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Abstract
We demonstrate an atomic magnetometry using amplitude-modulated pumping and hyperfine repumping techniques in a paraffin-coated cell. By exploiting the constructive interference between spins polarized by the pump beam and an additional repump beam, we observe a three-fold increase in the amplitude of magnetic resonance, along with a reduction in linewidth by approximately two times. The implementation of the repump beam effectively narrows the linewidth, demonstrating successful suppression of spin-exchange relaxation. This reduction in relaxation rate, combined with the enhanced signal, significantly improves the sensitivity of the magnetometer. Consequently, our technique offers a promising approach for achieving SERF-like magnetometry with sub-fT-level sensitivity in Earth-field range and room-temperature environment.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Atomic magnetometers with high sensitivity [1–8] are utilized in various of fields, including physics [9–14], biology [15–20], chemistry [21,22], materials science [23–27] and geology [28]. The sensitivity of these magnetometers is constrained by spin-projection noise $\delta \,B\simeq (\gamma \sqrt {NT\tau })^{-1},$ [4], which is determined by several factors, namely the gyromagnetic ratio ($\gamma$), the measurement time ($T$), the number of atoms ($N$), and the spin relaxation time ($\tau$). To improve the sensitivity, it is advantageous to maximize the atomic density and prolong the spin relaxation time.
Spin relaxation can be attributed to various processes, including spin-destructive collisions, spin-exchange (SE) collisions, spin-wall collisions, magnetic field gradients, and power broadening of the optical field [29]. Among these processes, spin-destructive collisions occur at a rate several orders of magnitude lower than SE collisions, while the influence of magnetic field gradients can be compensated by using gradient coils. To mitigate spin relaxation during spin-wall collisions, the collision rate can be effectively reduced by introducing a buffer gas in which the alkali atoms undergo a diffusive motion that slows down their wall collision rate. By operating such a cell at high temperatures and low magnetic fields, the atomic ensemble works in the spin-exchange-relaxation-free (SERF) regime, resulting in the most sensitive atomic magnetometer nowadays [3,6–8]. However, the requirement of high operating temperatures and low magnetic fields limits its application in the fields of biology and geology.
Outside the SERF regime, nonlinear-magnetic-optical-rotation (NMOR) magnetometry using paraffin coated cell is a promising candidate to achieve a sensitivity comparable to that of the SERF magnetometry in the Earth field range. To prevent spin relaxation during wall collisions, paraffin coatings are used supporting approximately $10^4$ spin-wall collisions before relaxation of the atomic spins [30–32]. Anti-spin-relaxation coated cells typically do not contain any buffer gas which allows the atoms to explore the whole cell volume at their thermal velocity. To further improve the sensitivity, it is essential to develop technologies to suppress SE in paraffin coated cell.
In the presence of magnetic field, the atomic spins in the two hyperfine ground states undergo precession in opposite directions. SE collisions alter the population distribution between these two hyperfine ground states, leading to the relaxation of atomic spins. In this scenario, the suppression of SE relaxation can be achieved through a phenomenon known as light narrowing, which has been extensively studied in buffer-gas cells but has not been observed in the absence of buffer gas [29,33–41]. By increasing the power of the pump beam, a majority of atoms can be efficiently pumped into the stretched state ($m_{F}=F$). This results in the suppression of SE relaxation due to the conservation of total angular momentum during SE collisions. In buffer-gas cells, only one laser is required to pump atoms in both hyperfine sublevels, because of pressure broadening. However, the presence of buffer gas renders the magnetometer more susceptible to magnetic-field gradients, which induces spin relaxation [29]. Without the buffer gas, an additional repump beam is necessary to transfer the atomic population to the desired hyperfine sublevel, while the pump beam polarizes the atoms into the stretched state. Nevertheless, the introduction of the repump beam disturbs the atomic states, leading to a significant broadening of the linewidth as the repump power increases.
In this work, we experimentally demonstrate the suppression of SE processes in a paraffin-coated cell using a pulsed repump beam. The pump and repump beams are utilized to create a near-zero population in the $F=1$ state while effectively pumping most of the atoms into the $F=2$, $m_{F}=2$ state. By manipulating the relative phase between the pump and repump beams, we are able to increase or eliminate the amplitude of the magnetic resonance signal. The constructive interference of the atomic spins generated by pump and repump beams leads to a reduction in the relaxation of atomic spins, resulting in the light narrowing effect. This effect is characterized by an enhanced signal and a narrowed linewidth, which consequently leads to an improvement in the sensitivity of the magnetometer. In addition, the reduction in transverse relaxation facilitates the increase in quantum-information storage time within the atomic vapor [42].
2. Experimental setup
The experimental setup is illustrated in Fig. 1. A paraffin-coated cylindrical cell [30–32], with dimensions of 5 cm in length and 5 cm in diameter, containing isotopically enriched $^{87}$Rb atoms is placed within a four-layer $\mu$-metal magnetic shield and operated at a temperature of 42 $^\circ$ C.
Fig. 1. Experimental setup. HWP: half-wave plate. QWP: quarter-wave plate. POL: polarizer. BPD: balanced photo-detector. LIA: lock-in amplifier. FG: function generator.
The atoms are stretched along the $\hat {x}$-axis through optical pumping using two circularly polarized laser beams (pump and repump) directed along $\hat {x}$. The pump beam is resonant with the $^{87}$Rb D1 $F=2$ to $F^{'}=2$ transition, while the repump beam is resonant with the $^{87}$Rb D1 $F=1$ to $F^{'}=1$ or $2$ transitions. A dichroic atomic vapor laser lock (DAVLL) technique is employed to stabilize the laser frequencies of the pump and repump beams [43]. The intensities of the pump and repump beams are modulated using two acousto-optic modulators (AOMs) controlled by two channels of a function generator. The optimal duty cycle for the pump and repump beams is determined through parameter optimization. Theoretically, an infinitely large amplitude delta function would be ideal. In experiment, for a certain power of pump and repump beams, expanding the duty cycle increases both the linewidth and amplitude of magnetic resonance. Taking into account the power and relaxation rate, a value of $3{\% }$ causes the ratio of amplitude to linewidth to be maximize, so it is chosen as the optimal duty cycle. The modulation frequency of the pump and repump beams is set to match the Larmor frequency of the applied magnetic field (aligned along the $\hat {z}$-axis), allowing for strengthening of the atomic polarization with each pumping pulse in every cycle. A linearly polarized probe beam, with a power of 10 $\mu$W, is used to detect the Larmor precession. After passing through the cell, the polarization of the probe beam is altered due to the atomic polarization, which is subsequently detected by a balanced polarimeter as the optical rotation signal. This optical rotation signal is fed into a lock-in amplifier and demodulated at the modulation frequency.
3. Experimental results
3.1 Magnetic resonance
To illustrate the magnetic resonance with and without the repump beam, we keep the modulation frequency fixed at a specific value and scan the leading magnetic field. Figure 2 presents the magnetic resonance data for three different pumping and probing schemes. In all schemes, the pump power was set at 150 $\mu$W, and the optical field is resonant with the D1 $F=2$ to $F^{'}=2$ transition. The probe power is fixed at 10 $\mu$W. Two probe schemes are employed to detect the polarized atoms populated in the $F=2$ and $F=1$ states, as depicted in Fig. 2 (a) and (b), respectively. in Fig. 2 (a), the probe light is red-detuned by 1.5 GHz from the D2 $F=2$ to $F^{'}=2$ transitions, enabling the detection of the Larmor precession of atomic spins in the $F=2$ state. in Fig. 2 (b), the probe light is red-detuned by 500 MHz from the D2 $F=1$ to $F^{'}=1$ transitions, detecting spins in the $F=1$ state. The amplitudes of the magnetic resonances in Figs. 2 (a) and (b) are approximately the same. The difference in the center frequency of the two resonances is due to the variation in the gyromagnetic ratio between the $F=1$ and $F=2$ states. in Fig. 2 (c), an additional repump beam with the power of 150 $\mu$W and resonating with the D1 $F=1$ to $F^{'}=2$ transition is introduced. Nearly all the atoms contribute to this magnetic resonance signal. It is evident from this figure that the amplitude of the resonance in the presence of the repump beam is larger than that of the traditional scheme.
Fig. 2. Magnetic resonance data for a pump-modulation frequency of 4932 Hz as a function of the leading magnetic field along the $\hat {z}$-axis. In all scheme, pump beam is on resonance with D1 $F=2$ to $F^{'}=2$ transition. (b) The probe light is 500 MHz red detunned from D2 $F=1$ to $F^{'}=1$ transitions. (c) The probe light has same frequency with scheme (a), The repump beam is on resonance with D1 $F=1$ to $F^{'}=2$ transition.
3.2 Spin interference
We notice that the repump beam not only pumps atoms back to the $F=2$ state but also contributes to spin polarization on its own. The polarized spins generated by the pump beam with amplitude $S_1$ and the repump beam with amplitude $S_2$ both oscillate at the Larmor frequency and can interfere with each other. The total spin $S$ can be described by the following equation:
where $\phi$ represents the relative phase between $S_1$ and $S_2$. Figure 3 illustrates the variation in the amplitude of the magnetic resonance as a function of the phase $\phi$, with a repump power of 150 $\mu$W (a) and 100 $\mu$W (b,c) respectively. When a repump beam power of 150 $\mu$W is applied, the repump beam generates more spins than the pump beam. In this case, the visibility of the magnetic resonance is approximately 0.6. On the other hand, when a repump beam power of 100 $\mu$W is applied, the magnetic resonance is completely eliminated, indicating that the spins generated by the pump and repump beams have the same amplitude. In Figs. 3 (a,b), the polarization of the repump beam is the same as that of the pump beam. The signal is maximized when the relative phase is zero. in Fig. 3 (c), where the polarization of the repump beam is $\sigma _{-}$, the signal is completely suppressed when the relative phase is zero.Fig. 3. The amplitude of magnetic resonance change with relative phase between pump and repump. The polarization of pump beam is $\sigma _+$. The pump power is 150 $\mu$W. (a) The polarization of repump beam is $\sigma _+$. The repump power is 150 $\mu$W. (b) The polarization of repump beam is $\sigma _+$. The repump power is 100 $\mu$W. (c) The polarization of repump beam is $\sigma _{-}$. The repump power is 100 $\mu$W.
Figure 4 depicts the measured Faraday rotation signal, which is proportional to the population of the ground state, as it changes with the optical detuning $\Delta$ of the probe beam at constructive interference. In the presence of the pump beam, a dispersion signal emerges when the optical field is resonant with the F=2 to excited states transition. Conversely, an absorption signal arises when the optical field is resonant with the F=1 to excited states transition. With the repump beam, the signal associated with the F=2 to excited states transition is enhanced, while the signal related to the F=1 to excited states transition is eliminated. This observation serves as evidence that the atoms originally populated in the F=1 state are all pumped to the F=2 state, satisfying the necessary condition for the suppression of spin-exchange processes.
Fig. 4. The optical rotation signal with (a) and without (b) repump beam. The Fano profile shown in (b) is caused by imbalance population of $F=1, m_{F}=1$ and $F=1, m_{F}=-1$ states. The absorption spectrum of the D2 line of $^{87}$Rb (c).
3.3 Spin relaxation time
In order to demonstrate the suppression of spin-exchange (SE) processes, it is important to maintain SE collisions as the dominant mechanism for spin relaxation. By employing a paraffin-coated cell, the magnetic sensor becomes insensitive to magnetic field gradients, and relaxation resulting from spin-wall collisions is significantly suppressed.
To further avoid power broadening effects resulting from the pump beam, we analyze the spin relaxation rate through the measurement of the FID signal. The transverse coherence in F=2 state is generated by applying a sequence of short pump pulses in the $\hat {x}$ direction, while the leading field is present. The repetition frequency of the pump beam is set to match the Larmor frequency of the leading field, maximizing the transverse coherence. After the pump beam is turned off, the optical rotation signal, demodulated by a lock-in amplifier, is observed as shown in Fig. 5 (i). In comparison to conventional FID detection, Fig. 5 (ii) demonstrates the application of an additional repump beam during the pumping period. With the presence of both the pump and repump beams, atoms initially located in the F=1 and F=2 states are now fully polarized to the F=2, $m_{F}=2$ state. This leads to an increase in the signal amplitude and the suppression of spin-exchange (SE) processes between the F=2 and F=1 hyperfine manifolds.
Fig. 5. Relaxation of atomic spins change with different repumping scheme. (i,ii) FID without and with per-repumping. (iii,iv) The polarized spins decay with in phase and out of phase repumping. Inset: the normalized relaxation signal.
However, despite the utilization of the sequence shown in Fig. 5 (ii), several decay effects can still cause a gradual transfer of some atoms back to the F=1 state during the probing period. Consequently, the decay induced by SE collisions becomes active once again. in Fig. 5 (iii), a synchronized repump beam is applied during both the pumping and detection periods to further eliminate the decoherence effect during the probing period. Atoms that have decayed to the F=1 state during the probing period can be repopulated back to the F=2 state by the repump beam. The repump beams correct the phase of atomic spins at every cycle. As a result, the relaxation time is further improved. The relative phase between the pump and repump beams plays a crucial role in suppressing SE processes. When the relative phase is non-zero, the medium polarization is washed out, resulting in a shorter relaxation time, as depicted in Fig. 5 (iv).
The variation of the experimental measured and theoretical simulated spin relaxation rate with repump power is demonstrated in Fig. 6 using in-phase repumping. The relaxation rate is measured by exponential Fitting of the FID signal. Here, the relaxation primarily occurs due to SE processes and power broadening. As the repump power increases, the population of the $F=1$ state decreases, leading to a suppression of SE relaxation, while the power broadening effect becomes more prominent. By balancing the influence of these two effects, the minimum relaxation rate is achieved at 2.2 Hz for a repump power of 3 mW.
Fig. 6. Experimental measured and theoretical simulated relaxation rate of atomic spin change with the repump power while the pump power is fixed at 150 $\mu$W.
In theoretical simulation, the relaxation rate is determined by adding the SE rate and optical power broadening. The SE rate is modeled as $\,n\rho _{11}\,\sigma _{SE}\sqrt {8k_{B}T/(\pi \,M)}$, where $n=6\times \,10^{16}$ m$^{-3}$ is the atomic density of $^{87}$Rb at 42 $^\circ$ C, $\rho _{11}$ is the population in the $F=1$ state which is calculated by Liouville equations, $\sigma _{SE}=1.8\times \,10^{-19}$ m$^{2}$ is the SE rate, $k_{B}$ is the Boltzmann constant, and $M=7.2\times \,10^{-26}$ kg is the reduced mass of the $^{87}$Rb-$^{87}$Rb collision [44–46]. The power broadening is modeled as linearly increasing with the power of the repump beam. To determine the population of atomic spin in the presence of the pump and repump beams, we solve the Liouville equation for the rotating-frame density matrix [47]
Fig. 7. The protocols of optical pumping without and with repump beam (a,b). The populations of $|F=1, m_{F}=-1\rangle$ state, $|F=1, m_{F}=1\rangle$ state, $|F=2, m_{F}=-2\rangle$ state, and $|F=2, m_{F}=2\rangle$ state during the optical pumping process without (c) and with repump beam (d).
4. Conclusion
In conclusion, we have demonstrated the suppression of spin-exchange (SE) relaxation in a paraffin-coated cell operating at 42 $^\circ$ C. By introducing an additional repump beam at spin constructive interference, we observe an increase in the amplitude of the magnetic resonance signal. In the case of FID, clear light narrowing is found, indicating the effective suppression of SE in the presence of a strong magnetic field. This suppression of SE relaxation results in a three-fold enhancement of the magnetic resonance signal and approximately two-fold reduction in the relaxation rate, leading to a significant improvement in sensitivity. This work has demonstrated the potential for achieving SERF-like magnetometry in a paraffin-coated cell with sub-fT/$\sqrt {\text {Hz}}$-level sensitivity in the Earth-field range. It should be noted that in theory, the amplitude of magnetic resonance with repump beam is anticipated to increase fourfold. However, the measured signal only exhibits a threefold increase. Further enhancement and suppression of the amplitude and linewidth can be achieved through improving the polarization of the spin state. Further studies are also needed to investigate light narrowing in paraffin-coated cells with high atomic density. This method has potential to be applied in the magnetic field measurement of biological samples that require a room-temperature environment, as well as geological applications in Earth field range. Our work opens up new possibilities for applications of SERF atomic system in quantum metrology achieving high sensitivity and quantum information with long coherence time.
Funding
Innovation Program for Quantum Science and Technology (2021ZD0303200); National Natural Science Foundation of China (12234014, 11654005, 12274132, 12204304, 91536114, 11874152); Fundamental Research Funds for the Central Universities; the Shanghai Municipal Science and Technology Major Project (2019SHZDZX01); Innovation Program of the Shanghai Municipal Education Commission (202101070008E00099); National Key Research and Development Program of China (2016YFA0302001); Fellowship of China Postdoctoral Science Foundation (2020TQ0193, 2021M702146).
Acknowledgments
W. Z. also acknowledges additional support from the Shanghai talent program.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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