1. INTRODUCTION

Recent advances in telecom photonic quantum information technology allow integrated photonic circuits, ultrafast switching, and highly efficient single-photon detection and wavelength conversion. Combining those technologies with matter quantum systems as shown in Fig. 1 will certainly open up a new avenue for advanced quantum information technologies, such as a long-distance quantum key distribution [1,2], quantum computation including measurement-based topological methods [3–5] and quantum communication among separated nodes [6], and for fundamental tests of the physics outside of the light cone [7]. Manipulation of a quantum state in matter quantum systems has been performed by various wavelengths of the photons [8–13], but the photons in the demonstrations are of visible or near-infrared wavelengths that are not compatible with the telecom regime. Thus to fill the wavelength mismatch, quantum frequency conversion (QFC) that preserves non-classical photon statistics and a quantum state of an input light has been studied [14].

 

Fig. 1. Concept of an elementary link of quantum matter systems through optical fiber quantum communication by telecom photons. The telecom photons converted from light pulses that have a correlation with the matter systems are measured for heralding the connection between the quantum matter systems.

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A pioneering work for this task is a QFC based on four wave mixing operated around near resonance in cold rubidium (Rb) atoms [15,16]. In this experiment, a visible photon that heralds spin-wave excitations in cold Rb atoms as a quantum memory was frequency-down-converted to a telecom photon by QFC by the atomic cloud. The QFC device has a high efficiency due to the operation near atomic resonance. Meanwhile, it limits the choice of wavelengths available to the QFC. Such a limitation can be relaxed by the use of a nonlinear optical crystal because the bulk crystal can satisfy the phase matching condition for various wavelengths of photons by employing the periodic poling technique [17]. Recently by using various nonlinear optical crystals, widely tunable solid-state-based QFCs have been demonstrated [18–22], and the potential ability for the single-photon source with a cold Rb atom ensemble has been demonstrated [23]. However, heralded single excitation (HSE) in a long-lived matter quantum system by telecom photon detection required for the quantum network illustrated in Fig. 1 has not been demonstrated.

We first show an HSE in a cold Rb atomic ensemble through the detection of the photon emission from the ${\mathrm{D}}_2$ line of Rb. Subsequently, we show the conversion of the wavelength of the photon to 1522 nm in the telecom range by QFC using a periodically-poled lithium niobate (PPLN) waveguide. Finally we show the demonstration of the HSE through telecom photon detection by superconducting single-photon detectors (SSPDs). Remarkably, we show the non-classical property of the HSE by observing the autocorrelation functions in addition to the cross correlation functions. Furthermore, we show that the telecom photons heralded by the atomic spin state also have non-classical photon statistics.

2. EXPERIMENTAL SETUP

The ${}^{87}\mathrm{Rb}$ atomic ensemble is prepared by a magneto-optical trap (MOT) for 20 ms. After the lasers and the magnetic field for the MOT are turned off, we use $\mathrm{\Lambda }$-type energy levels of the ${\mathrm{D}}_2$ line at 780 nm ($5^2{S}_{1/2}\leftrightarrow 5^2{P}_{3/2}$) for the experiment as shown in Fig. 2(a). Two of the ground levels having $F=2$ and $F=1$ are denoted by $g_{\mathrm{a}}$ and $g_{\mathrm{b}}$, respectively, in which magnetic sublevels are degenerated because of the absence of the magnetic field. At first, a horizontally (H-) polarized 300 ns clean pulse at the resonant frequency between $g_{\mathrm{b}}$ and the excited level ($F^{\prime }=2$) prepares the atomic ensemble into $g_{\mathrm{a}}$ [see also Fig. 2(b)]. Then a vertically ($V$-) polarized 100 ns write pulse near the resonant frequency between $g_{\mathrm{a}}$ and the excited level provides the Raman transition from $g_{\mathrm{a}}$ to $g_{\mathrm{b}}$ and anti-Stokes (AS) photons simultaneously. In our experiment, the AS photons emitted in a direction at a small angle ($\sim 3°$) relative to the direction of the write pulse are detected with H polarization. We will explain an optical circuit for the AS photons in detail later. The photon detection in mode AS tells us that the single excitation has been prepared in the atomic ensemble, which we call HSE. In order to read out the HSE, an H-polarized 100 ns read light at the resonant frequency between $g_{\mathrm{b}}$ and the excited level is injected into the atoms. The Raman transition to $g_{\mathrm{a}}$ provides Stokes (S) photons. By setting the direction of the read pulse to be opposite to the write pulse, the Stokes photons are emitted in a mode (S) traveling in the opposite direction to that of mode AS due to the phase matching condition of the four light pulses [24]. In our experiment, we detect the photons in mode S with $V$ polarization only. We chose this polarization setup because of removing the H-polarized strong read pulse from the S photons. In addition, selecting the H-polarized AS photons is not only for removing the $V$-polarized strong write pulse but also for extracting a large amount of the AS photons heralded by the $V$-polarized S photon, which is expected under the assumption that the atomic states in $g_{\mathrm{a}}$ are fully mixed over the magnetic sublevels (see Supplement 1). The S photons pass through a cavity-based bandpass filter [25] with a bandwidth of $\sim 100\mathrm{MHz}$, and then they are coupled to a single-mode optical fiber. The photons are divided into two by a fiber-based half beamsplitter (HBS), and then they are detected by silicon avalanche photon detectors (APDs) denoted by ${\mathrm{D}}_{\mathrm{s}1}$ and ${\mathrm{D}}_{\mathrm{s}2}$.

 

Fig. 2. (a) Our experimental setup without and with the QFC, and the $\mathrm{\Lambda }$-type energy levels of the ${\mathrm{D}}_2$ line in ${}^{87}\mathrm{Rb}$ with the relation of the light pulses used in our experiment. The strong write pulse is removed from the optical path of the anti-Stokes photons by the spatial, the polarizing, and the frequency separation. The filtering of the write pulse from the Stokes photons is performed by the large difference of the spatial direction and the temporal separation. The separation of the read light from the signal photons is performed in the same manner. (b) Time sequence of the experiment. (c) The left figure shows the relevant energy levels of QFC. The difference frequency generation of a photon from 780 to 1522 nm is performed by using a strong pump light at 1600 nm. The right graph shows the overall conversion efficiency of the QFC from the front of the PPLN waveguide to the end of the FBG, and the noise counts induced by the frequency converter.

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Let us explain the optical circuit for the photons in mode AS. The H-polarized AS photons from the atomic ensemble are coupled to a polarization maintaining fiber (PMF). Without QFC, the PMF is connected to an optical circuit for the AS photons passing through a cavity-based bandpass filter with a bandwidth of $\sim 100\mathrm{MHz}$. After the filtering, the AS photons are divided into two by a HBS. Then they are detected by using APDs denoted by ${\mathrm{D}}_{\mathrm{asv}1}$ and ${\mathrm{D}}_{\mathrm{asv}2}$. With QFC, the PMF is connected to the optical circuit for the QFC. The QFC converts the wavelength of the AS photons from 780 to 1522 nm [20,26]. The conversion efficiency and the background-noise rate induced by the 1600 nm pump light for the conversion with respect to the pump power are shown in Fig. 2(c). The details of the QFC device are shown in Supplement 1.

After the QFC, the 1522 nm photons are coupled to a single-mode optical fiber. The 1522 nm photons pass through a fiber Bragg grating (FBG) with a bandwidth of $\sim 1\mathrm{GHz}$ followed by a HBS. Finally, the 1522 nm photons divided by the HBS are detected by SSPDs [27,28] denoted by ${\mathrm{D}}_{\mathrm{ast}1}$ and ${\mathrm{D}}_{\mathrm{ast}2}$.

The period of the write pulses is 1 μs, as shown in Fig. 2(b). The injection of the write pulses is repeated 990 times until the MOT is turned on again. In each sequence, we collect coincidence events between S and AS photon detections by using a time-to-digital converter (TDC). A start signal of the TDC is synchronized to the timing of triggering the write pulse. All electric signals from photon detections, i.e., ${\mathrm{D}}_{\mathrm{s}1}$, ${\mathrm{D}}_{\mathrm{s}2}$, ${\mathrm{D}}_{\mathrm{asv}1}$, ${\mathrm{D}}_{\mathrm{asv}2}$, ${\mathrm{D}}_{\mathrm{ast}1}$, and ${\mathrm{D}}_{\mathrm{ast}2}$, can be used as stop signals for the TDC. Typical histograms of the coincidence events in one sequence are shown in Figs. 3(a)–3(c). In the following experiments, we postselect the coincidence events within the 250 and 100 ns time windows for the signals of modes S and AS, respectively. In the histograms, while several unwanted peaks coming from the write, read, and clean pulses are observed in one sequence, they are temporally separated from the main signals and can be eliminated by the selection of the time windows.

 

Fig. 3. Observed stop signals by (a) ${\mathrm{D}}_{\mathrm{s}1}$, (b) ${\mathrm{D}}_{\mathrm{asv}1}$, and (c) ${\mathrm{D}}_{\mathrm{ast}1}$. In every figure, the interval of the clean signals is 1 μs.

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3. EXPERIMENTAL RESULTS

A. Cross Correlation Function Versus the Write Power

As a preliminary experiment, we measured the cross correlation function between the Stokes and the anti-Stokes photons with and without QFC for various powers of the write pulse. We denote the detection probabilities of the detectors ${\mathrm{D}}_{\mathrm{s}1(2)}$, ${\mathrm{D}}_{\mathrm{asv}1(2)}$, and ${\mathrm{D}}_{\mathrm{ast}1(2)}$ by $p_{\mathrm{s}1(2)}$, $p_{\mathrm{asv}1(2)}$, and $p_{\mathrm{ast}1(2)}$, respectively. We derive the cross correlation functions by the equations $g_{\mathrm{s},\mathrm{asv}}^{(2)}=p_{\mathrm{s},\mathrm{asv}}/(p_{\mathrm{s}}{p}_{\mathrm{asv}})$ without the QFC and $g_{\mathrm{s},\mathrm{ast}}^{(2)}=p_{\mathrm{s},\mathrm{ast}}/(p_{\mathrm{s}}{p}_{\mathrm{ast}})$ with the QFC, where $p_i$ is a probability of the photon detection by ${\mathrm{D}}_{i1}$ or ${\mathrm{D}}_{i2}$ for $i=\mathrm{s},\mathrm{asv},\mathrm{ast}$, and $p_{\mathrm{s},\mathrm{asv}}$ and $p_{\mathrm{s},\mathrm{ast}}$ are coincidence probabilities between (${\mathrm{D}}_{\mathrm{s}1}$ or ${\mathrm{D}}_{\mathrm{s}2}$) and (${\mathrm{D}}_{\mathrm{asv}1}$ or ${\mathrm{D}}_{\mathrm{asv}2}$), and (${\mathrm{D}}_{\mathrm{s}1}$ or ${\mathrm{D}}_{\mathrm{s}2}$) and (${\mathrm{D}}_{\mathrm{ast}1}$ or ${\mathrm{D}}_{\mathrm{ast}2}$), respectively. The experimental results are shown in Fig. 4. From Fig. 4(a), without the QFC, we see that the AS photons that are well correlated with the Stokes photons were prepared for a small power of the write pulse. Figure 4(b) shows the cross correlation function when the QFC was performed. We see that the correlation is still kept after the QFC of the AS photons, while its value declines. From the experimental results in Figs. 4(a) and 4(b), we set the power of the write pulse to $\sim 15\mathrm{\mu W}$ in the following experiments.

 

Fig. 4. Dependencies of the cross correlation functions on the power of the write pulse. (a) $g_{\mathrm{s},\mathrm{asv}}^{(2)}$ versus write power without the QFC and (b) $g_{\mathrm{s},\mathrm{ast}}^{(2)}$ versus write power with the QFC.

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B. Correlation Functions Without QFC

Without the QFC, we performed the measurement with an integration measurement time of about 120 h. The observed cross correlation function was $g_{\mathrm{s},\mathrm{asv}}^{(2)}=9.69\pm 0.04$. The autocorrelation function $g_{\mathrm{s},\mathrm{s}}^{(2)}$ of the photons in mode S without the heralding signal of the photon detection of mode AS was observed by the Hanbury Brown and Twiss setup [29] using ${\mathrm{D}}_{\mathrm{s}1}$ and ${\mathrm{D}}_{\mathrm{s}2}$. It is defined by $g_{\mathrm{s},\mathrm{s}}^{(2)}=p_{\mathrm{s}1,\mathrm{s}2}/(p_{\mathrm{s}1}{p}_{\mathrm{s}2})$, where $p_{\mathrm{s}j}$ is a probability of the photon detection by ${\mathrm{D}}_{\mathrm{s}j}$ for $j=\mathrm{1,2}$, and $p_{\mathrm{s}1,\mathrm{s}2}$ is a coincidence probability between ${\mathrm{D}}_{\mathrm{s}1}$ and ${\mathrm{D}}_{\mathrm{s}2}$. The observed value was $g_{\mathrm{s},\mathrm{s}}^{(2)}=1.58\pm 0.03$. Similarly, the autocorrelation function of the AS photons without the heralding signal of the photon detection of mode S measured by ${\mathrm{D}}_{\mathrm{asv}1}$ and ${\mathrm{D}}_{\mathrm{asv}2}$ was $g_{\mathrm{asv},\mathrm{asv}}^{(2)}=1.99\pm 0.03$. The autocorrelation function of the S photons heralded by the photon detection of mode AS is denoted by $g_{\mathrm{s},\mathrm{s}|\mathrm{asv}}^{(2)}=p_{\mathrm{s}1,\mathrm{s}2,\mathrm{asv}}{p}_{\mathrm{asv}}/(p_{\mathrm{s}1,\mathrm{asv}}{p}_{\mathrm{s}2,\mathrm{asv}})$, where $p_{\mathrm{s}j,\mathrm{asv}}$ is a two-fold coincidence probability between ${\mathrm{D}}_{\mathrm{s}j}$ and (${\mathrm{D}}_{\mathrm{asv}1}$ or ${\mathrm{D}}_{\mathrm{asv}2}$) for $j=\mathrm{1,2}$, and $p_{\mathrm{s}1,\mathrm{s}2,\mathrm{asv}}$ is a three-fold coincidence probability among ${\mathrm{D}}_{\mathrm{s}1}$, ${\mathrm{D}}_{\mathrm{s}2}$, and (${\mathrm{D}}_{\mathrm{asv}1}$ or ${\mathrm{D}}_{\mathrm{asv}2}$). The observed autocorrelation function was $g_{\mathrm{s},\mathrm{s}|\mathrm{asv}}^{(2)}=0.34\pm 0.05$, which clearly shows non-classical statistics. This value also indicates that the heralded signal is in the so-called single-photon regime of $g_{\mathrm{s},\mathrm{s}|\mathrm{asv}}^{(2)}<0.5$ mentioned in the literature [30]. In the case of AS photons heralded by S photons, the autocorrelation function of the heralded AS photons was $g_{\mathrm{asv},\mathrm{asv}|\mathrm{s}}^{(2)}=0.47\pm 0.06$.

C. Correlation Functions With QFC

With the QFC, we performed the experiment with an integration time of about 200 h. The observed cross correlation function between the S and the 1522 nm photons converted from the AS photons was $g_{\mathrm{s},\mathrm{ast}}^{(2)}=4.09\pm 0.01$. The autocorrelation function of the 1522 nm photons without the heralding signal of the S photons was measured by using ${\mathrm{D}}_{\mathrm{ast}1}$ and ${\mathrm{D}}_{\mathrm{ast}2}$, and the observed value was $g_{\mathrm{ast},\mathrm{ast}}^{(2)}=1.12\pm 0.01$. The autocorrelation function of the S photons heralded by the 1522 nm photons converted from the AS photons was $g_{\mathrm{s},\mathrm{s}|\mathrm{ast}}^{(2)}=0.71\pm 0.10$. While this is not in the single-photon regime, the value remains smaller than 1 after the QFC. Thus we conclude that the demonstrated HSE in Rb atoms clearly shows non-classical statistics with the detection of the 1522 nm photons. In addition, the autocorrelation function of the 1522 nm photons with the heralding signal by the S photons was observed to be $g_{\mathrm{ast},\mathrm{ast}|\mathrm{s}}^{(2)}=0.54\pm 0.09$. In Table 1, we list all the observed correlation functions. All of the observed correlation functions are degraded due to the noise photons from the strong pump light of QFC. Nonetheless, autocorrelation functions having less than 1 unambiguously show the non-classical statistics. We will discuss the origin of the degradation and possible approaches for improving the correlation functions in the next section.

Table 1. Observed Values of the Correlation Functions

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In order to connect distant matter qubits through a quantum measurement based on two photon detections as shown in Fig. 1, Hong–Ou–Mandel (HOM) interference, which is implemented by a HBS followed by two photon detectors [31], is a vital tool [8–13,32]. From the observed value of $g_{\mathrm{ast},\mathrm{ast}|\mathrm{s}}^{(2)}=0.54$, we can estimate the visibility of the HOM interference between two independently prepared telecom photons, each of which comes from the atomic ensemble demonstrated here. The visibility of the HOM interference is described by $V=1/(1+g_{\mathrm{ast},\mathrm{ast}|\mathrm{s}}^{(2)})$ with assumptions that mode matching of the signal photons is perfect and stray photons do not exist (see Supplement 1). The estimated value is $V=0.65$, which exceeds the classical limit of 0.5.

4. DISCUSSION

In the following, we discuss the degradation of the observed autocorrelation functions with QFC ($g_{\mathrm{s},\mathrm{s}|\mathrm{ast}}^{(2)}$ and $g_{\mathrm{ast},\mathrm{ast}|\mathrm{s}}^{(2)}$) with respect to those without QFC ($g_{\mathrm{s},\mathrm{s}|\mathrm{asv}}^{(2)}$ and $g_{\mathrm{asv},\mathrm{asv}|\mathrm{s}}^{(2)}$). Because the APDs and the SSPDs have very small dark counts, the observed cross correlation functions and the autocorrelation functions in Table 1 are considered as intrinsic values of the measured photons. Therefore the degradations from $g_{\mathrm{s},\mathrm{s}|\mathrm{asv}}^{(2)}$ to $g_{\mathrm{s},\mathrm{s}|\mathrm{ast}}^{(2)}$ and from $g_{\mathrm{asv},\mathrm{asv}|\mathrm{s}}^{(2)}$ to $g_{\mathrm{ast},\mathrm{ast}|\mathrm{s}}^{(2)}$ are mainly caused by the background noise of the QFC process of the AS photons. We assume that the background noise is induced by Raman scattering of the QFC pump light, which is statistically independent of the signal photons.

Using the definition of the cross correlation functions $g_{\mathrm{s},\mathrm{asv}}^{(2)}$ and $g_{\mathrm{s},\mathrm{ast}}^{(2)}$, and the ratio $\zeta$ of the average photon number of the signal in mode AS to the equivalent input noise to the converter, we obtain (see Supplement 1)

In addition, $g_{\mathrm{s},\mathrm{s}|\mathrm{ast}}^{(2)}$ is described by using the observed values as (see Supplement 1)

Below, based on the above estimations, we discuss a possible improvement of $g_{\mathrm{s},\mathrm{s}|\mathrm{ast}}^{(2)}$ and $g_{\mathrm{ast},\mathrm{ast}|\mathrm{s}}^{(2)}$ achieved by increasing the value of ${\zeta }^{\prime }=g_{\mathrm{s},\mathrm{asv}}^{(2)}\zeta$ corresponding to the ratio of the average photon number of the signal in mode AS to the noise induced by QFC conditioned on the photon detection in mode S. For this, we discuss three possible methods without changing the performance of the QFC as follows: (1) increase of the collection efficiency of the AS photons, (2) proper selection of the polarization of the AS photons, and (3) refinement of the experimental system for improvement of the correlation functions without QFC. (1) In our experiment, the collection efficiency of the AS photons without QFC is roughly estimated to be several percent (see Supplement 1). Here we borrow the collection efficiency of the AS photons from the current state-of-the-art experiments [23,34], where the value is about 10 times larger than that in our experiment, resulting in $\zeta \to 10\zeta$. This implies that the values of the autocorrelation correlation functions will be $g_{\mathrm{s},\mathrm{s}|\mathrm{ast}}^{(2)}=0.39$ and $g_{\mathrm{ast},\mathrm{ast}|\mathrm{s}}^{(2)}=0.49$. In this regime, the QFC preserves almost the same statistics as before the conversion shown in Table 1. (2) In our experiment, the magnetic sublevels of the ground states $g_{\mathrm{a}}$ and $g_{\mathrm{b}}$ are degenerated, which results in the loss of the AS photons by the polarization selection. Such signal loss is estimated to be about 0.2 under an assumption that the atoms are uniformly distributed in the magnetic sublevels as the initial state (see Supplement 1). So its improvement will contribute to increase $\zeta$ by a factor of 1.25, resulting in $g_{\mathrm{s},\mathrm{s}|\mathrm{ast}}^{(2)}=0.68$ and $g_{\mathrm{ast},\mathrm{ast}|\mathrm{s}}^{(2)}=0.60$ from $g_{\mathrm{s},\mathrm{s}|\mathrm{ast}}^{(2)}=0.74$ and $g_{\mathrm{ast},\mathrm{ast}|\mathrm{s}}^{(2)}=0.62$. (3) Refinement of the measurement for the S photons will increase ${\zeta }^{\prime }$ through the improvement of $g_{\mathrm{s},\mathrm{asv}}^{(2)}$ and other correlation functions without QFC, while $\zeta$ is kept. In addition, the use of a smaller excitation probability will also be effective for increasing $g_{\mathrm{s},\mathrm{asv}}^{(2)}$ as shown in Fig. 4(a). While it may require a long experiment, the higher collection probabilities of modes AS and S discussed in (1) may enable us to compensate the reduction of the excitation probability.

5. CONCLUSION

In conclusion, we have clearly shown the HSE in a cold Rb atomic ensemble by detection of the photons at the telecom wavelength, which has been observed by the direct measurement of the autocorrelation function. It was achieved by using the solid-state-based QFC and detectors with high efficiency and low noise properties. In addition, we have observed the non-classical photon statistics of the converted telecom photons. It indicates that the observation of non-classical interference between the two telecom photons prepared by duplicating the system demonstrated here will be possible. The quantum system composed of the matter systems and the telecom photons with the solid-state-based QFC and detectors will be useful for connecting various kinds of matter systems through mature telecom technology.

Note added: After submission of our paper, we found a related experiment [35].