” Phys. Rev. Applied 13(4), 044021 (2020).
[Crossref]

Han, Z. K.

L. Q. Qiu, H. Li, Z. K. Han, W. Zheng, X. P. Yang, Y. Q. Dong, S. Q. Song, D. Lan, X. S. Tan, and Y. Yu, “Experimental realization of noncyclic geometric gates with shortcut to adiabaticity in a superconducting circuit,” Appl. Phys. Lett. 118(25), 254002 (2021).
[Crossref]

D. Y. Li, W. Zheng, J. Chu, X. P. Yang, S. Q. Song, Z. K. Han, Y. Q. Dong, Z. M. Wang, X. M. Yu, D. Lan, J. Zhao, S. X. Li, X. S. Tan, and Y. Yu, “Coherent state transfer between superconducting qubits via stimulated Raman adiabatic passage,” Appl. Phys. Lett. 118(10), 104003 (2021).
[Crossref]

Z. K. Han, Y. Q. Dong, X. P. Yang, S. Q. Song, L. Q. Qiu, W. Zheng, J. W. Xu, T. Q. Huang, Z. M. Wang, D. Lan, X. S. Tan, and Y. Yu, “Realization of invariant-based shortcuts to population inversion with a superconducting circuit,” Appl. Phys. Lett. 118(22), 224003 (2021).
[Crossref]

He, Z.-C.

Z.-C. He and Z.-Y. Xue, “Robust nonadiabatic holonomic quantum gates on decoherence-protected qubits,” Appl. Phys. Lett. 119(10), 104001 (2021).
[Crossref]

Huang, T. Q.

Z. K. Han, Y. Q. Dong, X. P. Yang, S. Q. Song, L. Q. Qiu, W. Zheng, J. W. Xu, T. Q. Huang, Z. M. Wang, D. Lan, X. S. Tan, and Y. Yu, “Realization of invariant-based shortcuts to population inversion with a superconducting circuit,” Appl. Phys. Lett. 118(22), 224003 (2021).
[Crossref]

Huang, W.

Y.-X. Du, Z.-T. Liang, Y.-C. Li, X.-X. Yue, Q.-X. Lv, W. Huang, X. Chen, H. Yan, and S.-L. Zhu, “Experimental realization of stimulated Raman shortcut-to-adiabatic passage with cold atoms,” Nat. Commun. 7(1), 12479 (2016).
[Crossref]

Jiang, Y.

J.-L. Wu, Y. Wang, J.-X. Han, C. Wang, S.-L. Su, Y. Xia, Y. Jiang, and J. Song, “Two-path interference for enantiomer-selective state transfer of chiral molecules,” Phys. Rev. Applied 13(4), 044021 (2020).
[Crossref]

Kestner, J. P.

X. Wang, L. S. Bishop, J. P. Kestner, E. Barnes, K. Sun, and S. D. Sarma, “Composite pulses for robust universal control of singlet–triplet qubits,” Nature Commun. 3(1), 997 (2012).
[Crossref]

Kimble, H. J.

H. J. Kimble, “The quantum internet,” Nature 453(7198), 1023–1030 (2008).
[Crossref]

Kong, X.-Y.

X.-S. Xu, H. Zhang, X.-Y. Kong, M. Wang, and G. L. Long, “Frequency-tuning-induced state transfer in optical microcavities,” Photon. Research 8(4), 490–496 (2020).
[Crossref]

Král, P.

P. Král, I. Thanopulos, and M. Shapiro, “Colloquium: Coherently controlled adiabatic passage,” Rev. Mod. Phys. 79(1), 53–77 (2007).
[Crossref]

Lan, D.

L. Q. Qiu, H. Li, Z. K. Han, W. Zheng, X. P. Yang, Y. Q. Dong, S. Q. Song, D. Lan, X. S. Tan, and Y. Yu, “Experimental realization of noncyclic geometric gates with shortcut to adiabaticity in a superconducting circuit,” Appl. Phys. Lett. 118(25), 254002 (2021).
[Crossref]

D. Y. Li, W. Zheng, J. Chu, X. P. Yang, S. Q. Song, Z. K. Han, Y. Q. Dong, Z. M. Wang, X. M. Yu, D. Lan, J. Zhao, S. X. Li, X. S. Tan, and Y. Yu, “Coherent state transfer between superconducting qubits via stimulated Raman adiabatic passage,” Appl. Phys. Lett. 118(10), 104003 (2021).
[Crossref]

Z. K. Han, Y. Q. Dong, X. P. Yang, S. Q. Song, L. Q. Qiu, W. Zheng, J. W. Xu, T. Q. Huang, Z. M. Wang, D. Lan, X. S. Tan, and Y. Yu, “Realization of invariant-based shortcuts to population inversion with a superconducting circuit,” Appl. Phys. Lett. 118(22), 224003 (2021).
[Crossref]

Laporta, P.

M. Ornigotti, G. D. Valle, T. T. Fernandez, A. Coppa, V. Foglietti, P. Laporta, and S. Longhi, “Visualization of two-photon Rabi oscillations in evanescently coupled optical waveguides,” J. Phys. B: At., Mol. Opt. Phys. 41(8), 085402 (2008).
[Crossref]

Lewenstein, M.

K. Eckert, M. Lewenstein, R. Corbalan, G. Birkl, W. Ertmer, and J. Mompart, “Three-level atom optics via the tunneling interaction,” Phys. Rev. A 70(2), 023606 (2004).
[Crossref]

Lewis, H. R.

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L. Q. Qiu, H. Li, Z. K. Han, W. Zheng, X. P. Yang, Y. Q. Dong, S. Q. Song, D. Lan, X. S. Tan, and Y. Yu, “Experimental realization of noncyclic geometric gates with shortcut to adiabaticity in a superconducting circuit,” Appl. Phys. Lett. 118(25), 254002 (2021).
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D. Y. Li, W. Zheng, J. Chu, X. P. Yang, S. Q. Song, Z. K. Han, Y. Q. Dong, Z. M. Wang, X. M. Yu, D. Lan, J. Zhao, S. X. Li, X. S. Tan, and Y. Yu, “Coherent state transfer between superconducting qubits via stimulated Raman adiabatic passage,” Appl. Phys. Lett. 118(10), 104003 (2021).
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X.-S. Xu, H. Zhang, X.-Y. Kong, M. Wang, and G. L. Long, “Frequency-tuning-induced state transfer in optical microcavities,” Photon. Research 8(4), 490–496 (2020).
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Menzel-Jones, C.

E. A. Shapiro, V. Milner, C. Menzel-Jones, and M. Shapiro, “Piecewise adiabatic passage with a series of femtosecond pulses,” Phys. Rev. Lett. 99(3), 033002 (2007).
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Y.-H. Chen, W. Qin, X. Wang, A. Miranowicz, and F. Nori, “Shortcuts to adiabaticity for the quantum Rabi model: Efficient generation of giant entangled cat states via parametric amplification,” Phys. Rev. Lett. 126(2), 023602 (2021).
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S. Martínez-Garaot, E. Torrontegui, X. Chen, and J. G. Muga, “Shortcuts to adiabaticity in three-level systems using Lie transforms,” Phys. Rev. A 89(5), 053408 (2014).
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A. Ruschhaupt, X. Chen, D. Alonso, and J. G. Muga, “Optimally robust shortcuts to population inversion in two-level quantum systems,” New J. Phys. 14(9), 093040 (2012).
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X. Chen, A. Ruschhaupt, S. Schmidt, A. del Campo, D. Guéry-Odelin, and J. G. Muga, “Fast optimal frictionless atom cooling in harmonic traps: Shortcut to adiabaticity,” Phys. Rev. Lett. 104(6), 063002 (2010).
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X. Chen, I. Lizuain, A. Ruschhaupt, D. Guéry-Odelin, and J. G. Muga, “Shortcut to adiabatic passage in two- and three-level atoms,” Phys. Rev. Lett. 105(12), 123003 (2010).
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Y.-H. Chen, W. Qin, X. Wang, A. Miranowicz, and F. Nori, “Shortcuts to adiabaticity for the quantum Rabi model: Efficient generation of giant entangled cat states via parametric amplification,” Phys. Rev. Lett. 126(2), 023602 (2021).
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T. Opatrný and K. Mølmer, “Partial suppression of nonadiabatic transitions,” New J. Phys. 16(1), 015025 (2014).
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M. Ornigotti, G. D. Valle, T. T. Fernandez, A. Coppa, V. Foglietti, P. Laporta, and S. Longhi, “Visualization of two-photon Rabi oscillations in evanescently coupled optical waveguides,” J. Phys. B: At., Mol. Opt. Phys. 41(8), 085402 (2008).
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M. Bukov, A. G. R. Day, D. Sels, P. Weinberg, A. Polkovnikov, and P. Mehta, “Reinforcement learning in different phases of quantum control,” Phys. Rev. X 8, 031086 (2018).
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Y.-H. Chen, W. Qin, X. Wang, A. Miranowicz, and F. Nori, “Shortcuts to adiabaticity for the quantum Rabi model: Efficient generation of giant entangled cat states via parametric amplification,” Phys. Rev. Lett. 126(2), 023602 (2021).
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X.-K. Song, Q. Ai, J. Qiu, and F.-G. Deng, “Physically feasible three-level transitionless quantum driving with multiple Schrödinger dynamics,” Phys. Rev. A 93(5), 052324 (2016).
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X.-K. Song, H. Zhang, Q. Ai, J. Qiu, and F.-G. Deng, “Shortcuts to adiabatic holonomic quantum computation in decoherence-free subspace with transitionless quantum driving algorithm,” New J. Phys. 18(2), 023001 (2016).
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L. Q. Qiu, H. Li, Z. K. Han, W. Zheng, X. P. Yang, Y. Q. Dong, S. Q. Song, D. Lan, X. S. Tan, and Y. Yu, “Experimental realization of noncyclic geometric gates with shortcut to adiabaticity in a superconducting circuit,” Appl. Phys. Lett. 118(25), 254002 (2021).
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Z. K. Han, Y. Q. Dong, X. P. Yang, S. Q. Song, L. Q. Qiu, W. Zheng, J. W. Xu, T. Q. Huang, Z. M. Wang, D. Lan, X. S. Tan, and Y. Yu, “Realization of invariant-based shortcuts to population inversion with a superconducting circuit,” Appl. Phys. Lett. 118(22), 224003 (2021).
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A. A. Rangelov and N. V. Vitanov, “Achromatic multiple beam splitting by adiabatic passage in optical waveguides,” Phys. Rev. A 85(5), 055803 (2012).
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A. A. Rangelov, N. V. Vitanov, L. P. Yatsenko, B. W. Shore, T. Halfmann, and K. Bergmann, “Stark-shift-chirped rapid-adiabatic-passage technique among three states,” Phys. Rev. A 72(5), 053403 (2005).
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H. R. Lewis and W. B. Riesenfeld, “An exact quantum theory of the time-dependent harmonic oscillator and of a charged particle in a time-dependent electromagnetic field,” J. Math. Phys. 10(8), 1458–1473 (1969).
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A. Ruschhaupt, X. Chen, D. Alonso, and J. G. Muga, “Optimally robust shortcuts to population inversion in two-level quantum systems,” New J. Phys. 14(9), 093040 (2012).
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X. Chen, I. Lizuain, A. Ruschhaupt, D. Guéry-Odelin, and J. G. Muga, “Shortcut to adiabatic passage in two- and three-level atoms,” Phys. Rev. Lett. 105(12), 123003 (2010).
[Crossref]

X. Chen, A. Ruschhaupt, S. Schmidt, A. del Campo, D. Guéry-Odelin, and J. G. Muga, “Fast optimal frictionless atom cooling in harmonic traps: Shortcut to adiabaticity,” Phys. Rev. Lett. 104(6), 063002 (2010).
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M. Saffman, T. G. Walker, and K. Mølmer, “Quantum information with Rydberg atoms,” Rev. Mod. Phys. 82(3), 2313–2363 (2010).
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X. Wang, L. S. Bishop, J. P. Kestner, E. Barnes, K. Sun, and S. D. Sarma, “Composite pulses for robust universal control of singlet–triplet qubits,” Nature Commun. 3(1), 997 (2012).
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Schmidt, S.

X. Chen, A. Ruschhaupt, S. Schmidt, A. del Campo, D. Guéry-Odelin, and J. G. Muga, “Fast optimal frictionless atom cooling in harmonic traps: Shortcut to adiabaticity,” Phys. Rev. Lett. 104(6), 063002 (2010).
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G. T. Genov, D. Schraft, N. V. Vitanov, and T. Halfmann, “Arbitrarily accurate pulse sequences for robust dynamical decoupling,” Phys. Rev. Lett. 118(13), 133202 (2017).
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G. T. Genov, D. Schraft, T. Halfmann, and N. V. Vitanov, “Correction of arbitrary field errors in population inversion of quantum systems by universal composite pulses,” Phys. Rev. Lett. 113(4), 043001 (2014).
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D. Schraft, T. Halfmann, G. T. Genov, and N. V. Vitanov, “Experimental demonstration of composite adiabatic passage,” Phys. Rev. A 88(6), 063406 (2013).
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M. Bukov, A. G. R. Day, D. Sels, P. Weinberg, A. Polkovnikov, and P. Mehta, “Reinforcement learning in different phases of quantum control,” Phys. Rev. X 8, 031086 (2018).
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E. A. Shapiro, V. Milner, C. Menzel-Jones, and M. Shapiro, “Piecewise adiabatic passage with a series of femtosecond pulses,” Phys. Rev. Lett. 99(3), 033002 (2007).
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Shapiro, M.

E. A. Shapiro, V. Milner, C. Menzel-Jones, and M. Shapiro, “Piecewise adiabatic passage with a series of femtosecond pulses,” Phys. Rev. Lett. 99(3), 033002 (2007).
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P. Král, I. Thanopulos, and M. Shapiro, “Colloquium: Coherently controlled adiabatic passage,” Rev. Mod. Phys. 79(1), 53–77 (2007).
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Z.-C. Shi, H.-N. Wu, L.-T. Shen, J. Song, Y. Xia, X. X. Yi, and S.-B. Zheng, “Robust single-qubit gates by composite pulses in three-level systems,” Phys. Rev. A 103(5), 052612 (2021).
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B. T. Torosov, B. W. Shore, and N. V. Vitanov, “Coherent control techniques for two-state quantum systems: A comparative study,” Phys. Rev. A 103(3), 033110 (2021).
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N. V. Vitanov, A. A. Rangelov, B. W. Shore, and K. Bergmann, “Stimulated Raman adiabatic passage in physics, chemistry, and beyond,” Rev. Mod. Phys. 89(1), 015006 (2017).
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A. A. Rangelov, N. V. Vitanov, L. P. Yatsenko, B. W. Shore, T. Halfmann, and K. Bergmann, “Stark-shift-chirped rapid-adiabatic-passage technique among three states,” Phys. Rev. A 72(5), 053403 (2005).
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K. Bergmann, H. Theuer, and B. W. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys. 70(3), 1003–1025 (1998).
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Z.-C. Shi, H.-N. Wu, L.-T. Shen, J. Song, Y. Xia, X. X. Yi, and S.-B. Zheng, “Robust single-qubit gates by composite pulses in three-level systems,” Phys. Rev. A 103(5), 052612 (2021).
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J.-L. Wu, Y. Wang, J.-X. Han, C. Wang, S.-L. Su, Y. Xia, Y. Jiang, and J. Song, “Two-path interference for enantiomer-selective state transfer of chiral molecules,” Phys. Rev. Applied 13(4), 044021 (2020).
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Y.-H. Chen, Y. Xia, Q.-Q. Chen, and J. Song, “Ef?cient shortcuts to adiabatic passage for fast population transfer in multiparticle systems,” Phys. Rev. A 89(3), 033856 (2014).
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L. Q. Qiu, H. Li, Z. K. Han, W. Zheng, X. P. Yang, Y. Q. Dong, S. Q. Song, D. Lan, X. S. Tan, and Y. Yu, “Experimental realization of noncyclic geometric gates with shortcut to adiabaticity in a superconducting circuit,” Appl. Phys. Lett. 118(25), 254002 (2021).
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D. Y. Li, W. Zheng, J. Chu, X. P. Yang, S. Q. Song, Z. K. Han, Y. Q. Dong, Z. M. Wang, X. M. Yu, D. Lan, J. Zhao, S. X. Li, X. S. Tan, and Y. Yu, “Coherent state transfer between superconducting qubits via stimulated Raman adiabatic passage,” Appl. Phys. Lett. 118(10), 104003 (2021).
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Z. K. Han, Y. Q. Dong, X. P. Yang, S. Q. Song, L. Q. Qiu, W. Zheng, J. W. Xu, T. Q. Huang, Z. M. Wang, D. Lan, X. S. Tan, and Y. Yu, “Realization of invariant-based shortcuts to population inversion with a superconducting circuit,” Appl. Phys. Lett. 118(22), 224003 (2021).
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X.-K. Song, F. Meng, B.-J. Liu, D. Wang, L. Ye, and M.-H. Yung, “Robust stimulated Raman shortcut-to-adiabatic passage with invariant-based optimal control,” Opt. Express 29(6), 7998–8014 (2021).
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H. Zhang, X.-K. Song, Q. Ai, H. Wang, G.-J. Yang, and F.-G. Deng, “Fast and robust quantum control for multimode interactions using shortcuts to adiabaticity,” Opt. Express 27(5), 7384–7392 (2019).
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X.-K. Song, Q. Ai, J. Qiu, and F.-G. Deng, “Physically feasible three-level transitionless quantum driving with multiple Schrödinger dynamics,” Phys. Rev. A 93(5), 052324 (2016).
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X.-K. Song, H. Zhang, Q. Ai, J. Qiu, and F.-G. Deng, “Shortcuts to adiabatic holonomic quantum computation in decoherence-free subspace with transitionless quantum driving algorithm,” New J. Phys. 18(2), 023001 (2016).
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J.-L. Wu, Y. Wang, J.-X. Han, C. Wang, S.-L. Su, Y. Xia, Y. Jiang, and J. Song, “Two-path interference for enantiomer-selective state transfer of chiral molecules,” Phys. Rev. Applied 13(4), 044021 (2020).
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D. Y. Li, W. Zheng, J. Chu, X. P. Yang, S. Q. Song, Z. K. Han, Y. Q. Dong, Z. M. Wang, X. M. Yu, D. Lan, J. Zhao, S. X. Li, X. S. Tan, and Y. Yu, “Coherent state transfer between superconducting qubits via stimulated Raman adiabatic passage,” Appl. Phys. Lett. 118(10), 104003 (2021).
[Crossref]

L. Q. Qiu, H. Li, Z. K. Han, W. Zheng, X. P. Yang, Y. Q. Dong, S. Q. Song, D. Lan, X. S. Tan, and Y. Yu, “Experimental realization of noncyclic geometric gates with shortcut to adiabaticity in a superconducting circuit,” Appl. Phys. Lett. 118(25), 254002 (2021).
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Z. K. Han, Y. Q. Dong, X. P. Yang, S. Q. Song, L. Q. Qiu, W. Zheng, J. W. Xu, T. Q. Huang, Z. M. Wang, D. Lan, X. S. Tan, and Y. Yu, “Realization of invariant-based shortcuts to population inversion with a superconducting circuit,” Appl. Phys. Lett. 118(22), 224003 (2021).
[Crossref]

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P. Král, I. Thanopulos, and M. Shapiro, “Colloquium: Coherently controlled adiabatic passage,” Rev. Mod. Phys. 79(1), 53–77 (2007).
[Crossref]

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K. Bergmann, H. Theuer, and B. W. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys. 70(3), 1003–1025 (1998).
[Crossref]

Torosov, B. T.

B. T. Torosov, B. W. Shore, and N. V. Vitanov, “Coherent control techniques for two-state quantum systems: A comparative study,” Phys. Rev. A 103(3), 033110 (2021).
[Crossref]

B. T. Torosov and N. V. Vitanov, “Arbitrarily accurate twin composite π-pulse sequences,” Phys. Rev. A 97(4), 043408 (2018).
[Crossref]

B. T. Torosov, S. Guérin, and N. V. Vitanov, “High-fidelity adiabatic passage by composite sequences of chirped pulses,” Phys. Rev. Lett. 106(23), 233001 (2011).
[Crossref]

B. T. Torosov and N. V. Vitanov, “Smooth composite pulses for high-?delity quantum information processing,” Phys. Rev. A 83(5), 053420 (2011).
[Crossref]

Torrontegui, E.

S. Martínez-Garaot, E. Torrontegui, X. Chen, and J. G. Muga, “Shortcuts to adiabaticity in three-level systems using Lie transforms,” Phys. Rev. A 89(5), 053408 (2014).
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Tseng, S.-Y.

Ueda, M.

Z. T. Wang, Y. Ashida, and M. Ueda, “Deep reinforcement learning control of quantum cartpoles,” Phys. Rev. Lett. 125(10), 100401 (2020).
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M. Ornigotti, G. D. Valle, T. T. Fernandez, A. Coppa, V. Foglietti, P. Laporta, and S. Longhi, “Visualization of two-photon Rabi oscillations in evanescently coupled optical waveguides,” J. Phys. B: At., Mol. Opt. Phys. 41(8), 085402 (2008).
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G. S. Vasilev and N. V. Vitanov, “Coherent excitation of a two-state system by a linearly chirped Gaussian pulse,” J. Chem. Phys. 123(17), 174106 (2005).
[Crossref]

Vitanov, N. V.

B. T. Torosov, B. W. Shore, and N. V. Vitanov, “Coherent control techniques for two-state quantum systems: A comparative study,” Phys. Rev. A 103(3), 033110 (2021).
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A. Bruns, G. T. Genov, M. Hain, N. V. Vitanov, and T. Halfmann, “Experimental demonstration of composite stimulated Raman adiabatic passage,” Phys. Rev. A 98(5), 053413 (2018).
[Crossref]

B. T. Torosov and N. V. Vitanov, “Arbitrarily accurate twin composite π-pulse sequences,” Phys. Rev. A 97(4), 043408 (2018).
[Crossref]

G. T. Genov, D. Schraft, N. V. Vitanov, and T. Halfmann, “Arbitrarily accurate pulse sequences for robust dynamical decoupling,” Phys. Rev. Lett. 118(13), 133202 (2017).
[Crossref]

N. V. Vitanov, A. A. Rangelov, B. W. Shore, and K. Bergmann, “Stimulated Raman adiabatic passage in physics, chemistry, and beyond,” Rev. Mod. Phys. 89(1), 015006 (2017).
[Crossref]

G. T. Genov, D. Schraft, T. Halfmann, and N. V. Vitanov, “Correction of arbitrary field errors in population inversion of quantum systems by universal composite pulses,” Phys. Rev. Lett. 113(4), 043001 (2014).
[Crossref]

D. Schraft, T. Halfmann, G. T. Genov, and N. V. Vitanov, “Experimental demonstration of composite adiabatic passage,” Phys. Rev. A 88(6), 063406 (2013).
[Crossref]

A. A. Rangelov and N. V. Vitanov, “Achromatic multiple beam splitting by adiabatic passage in optical waveguides,” Phys. Rev. A 85(5), 055803 (2012).
[Crossref]

B. T. Torosov, S. Guérin, and N. V. Vitanov, “High-fidelity adiabatic passage by composite sequences of chirped pulses,” Phys. Rev. Lett. 106(23), 233001 (2011).
[Crossref]

B. T. Torosov and N. V. Vitanov, “Smooth composite pulses for high-?delity quantum information processing,” Phys. Rev. A 83(5), 053420 (2011).
[Crossref]

A. A. Rangelov, N. V. Vitanov, L. P. Yatsenko, B. W. Shore, T. Halfmann, and K. Bergmann, “Stark-shift-chirped rapid-adiabatic-passage technique among three states,” Phys. Rev. A 72(5), 053403 (2005).
[Crossref]

G. S. Vasilev and N. V. Vitanov, “Coherent excitation of a two-state system by a linearly chirped Gaussian pulse,” J. Chem. Phys. 123(17), 174106 (2005).
[Crossref]

N. V. Vitanov, T. Halfmann, B. W. Shore, and K. Bergmann, “Laser-induced population transfer by adiabatic passage techniques,” Annu. Rev. Phys. Chem. 52(1), 763–809 (2001).
[Crossref]

Walker, T. G.

M. Saffman, T. G. Walker, and K. Mølmer, “Quantum information with Rydberg atoms,” Rev. Mod. Phys. 82(3), 2313–2363 (2010).
[Crossref]

Wang, C.

J.-L. Wu, Y. Wang, J.-X. Han, C. Wang, S.-L. Su, Y. Xia, Y. Jiang, and J. Song, “Two-path interference for enantiomer-selective state transfer of chiral molecules,” Phys. Rev. Applied 13(4), 044021 (2020).
[Crossref]

Wang, D.

Wang, H.

Wang, M.

X.-S. Xu, H. Zhang, X.-Y. Kong, M. Wang, and G. L. Long, “Frequency-tuning-induced state transfer in optical microcavities,” Photon. Research 8(4), 490–496 (2020).
[Crossref]

Wang, X.

Y.-H. Chen, W. Qin, X. Wang, A. Miranowicz, and F. Nori, “Shortcuts to adiabaticity for the quantum Rabi model: Efficient generation of giant entangled cat states via parametric amplification,” Phys. Rev. Lett. 126(2), 023602 (2021).
[Crossref]

X. Wang, L. S. Bishop, J. P. Kestner, E. Barnes, K. Sun, and S. D. Sarma, “Composite pulses for robust universal control of singlet–triplet qubits,” Nature Commun. 3(1), 997 (2012).
[Crossref]

Wang, Y.

J.-L. Wu, Y. Wang, J.-X. Han, C. Wang, S.-L. Su, Y. Xia, Y. Jiang, and J. Song, “Two-path interference for enantiomer-selective state transfer of chiral molecules,” Phys. Rev. Applied 13(4), 044021 (2020).
[Crossref]

Wang, Z. M.

D. Y. Li, W. Zheng, J. Chu, X. P. Yang, S. Q. Song, Z. K. Han, Y. Q. Dong, Z. M. Wang, X. M. Yu, D. Lan, J. Zhao, S. X. Li, X. S. Tan, and Y. Yu, “Coherent state transfer between superconducting qubits via stimulated Raman adiabatic passage,” Appl. Phys. Lett. 118(10), 104003 (2021).
[Crossref]

Z. K. Han, Y. Q. Dong, X. P. Yang, S. Q. Song, L. Q. Qiu, W. Zheng, J. W. Xu, T. Q. Huang, Z. M. Wang, D. Lan, X. S. Tan, and Y. Yu, “Realization of invariant-based shortcuts to population inversion with a superconducting circuit,” Appl. Phys. Lett. 118(22), 224003 (2021).
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Wang, Z. T.

Z. T. Wang, Y. Ashida, and M. Ueda, “Deep reinforcement learning control of quantum cartpoles,” Phys. Rev. Lett. 125(10), 100401 (2020).
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Weinberg, P.

M. Bukov, A. G. R. Day, D. Sels, P. Weinberg, A. Polkovnikov, and P. Mehta, “Reinforcement learning in different phases of quantum control,” Phys. Rev. X 8, 031086 (2018).
[Crossref]

Wu, H.-N.

Z.-C. Shi, H.-N. Wu, L.-T. Shen, J. Song, Y. Xia, X. X. Yi, and S.-B. Zheng, “Robust single-qubit gates by composite pulses in three-level systems,” Phys. Rev. A 103(5), 052612 (2021).
[Crossref]

Wu, J.-L.

J.-L. Wu, Y. Wang, J.-X. Han, C. Wang, S.-L. Su, Y. Xia, Y. Jiang, and J. Song, “Two-path interference for enantiomer-selective state transfer of chiral molecules,” Phys. Rev. Applied 13(4), 044021 (2020).
[Crossref]

Xia, Y.

Z.-C. Shi, H.-N. Wu, L.-T. Shen, J. Song, Y. Xia, X. X. Yi, and S.-B. Zheng, “Robust single-qubit gates by composite pulses in three-level systems,” Phys. Rev. A 103(5), 052612 (2021).
[Crossref]

J.-L. Wu, Y. Wang, J.-X. Han, C. Wang, S.-L. Su, Y. Xia, Y. Jiang, and J. Song, “Two-path interference for enantiomer-selective state transfer of chiral molecules,” Phys. Rev. Applied 13(4), 044021 (2020).
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[Crossref]

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G. R. Feng, G. F. Xu, and G. L. Long, “Experimental realization of nonadiabatic holonomic quantum computation,” Phys. Rev. Lett. 110(19), 190501 (2013).
[Crossref]

Xu, J. W.

Z. K. Han, Y. Q. Dong, X. P. Yang, S. Q. Song, L. Q. Qiu, W. Zheng, J. W. Xu, T. Q. Huang, Z. M. Wang, D. Lan, X. S. Tan, and Y. Yu, “Realization of invariant-based shortcuts to population inversion with a superconducting circuit,” Appl. Phys. Lett. 118(22), 224003 (2021).
[Crossref]

Xu, X.-S.

X.-S. Xu, H. Zhang, X.-Y. Kong, M. Wang, and G. L. Long, “Frequency-tuning-induced state transfer in optical microcavities,” Photon. Research 8(4), 490–496 (2020).
[Crossref]

Xue, Z.-Y.

S. Li and Z.-Y. Xue, “Dynamically corrected nonadiabatic holonomic quantum gates,” Phys. Rev. Applied 16(4), 044005 (2021).
[Crossref]

Z.-C. He and Z.-Y. Xue, “Robust nonadiabatic holonomic quantum gates on decoherence-protected qubits,” Appl. Phys. Lett. 119(10), 104001 (2021).
[Crossref]

Yan, H.

Y.-X. Du, Z.-T. Liang, Y.-C. Li, X.-X. Yue, Q.-X. Lv, W. Huang, X. Chen, H. Yan, and S.-L. Zhu, “Experimental realization of stimulated Raman shortcut-to-adiabatic passage with cold atoms,” Nat. Commun. 7(1), 12479 (2016).
[Crossref]

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Yang, X. P.

D. Y. Li, W. Zheng, J. Chu, X. P. Yang, S. Q. Song, Z. K. Han, Y. Q. Dong, Z. M. Wang, X. M. Yu, D. Lan, J. Zhao, S. X. Li, X. S. Tan, and Y. Yu, “Coherent state transfer between superconducting qubits via stimulated Raman adiabatic passage,” Appl. Phys. Lett. 118(10), 104003 (2021).
[Crossref]

L. Q. Qiu, H. Li, Z. K. Han, W. Zheng, X. P. Yang, Y. Q. Dong, S. Q. Song, D. Lan, X. S. Tan, and Y. Yu, “Experimental realization of noncyclic geometric gates with shortcut to adiabaticity in a superconducting circuit,” Appl. Phys. Lett. 118(25), 254002 (2021).
[Crossref]

Z. K. Han, Y. Q. Dong, X. P. Yang, S. Q. Song, L. Q. Qiu, W. Zheng, J. W. Xu, T. Q. Huang, Z. M. Wang, D. Lan, X. S. Tan, and Y. Yu, “Realization of invariant-based shortcuts to population inversion with a superconducting circuit,” Appl. Phys. Lett. 118(22), 224003 (2021).
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D. Y. Li, W. Zheng, J. Chu, X. P. Yang, S. Q. Song, Z. K. Han, Y. Q. Dong, Z. M. Wang, X. M. Yu, D. Lan, J. Zhao, S. X. Li, X. S. Tan, and Y. Yu, “Coherent state transfer between superconducting qubits via stimulated Raman adiabatic passage,” Appl. Phys. Lett. 118(10), 104003 (2021).
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X.-T. Yu, Q. Zhang, Y. Ban, and X. Chen, “Fast and robust control of two interacting spins,” Phys. Rev. A 97(6), 062317 (2018).
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D. Y. Li, W. Zheng, J. Chu, X. P. Yang, S. Q. Song, Z. K. Han, Y. Q. Dong, Z. M. Wang, X. M. Yu, D. Lan, J. Zhao, S. X. Li, X. S. Tan, and Y. Yu, “Coherent state transfer between superconducting qubits via stimulated Raman adiabatic passage,” Appl. Phys. Lett. 118(10), 104003 (2021).
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Zheng, S.-B.

Z.-C. Shi, H.-N. Wu, L.-T. Shen, J. Song, Y. Xia, X. X. Yi, and S.-B. Zheng, “Robust single-qubit gates by composite pulses in three-level systems,” Phys. Rev. A 103(5), 052612 (2021).
[Crossref]

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Z. K. Han, Y. Q. Dong, X. P. Yang, S. Q. Song, L. Q. Qiu, W. Zheng, J. W. Xu, T. Q. Huang, Z. M. Wang, D. Lan, X. S. Tan, and Y. Yu, “Realization of invariant-based shortcuts to population inversion with a superconducting circuit,” Appl. Phys. Lett. 118(22), 224003 (2021).
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Data availability

Data produced by numerical simulations in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (8)

Fig. 1.
Fig. 1. Illustration of 1:2 beam splitter.
Fig. 2.
Fig. 2. Time dependence of parameters $\Omega$ and population $P(t)$ of state $\left | {{\Phi _ + }} \right \rangle$ of RE method: (a) $\Omega$ (blue, solid line), (b) Population $P(t)$ (red, solid line).
Fig. 3.
Fig. 3. Time dependence of parameters $\Omega$ and population $P(t)$ of state $\left | {{\Phi _ + }} \right \rangle$ of AP method: (a) $\Delta$ (red, dashed line) and $\Omega$ (blue, solid line), (b) Population $P(t)$ (red, solid line).
Fig. 4.
Fig. 4. Time dependence of parameters $\Delta$, $\Omega$, and population $P(t)$ of state $\left | {{\Phi _ + }} \right \rangle$ of CD method: (a) $\Delta$ (red, dashed line), $\Omega$ (blue, solid line), and CD term ${\Omega _c}$ (green, dashed-dotted line), (b) Population $P(t)$ (red, solid line).
Fig. 5.
Fig. 5. Time dependence of parameters $\Delta$, $\Omega$, and population $P(t)$ of state $\left | {{\Phi _ + }} \right \rangle$ of LRI method. (a) n = $-$0.5, $\Delta$ (red, dashed line) and $\Omega$ (blue, solid line); n = 0.125, $\Delta$ (yellow, dashed line) and $\Omega$ (purple, solid line), (b) Population $P(t)$ (red, solid line). It is worth noting that for all n, time-dependent functions of populations are same, because n affects only phases.
Fig. 6.
Fig. 6. Time dependence of parameters $\Delta$, $\Omega$, and population $P(t)$ of state $\left | {{\Phi _ + }} \right \rangle$ of CAP method. In protocol, we employ five-pulse sequence to construct CAP, in which all pulses have the same Rabi frequencies and detunings. $\Delta$ (red, dashed line) and $\Omega$ (blue, solid line) of single pulse are plotted in (a). (b) Population $P(t)$ of CAP with five-pulse sequence (red, solid line), where duration of each pulse is 6T.
Fig. 7.
Fig. 7. Transition probability $P({t_f})$ versus Rabi frequency error parameter $\delta$ (dimensionless parameter): RE (black, dashed line), CD (yellow, solid line), LRI (blue, dashed line), AP (green, dashed-dotted line), and CAP (red, solid line).
Fig. 8.
Fig. 8. Transition probability $P({t_f})$ versus systematic error parameter $\delta$ (dimensionless parameter): RE (black, dashed line), CD (yellow, solid line), LRI (blue, dashed line), AP (green, dashed-dotted line), and CAP (red, solid line).

Equations (33)

Equations on this page are rendered with MathJax. Learn more.

H 0 ( t ) = ( K 2 J 0 2 J 0 2 J 0 2 J K ) ,
H 0 ( t ) = 1 2 ( K 4 J 0 4 J K 0 0 0 K )
H ( t ) = 1 2 ( Δ Ω Ω Δ ) ,
P ( t ) = 1 2 [ 1 cos ( A ) ] ,
Ω ( t ) = π e ( t / T ) 2 / T ,
Δ = α t T , Ω = Ω 0 e ( t / T ) 2 ,
2 Ω 0 > α 2 T ,
Δ = 5 T t T , Ω = 5 π T e ( t / T ) 2 ,
H c = i ± ( | t ϕ ± ϕ ± | ϕ ± | ϕ ± t ϕ ± t ϕ ± | ϕ ± ϕ ± | ) ,
| ϕ + = ( sin γ cos γ ) , | ϕ = ( cos γ sin γ )
H c = 1 2 ( 0 i Ω c i Ω c 0 ) ,
Δ = 2 T t T , Ω = π T e ( t / T ) 2 ,
Ω c = 2 π e ( t / T ) 2 [ 2 ( t / T ) 2 + 1 ] / [ 4 ( t / T ) 2 T e ( t / T ) 2 + π T ] .
I = 1 2 ( cos θ sin θ e i β sin θ e i β cos θ )
d I d t = 1 i [ I , H ] + I t = 0.
θ ˙ = Ω sin β , β ˙ = Ω cot θ cos β Δ .
| ψ ( t ) = j = ± C j e i η j ( t ) | φ j ( t ) , U ( t , t 0 ) = j = ± e i η j ( t ) | φ j ( t ) φ j ( t 0 ) | ,
| φ + ( t ) = ( e i β / 2 cos θ 2 e i β / 2 sin θ 2 ) , | φ ( t ) = ( e i β / 2 sin θ 2 e i β / 2 cos θ 2 ) ,
η ˙ j ( t ) = 1 φ j ( t ) | i t H | φ j ( t ) .
η ˙ + ( t ) = η ˙ ( t ) = θ ˙ cos β 2 sin θ sin β .
θ ( t ) = 3 π ( t 6 T + 1 2 ) 2 2 π ( t 6 T + 1 2 ) 3 ,
η + ( t ) = θ n sin [ 2 θ ] ,
β ( t ) = a r c c o t [ 2 ( 1 + 2 n cos 2 θ ) sin θ ] .
q s = 2 P ( t f ) 2 δ 2 | δ = 0 ,
U = ( a b b a ) ,
H ( ϕ ) = 1 2 ( Δ Ω e i ϕ Ω e i ϕ Δ ) .
U ( ϕ ) = ( a b e i ϕ b e i ϕ a ) .
U ( N ) = U ( ϕ N ) U ( ϕ N 1 ) U ( ϕ 2 ) U ( ϕ 1 ) ,
Δ ( t ) = Δ ( t ) , Ω ( t ) = Ω ( t ) ,
U 11 ( 3 ) = a 3 a | b | 2 ( 1 + 2 cos ϕ 2 ) .
U 11 ( 5 ) = a 5 + a | b | 4 [ 2 cos ( ϕ 2 ϕ 3 ) + 2 cos ( 2 ϕ 2 ϕ 3 ) + 1 ] 2 a 3 | b | 2 [ 2 cos ϕ 2 + cos ( ϕ 2 ϕ 3 ) + cos ϕ 3 + 1 ] .
P = 1 a 2 N .
Δ = 2 T t T , Ω = π T e ( t / T ) 2 ,