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In-situ determination of spin polarization in a single-beam fiber-coupled spin-exchange-relaxation-free atomic magnetometer with differential detection

Yintao Ma, Zhixia Qiao, Yao Chen, Guoxi Luo, Mingzhi Yu, Yanbin Wang, Dejiang Lu, Libo Zhao, Ping Yang, Qijing Lin, and Zhuangde Jiang

Open Access Open Access

Abstract

The electronic spin polarization of alkali-metal-vapor atoms is a pivotal parameter for atomic magnetometers. Herein, a novel method is presented for determining the spin polarization with a miniaturized single-beam spin-exchange-relaxation-free (SERF) magnetometer on the basis of zero-field cross-over resonance. Two separate laser beams are utilized to heat the cell and interrogate the vapor atoms, respectively. Spin polarization can be extracted by measuring the resonance response signal of the magnetometer to the transverse magnetic field under different irradiances. Results of these experiments are consistent well with the theoretical predictions with the maximum deviation less than 4%. The proposed method has the integrated advantages of possessing a simple configuration and in-situ measurement. Furthermore, combined with a homemade optical differential detection system with a factor of approximately three of the power noise suppression, the developed single-beam SERF atomic magnetometer with a measuring sensitivity of 32 fT/Hz1/2 has been achieved. This demonstrated approach can help guide the development of chip-scale atomic magnetometers for bio-magnetic field imaging applications.

© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

As a class of ultra-sensitive magnetic field sensors, alkali-metal-vapor atomic magnetometers hold a grand range of applications including testing of fundamental physics experiment [1], detection of weak remnant rock magnetization [2], NMR spectroscopy [3,4], conductive object detection and imaging [5,6], and especially bio-magnetic measurement [7–9]. Compared to superconducting quantum interference devices (SQUIDs), atomic magnetometers do not require cryogenic cooling equipment, and therefore have lower installation and maintenance cost as well as more flexible configuration, resulting in particularly suitable for wearable system combined with 3D printing technology [10]. The SERF atomic magnetometer, as an outstanding representative of atomic sensors, has demonstrated the highest magnetic field sensitivity by eliminating the spin-exchange relaxation effect between alkali-alkali [11,12]. Therefore, it has been a flourishing research subject. From the perspective of structural configuration, the SERF magnetometer can be roughly divided into two categories [13,14]: orthogonally propagating pump-probe beams and single-beam absorption-based arrangement. The former generally monitors the small optical rotation angle of polarized plane of a linearly polarized beam as a function of magnetic field; this methodology is called polarimetry measurement [15]. However, the latter uses the absorption of circularly polarized pumping beam to characterize the magnetic field, which is also known as absorption measurement [16]. Typically, the single-beam atomic magnetometer (SAM) has an inferior sensitivity than orthogonal pump-probe scheme due to the excess laser amplitude noise. Several noise suppression methods have been proposed, including light intensity stabilization [17] and gradiometer arrangement [18]. Even though the SAM exhibits the lower sensitivity, it is particularly attractive for bio-magnetic field imaging applications that are usually measured with noninvasive magnetoencephalography (MEG) and magnetocardiography (MCG). Most importantly, the SAM possesses a more simplified configuration, which makes it especially suitable to develop chip-scale atomic magnetometer [19,20].

In SAM, the precise measurement of electronic spin polarization is essential and valuable because the spin polarization directly affects the signal-to-noise ratio (SNR) and measuring sensitivity [21]. As a result, considerable efforts have made to accurately determine the electronic spin polarization in recent decades. Zhao et al. [22] innovatively monitored the potassium atoms spin polarization and distribution by using the transient response to step-changed magnetic field. Although this method can measure the spin polarization under SERF regime, the process was really complicated with a high cost due to the additional probing laser and photoelastic modulator (PEM) in the experiment. Li et al. [23] successfully measured the spin polarization of Cs atoms by analyzing the circularly polarized transmitted light, However, this method was unfavorable when the light was almost completely absorbed at high enough atomic density, which meant it could not well operate in SERF regime. Ding et al. [24] determined the spin polarization by utilizing a near-resonant pumping beam operated at 65 °C. At this temperature, the spin-exchange relaxation between alkali atoms was not fully suppressed, leading to the failure of the SERF regime. Although some methods for determining the spin polarization of alkali-metal-vapor atoms have emerged, reports about it are few in SAM despite that such magnetometer has great potential for practical applications.

In this paper, we propose a novel approach for determining the electronic spin polarization in a single-beam Cs-Ne SERF atomic magnetometer on the basis of the resonance response to the transverse magnetic field. Firstly, the dispersive response signals, which are the derivatives of Lorentzian function, are measured by using the optical absorption of incident pumping light as a function of magnetic field. Next, the relationship between the total spin relaxation rate and irradiance (i.e. light intensity) is fitted linearly. Finally, the spin polarization at different irradiances can be extracted directly. The method only utilizes the configuration of the SAM itself without additional optical components and it does not disturb the normal operation of SAM. Furthermore, a miniaturized SAM with a high measuring sensitivity of 32 fT/Hz1/2 has been achieved under optimized experimental conditions by means of the homemade differential detection system.

2. Theory

The SERF regime of atomic magnetometers can be accomplished when the spin-exchange rate between alkali atoms is much faster than Larmor precession. In this case, the ground state evolution of electron spin polarization P can be greatly simplified, which can be well expressed by the Bloch equation [25,26]:

$$\frac{{d\boldsymbol{P}}}{{dt}}\boldsymbol{ = }D{\nabla ^2}\boldsymbol{P} + \frac{1}{{Q(P)}}({\gamma ^e}\boldsymbol{P} \times \boldsymbol{B} + {R_{op}}(\boldsymbol{s} - \boldsymbol{P}) - {R_{rel}}\boldsymbol{P}),$$
where D is the diffusion constant, Q(P) is the nuclear slowing-down factor depending on the electron spin polarization, γe is the gyromagnetic ratio of the electron, B is the applied magnetic field, Rop is the optical pumping rate of circularly polarized light, s is the optical pumping vector along the direction of the pumping beam, and Rrel is the spin relaxation rate except for optical pumping effect.

To facilitate the theoretical analysis, we suppose that the pumping beam propagates along the z-axis. Generally, the atomic diffusion can be neglected in miniatured vapor cell with high pressure buffer gas. A modulation magnetic field Bx = Bx0 + Bmcos(ωt) perpendicular to the pumping beam direction is often applied in the x-axis to suppress the low-frequency noise in SAM, which results in the spin polarization Pz(ω) at the modulation frequency ω with the first harmonic component [18,27]

$${P_Z}(\omega ) = {P_0}\frac{{{B_{x0}}\Delta B\sin (\omega t)}}{{\Delta {B^2} + B_{x0}^2}}{J_0}(\frac{{{\gamma ^e}{B_m}}}{{Q(P)\omega }}){J_1}(\frac{{{\gamma ^e}{B_m}}}{{Q(P)\omega }}), $$
$$\Delta B = \frac{{{R_{op}} + {R_{rel}}}}{{{\gamma ^e}}} = \frac{{{R_{tot}}}}{{{\gamma ^e}}}, $$
where J0 and J1 are the Bessel functions of the first kind, P0 is the equilibrium electronic spin polarization in the z-axis, and Rtot is the total depolarization rate. For the purpose of determining the electronic spin polarization, the optimal modulation amplitude Bm and modulation frequency ω need to be determined by means of two-variate optimization procedure. Under a specific irradiance, Bm is continuously changed, and then the output response signal, which is proportional to the spin polarization component in the direction of pumping beam propagation, is recorded under the same transverse DC magnetic field. Theoretically, when a response signal reaches the largest value (i.e., the optimal scale factor, which is defined as the magnitude of the magnetometer output signal under a constant transverse DC magnetic field), the preliminary Bm is obtained. Then the process is repeated continuously to acquire the optimal Bm. However, the modulation frequency ω is typically more than three times the magnetometer bandwidth according to the sampling theorem; in experiments, we usually choose about an order of magnitude higher.

At each irradiance, the response of magnetometer to the transverse magnetic field is recorded by sweeping the transverse offset field crossing over zero, and the dispersive response curve is fitted for the determination the total spin relaxation rate Rtot(I), which is given theoretically at atomic resonance frequency by [28]

$${R_{tot}}(I) = {R_{rel}} + {R_{op}} = {R_{rel}} + \frac{{2{r_e}cfI\mathbf{s}}}{{h{\nu _0}\mathrm{\varGamma }A}}, $$
where re is the classical electron radius, c is the speed of light, f is the oscillator strength, I is the irradiance, h is the Planck constant, ν0 is the resonance frequency of alkali-metal-vapor atom, Γ is the pressure broadening with half width at half maximum, and A is the area of pumping light.

As a result, the relationship between total spin relaxation rate and irradiance can be fitted linearly, and the electronic spin polarization P(I) at arbitrary irradiance can be directly calculated by

$$P(I) = 1 - \frac{{{R_{rel}}}}{{{R_{tot}}(I)}}. $$

By setting ∂Pz/ ∂Rop = 0, it can be found that the maximum SAM signal can be obtained when Rop = Rrel, which indicates that the optimal electronic spin polarization P0 is 50%. Moreover, it is important to note that the fluctuation in pumping optical irradiance will cause the change of the scale factor δK/K=δI/I according to the variational method, where K is the scale factor, and it has been identified as the main source of noise in SAM [13]. Since the absorption of the pumping light is detected to measure magnetic field in SAM, there will also be a large background offset in detected signal. As a result, in the absence of a modulation magnetic field, the output of pumping light passing through the vapor cell can be expressed by

$$U = {U_0} + k{I_0}OD\Delta {P_z}{e^{({ - OD({1 - {P_z}} )} )}} + \delta N,$$
where U0 is the background offset, k is the scale factor, I0 is the incident irradiance, OD is the optical depth, ΔPz is change in polarization in the direction of pumping light propagation due to the external magnetic field and δN is the noise including the laser amplitude noise and common mode noise. The variation of spin polarization caused by the applied modulation field is
$$\Delta {P_z} = \frac{{{P_z}{\gamma ^e}{B_{x0}}}}{{{R_{tot}}}}.$$

Substituting Eq. (7) into Eq. (6), the output signal can be closely related to the magnetic field Bx0, and the output signal is proportional to the magnetic field

$$U = {U_0} + \frac{{k{P_z}{\gamma ^e}{B_{x0}}}}{{{R_{tot}}}}{I_0}OD{e^{({ - OD({1 - {P_z}} )} )}} + \delta N.$$

Therefore, an optical differential detection system is developed for cancelling the background offset U0, suppressing laser amplitude noise and other common mode noise δN, which will be described in detail in the experimental setup section. In addition, the non-orthogonality between the direction of the pumping laser propagation and the modulation magnetic field also need to be considered. The product of the non-orthogonal angle φ and the spin polarization Pz is equivalent to an external input magnetic field

$$\varphi {P_z} = {P_z}\frac{{{\gamma ^e}}}{{{R_{tot}}}}{B_{x0}}.$$

We can derive an equivalent input magnetic field of approximately 2 pT. Actually, the resolution of the magnetic compensation in the x-axis is 16 pT in our experimental. Accordingly, the equivalent input magnetic field due to non-orthogonal angle φ can be considered negligible.

3. Experimental setup

The schematic of experimental setup is shown in Fig. 1(a). A cylindrical vapor cell with an inner dimension of Φ 3 mm × 3 mm is fabricated by high borosilicate glass, which contains a droplet of Cs atoms, 50 torr N2 for quenching the excited Cs atoms to minimize radiation trapping and about 3 amagat Ne for slowing diffusion of Cs atoms to suppress the cell wall collision relaxation. The Cs atoms are chosen as the sensitive source due to its highest saturated vapor pressure among all the stable alkali metals, which results in the lower working temperature, easier temperature controlling and thermal insulation. The heating of the vapor cell is accomplished by optical absorption using a black filter made from Schott RG-9 glass attached to the vapor cell. A commercially available 1550 nm laser with a power of 1 W is utilized and coupled to the vapor cell through a 400 µm core diameter multi-mode fiber (MMF). In order to irradiate the sidewalls of the vapor cell uniformly, the heating laser is divergent. At the same time, the good thermal insulation of the vapor cell is guaranteed by surrounding it with PEEK material, which further improves temperature uniformity. The vapor cell is heated to 393 K, at which temperature the corresponding Cs atomic density is about 5 × 1013 cm-3. And the resulting temperature uniformity is better than ±10 mK. This optical heating method completely eliminates the effect of stray fields caused by common AC electric heating. Moreover, a nested cylindrical magnetic shield, which is comprised of five µ-metal shields and the innermost Mn-Zn ferrite shield [29,30], as shown in Fig. 1(b), is used to attenuate the Earth’s magnetic field below 10 nT. The homemade high precision tri-axial coils are composed of Helmholtz coil in the z-axis and cosine θ coils in the x-axis and y-axis [31]. And the coil constants are 81.1 nT/mA, 80.7 nT/mA and 200.7 nT/mA in the x, y and z axis, respectively. All coils are utilized to compensate residual magnetic field around the vapor cell to zero. Furthermore, the cosine θ coils are also used to apply the modulation magnetic field and calibration magnetic field.

 figure: Fig. 1.

Fig. 1. Experimental setup of single-beam Cs-Ne SERF atomic magnetometer. (a) Magnetometer schematic. MMF, multi-mode fiber; PMF, polarization maintaining fiber; P, fiber port; PCL, planoconvex lens; LP, linear polarizer; QWP, quarter wave plate; PD, photodiode; DD: differential detection system; TIA, transimpedance amplifier; LIA, lock-in amplifier. (b) Nested magnetic shields. (c) The picture of the experimental platform. (d) The photo of Cs miniatured cell with inner dimension of Φ3 mm × 3 mm, the yellow grains are the condensed Cs atoms. (e) Photograph of the as-prepared magnetometer sensor head with the overall size of 50 mm × 18 mm × 18 mm.

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For optical configuration, the light from distributed-feedback (DFB) laser on-resonance with the center of the Cs atoms D1 transition line is split into two beams, one as the pumping beam and the other as the reference beam. The pumping beam is coupled to the magnetometer head through a single-mode polarization maintaining fiber (PMF). Then the beam passes through a planoconvex lens (PCL), a linear polarizer (LP), and a zero-order quarter wave plate (QWP) in sequence to circularly polarize the pumping beam. Then the Cs vapor atoms can be optically polarized by the transfer of photon angular momentum from the circularly polarized pump light. The transmitted beam passing through the vapor cell is subtracted from the reference beam utilizing our homemade differential detection system (DD) and the total photocurrent can be attenuated to as low as 500 nA by carefully controlling the reference beam. Then the output differential signal is amplified and converted to voltage signal by a transimpedance amplifier (TIA). Eventually, the phase-sensitive detection is conducted with a lock-in amplifier (LIA) with reference to modulation frequency ω to extract the first harmonic component. The out-of-phase component of the LIA is stored by NI data acquisition system as the output signal of the SAM. The amplitude spectral density (ASD) of the magnetometer signal can be obtained by fast Fourier transform (FFT). Figure 1(b) and Fig. 1(c) shows the practicality picture of the experimental platform. The sensitive sensor head is shown in Fig. 1(e), and the overall size was approximately 50mm × 18 mm × 18 mm, which is fabricated by 3D printer utilizing PEEK material.

4. Experimental results and discussion

The resonance response of the magnetometer to modulation magnetic field under different pumping irradiances is shown in Fig. 2. The fit is based on Eq. (2), from which the magnetic resonance linewidth ΔB (i.e., the total spin relaxation rate Rtot) can be acquired directly. Moreover, it can be seen clearly that as the irradiance increases, the magnetic resonance linewidth gradually broadens. The relationship between total spin relaxation rate Rtot =γeΔB and irradiance is fitted linearly in Fig. 3. Overlaying the experimental data is a fit based on Eq. (4). The extrapolation of the spin relaxation rate to zero corresponds to a minimum relaxation rate Rrel = 1976 s-1 and is mainly caused by spin destruction collision relaxation, including Cs-Ne spin-destruction collisions, Cs-Cs spin-destruction collisions, wall collisions with the bare cell surface and other spin relaxation mechanism, which also demonstrates that the SAM works well in SERF regime. And the total relaxation rate Rtot(I) at arbitrary irradiance can also be determined from Fig. 3. Figure 4 presents the comparison of the electronic spin polarization between experimental results and theoretical predictions, which are in good agreement. As the irradiance increases, the spin polarization also enlarges progressively and tends to a stable value, which represents the state of almost all atoms pumped into the stretched state. Therefore, the electronic spin polarization at arbitrary irradiance can be extracted conveniently from the presented experimental results.

 figure: Fig. 2.

Fig. 2. Resonance response of magnetometer to transverse modulation magnetic field at different irradiances fitted by the dispersive resonance functions.

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 figure: Fig. 3.

Fig. 3. Relationship between total relaxation rate and irradiance.

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 figure: Fig. 4.

Fig. 4. Comparison of spin polarizations of the alkali-metal-vapor atoms as the function of the irradiance based on experimental results and theoretical predictions. The black triangles are the data obtained by the proposed method, the blue line is the fitting curve of experimental data based on y = a*x/(a*x + b) with R-square better than 99.5% (where a and b are free parameters), the red line is the theoretical predication, and the magenta line is the deviation between the experimental and the theoretical results with the maximum value about 4%.

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The deviation between theoretical values and experimental results is attributed to two principal reasons. The first one is that the spin-destruction collisional cross-section between Cs atoms and Ne buffer gas is not determined experimentally. Therefore, there will inevitably be some deviation between calculated relaxation rate and experimental results [32]. The other one is that the experimental fitting error, which is caused by the minor differences between ideal dispersive resonance signals and experimental data, further leading to small divergence from the linear relationship between total relaxation rate and irradiance. To solve these problems, the cross-section of Cs-Ne spin destruction collisions should be measured in the future, and accuracy should be further improved by minimizing various errors that affect the measurement process, such as ameliorating temperature control accuracy and weighting various error sources.

Before exploring the sensitivity, we first evaluate the performance of the differential detection system. The frequency of the pumping laser is tuned far away from the resonant frequency of the atoms by manually adjusting the injection current of the laser diode, that is, the laser does not interact with the atoms. The total output photocurrent can be managed to less than 500 nA by carefully controlling the reference beam, which means that the large background offset U0 in detected signal is greatly attenuated. Besides, the laser amplitude noise and common mode noise δN are also considerably suppressed. The differential detection effect is shown in Fig. 5, from which it can be seen clearly that 2-3 times of noise suppression result has been achieved.

 figure: Fig. 5.

Fig. 5. Noise spectrums density of laser power for differential detection scheme.

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Then the magnetic field sensitivity is measured and analyzed under different irradiances. The highest measuring sensitivity is obtained at the spin polarization approximately 50%. Then a modulation magnetic field with modulation frequency ω of 1 kHz and amplitude Bm of 180 nT is applied in the x-axis. We firstly test the -3 dB bandwidth of the SAM. A transverse magnetic field with an amplitude of 0.8 nT is applied, and the corresponding magnetometer output signal is recorded at different frequencies from 1 Hz to 230 Hz. Figure 6 presents the normalized frequency response curve. The experimental result can be well fitted by a first-order low-pass filter function [33–35]:

$$R(f) = \frac{K}{{\sqrt {f_s^2 + f_{3dB}^2} }},$$
where K is a constant, fs is the frequency of applied magnetic field, and f3dB is the -3 dB bandwidth. The fitting result shows that -3 dB bandwidth is 115 Hz.

 figure: Fig. 6.

Fig. 6. Normalized frequency response of the SERF magnetometer.

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Then we carry out experiments to obtain the magnetic field noise spectrum by means of two different calibration methods when the SAM is operated in the neighborhood of |Bx|=0. The specific calibration process of the first method is as follows: a small sinusoidal calibration magnetic field with an amplitude of 30 pTrms is applied. Then the first harmonic signal of the out-of-phase component is extracted with a LIA with the reference to 1 kHz. Each noise spectrum trace is yielded by averaging the spectrum in 1 Hz range for 20 s-long samples. The magnetic sensitivity of 32 fT/Hz1/2 can be determined by the amplitude of the calibration field and signal-to-noise ratio, as shown in Fig. 7 (a). The second calibration method is to directly convert the first harmonic signal into magnetic field information using the scale factor near zero field, which is presented in Fig. 7 (b). This method can detect unknown magnetic field. As a result, a sensitivity of 32 fT/Hz1/2 in miniaturized SAM has been achieved. As can be clearly seen from Fig. 7 (a), the estimated photon shot noise is approximately 3 fT/Hz1/2; and the total of electronic noise and photodiode dark current noise is about 1 fT/Hz1/2.

 figure: Fig. 7.

Fig. 7. Magnetic field sensitivity of the single-beam Cs-Ne SERF magnetometer under optimal polarization. (a) Noise spectral density at different calibration frequencies with an amplitude of calibration signal 30 pTrms, the black line is electronic noise and dark current noise, and the green line indicate the estimated photon shot noise; (b) Obtained magnetic field sensitivity by scale factor around zero magnetic field without calibration field.

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5. Conclusion

In summary, we have proposed a method for measuring the electronic spin polarization of optically pumped alkali-metal-vapor atoms utilizing only single-beam SERF atomic magnetometer. Spin polarization is estimated conveniently by measuring the magnetic resonance response to transverse magnetic field at different irradiances. The experimental results are in good agreement with the theoretical predictions. At an optimized irradiance corresponding to the spin polarization of approximately 50%, a sensitivity of 32 fT/Hz1/2 in miniaturized SAM has been demonstrated. Attributed to the merits of simplicity and in-suit measurement, the presented method is of great value for the development of chip-scale atomic devices based on the precise measurement of spin polarization, such as atomic magnetometers.

Funding

National Key Research and Development Program of China (2022YFB3203400); National Natural Science Foundation of China (U1909221,62103324); Science Research Foundation of Zhejiang Province (2019MB0AB02).

Disclosures

The authors have no conflicts to disclose.

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.

References

1. T. Wang, D. F. J. Kimball, A. O. Sushkov, D. Aybas, J. W. Blanchard, G. Centers, S. R. O. Kelley, A. Wickenbrock, J. Fang, and D. Budker, “Application of spin-exchange relaxation-free magnetometry to the Cosmic Axion Spin Precession Experiment,” Phys. Dark Universe 19, 27–35 (2018). [CrossRef]  

2. H. B. Dang, A. C. Maloof, and M. V. Romalis, “Ultrahigh sensitivity magnetic field and magnetization measurements with an atomic magnetometer,” Appl. Phys. Lett. 97(15), 151110 (2010). [CrossRef]  

3. S. Xu, V. V. Yashchuk, M. H. Donaldson, S. M. Rochester, D. Budker, and A. Pines, “Magnetic resonance imaging with an optical atomic magnetometer,” Proc. Natl. Acad. Sci. U. S. A. 103(34), 12668–12671 (2006). [CrossRef]  

4. I. M. Savukov and M. V. Romalis, “NMR detection with an atomic magnetometer,” Phys. Rev. Lett. 94(12), 123001 (2005). [CrossRef]  

5. L. Marmugi, C. Deans, and F. Renzoni, “Electromagnetic induction imaging with atomic magnetometers: Unlocking the low-conductivity regime,” Appl. Phys. Lett. 115(8), 083503 (2019). [CrossRef]  

6. B. Maddox, Y. Cohen, and F. Renzoni, “Through-skin pilot-hole detection and localization with a mechanically translatable atomic magnetometer,” Appl. Phys. Lett. 120(1), 014002 (2022). [CrossRef]  

7. C. Johnson, P. D. D. Schwindt, and M. Weisend, “Magnetoencephalography with a two-color pump-probe, fiber-coupled atomic magnetometer,” Appl. Phys. Lett. 97(24), 243703 (2010). [CrossRef]  

8. G. Zhang, S. Huang, and Q. Lin, “Magnetoencephalography using a compact multichannel atomic magnetometer with pump-probe configuration,” AIP Adv. 8(12), 125028 (2018). [CrossRef]  

9. J. Iivanainen, R. Zetter, M. Gron, K. Hakkarainen, and L. Parkkonen, “On-scalp MEG system utilizing an actively shielded array of optically-pumped magnetometers,” NeuroImage 194, 244–258 (2019). [CrossRef]  

10. E. Boto, N. Holmes, J. Leggett, G. Roberts, V. Shah, S. S. Meyer, L. D. Munoz, K. J. Mullinger, T. M. Tierney, S. Bestmann, G. R. Barnes, R. Bowtell, and M. J. Brookes, “Moving magnetoencephalography towards real-world applications with a wearable system,” Nature 555(7698), 657–661 (2018). [CrossRef]  

11. W. Happer and A. C. Tam, “Effect of rapid spin exchange on the magnetic-resonance spectrum of alkali vapors,” Phys. Rev. A 16(5), 1877–1891 (1977). [CrossRef]  

12. J. C. Allred, R. N. Lyman, T. W. Kornack, and M. V. Romalis, “High-sensitivity atomic magnetometer unaffected by spin-exchange relaxation,” Phys. Rev. Lett. 89(13), 130801 (2002). [CrossRef]  

13. V. Shah, S. Knappe, P. D. D. Schwindt, and J. Kitching, “Subpicotesla atomic magnetometry with a microfabricated vapour cell,” Nat. Photonics 1(11), 649–652 (2007). [CrossRef]  

14. R. Mhaskar, S. Knappe, and J. Kitching, “A low-power, high-sensitivity micromachined optical magnetometer,” Appl. Phys. Lett. 101(24), 241105 (2012). [CrossRef]  

15. W. C. Griffith, S. Knappe, and J. Kitching, “Femtotesla atomic magnetometry in a microfabricated vapor cell,” Opt. Express 18(26), 27167–27172 (2010). [CrossRef]  

16. T. H. Sander, J. Preusser, R. Mhaskar, J. Kitching, L. Trahms, and S. Knappe, “Magnetoencephalography with a chip-scale atomic magnetometer,” Biomed. Opt. Express 3(5), 981–990 (2012). [CrossRef]  

17. L. Duan, J. Fang, R. Li, L. Jiang, M. Ding, and W. Wang, “Light intensity stabilization based on the second harmonic of the photoelastic modulator detection in the atomic magnetometer,” Opt. Express 23(25), 32481–32489 (2015). [CrossRef]  

18. D. Sheng, A. R. Perry, S. P. Krzyzewski, S. Geller, J. Kitching, and S. Knappe, “A microfabricated optically-pumped magnetic gradiometer,” Appl. Phys. Lett. 110(3), 031106 (2017). [CrossRef]  

19. E. Boto, S. S. Meyer, V. Shah, O. Alem, S. Knappe, P. Kruger, T. M. Fromhold, M. Lim, P. M. Glover, P. G. Morris, R. Bowtell, G. R. Barnes, and M. J. Brookes, “A new generation of magnetoencephalography: Room temperature measurements using optically-pumped magnetometers,” NeuroImage 149, 404–414 (2017). [CrossRef]  

20. Y. Yang, M. Xu, A. Liang, Y. Yin, X. Ma, Y. Gao, and X. Ning, “A new wearable multichannel magnetocardiogram system with a SERF atomic magnetometer array,” Sci. Rep. 11(1), 5564 (2021). [CrossRef]  

21. M. V. Romalis, “Hybrid optical pumping of optically dense alkali-metal vapor without quenching gas,” Phys. Rev. Lett. 105(24), 243001 (2010). [CrossRef]  

22. J. Zhao, M. Ding, J. Lu, K. Yang, D. Ma, H. Yao, B. Han, and G. Liu, “Determination of Spin Polarization in Spin-Exchange Relaxation-Free Atomic Magnetometer Using Transient Response,” IEEE Trans. Instrum. Meas. 69(3), 845–852 (2020). [CrossRef]  

23. R. Li, W. Quan, and J. Fang, “Polarization Measurement of Cs Using the Pump Laser Beam,” IEEE Photonics J. 9(6), 1–7 (2017). [CrossRef]  

24. Z. Ding, X. Long, J. Yuan, Z. Fan, and H. Luo, “Sensitive determination of the spin polarization of optically pumped alkali-metal atoms using near-resonant light,” Sci. Rep. 6(1), 32605 (2016). [CrossRef]  

25. S. J. Seltzer and M. V. Romalis, “Unshielded three-axis vector operation of a spin-exchange-relaxation-free atomic magnetometer,” Appl. Phys. Lett. 85(20), 4804–4806 (2004). [CrossRef]  

26. M. P. Ledbetter, I. M. Savukov, V. M. Acosta, D. Budker, and M. V. Romalis, “Spin-exchange-relaxation-free magnetometry with Cs vapor,” Phys. Rev. A 77(3), 033408 (2008). [CrossRef]  

27. V. Shah and M. V. Romalis, “Spin-exchange relaxation-free magnetometry using elliptically polarized light,” Phys. Rev. A 80(1), 013416 (2009). [CrossRef]  

28. J.-C. Fang, T. Wang, H. Zhang, Y. Li, and H.-W. Cai, “In-situ measurement of magnetic field gradient in a magnetic shield by a spin-exchange relaxation-free magnetometer,” Chin. Phys. B 24(6), 060702 (2015). [CrossRef]  

29. T. W. Kornack, S. J. Smullin, S. K. Lee, and M. V. Romalis, “A low-noise ferrite magnetic shield,” Appl. Phys. Lett. 90(22), 223501 (2007). [CrossRef]  

30. S. P. Krzyzewski, A. R. Perry, V. Gerginov, and S. Knappe, “Characterization of noise sources in a microfabricated single-beam zero-field optically-pumped magnetometer,” J. Appl. Phys. 126(4), 044504 (2019). [CrossRef]  

31. Z. Ding, B. Han, and J. Tang, “Single-Beam Miniaturized Atomic Magnetometer With Square-Wave Modulation for Magnetoencephalography,” IEEE Trans. Instrum. Meas. 70, 1–6 (2021). [CrossRef]  

32. T. G. Walker, “Estimates of spin-exchange parameters for alkali-metal-noble-gas pairs,” Phys. Rev. A 40(9), 4959–4964 (1989). [CrossRef]  

33. A. Gusarov, D. Levron, A. B.-A. Baranga, E. Paperno, and R. Shuker, “An all-optical scalar and vector spin-exchange relaxation-free magnetometer employing on–off pump modulation,” J. Appl. Phys. 109(7), 07E507 (2011). [CrossRef]  

34. J. Tang, Y. Yin, Y. Zhai, B. Zhou, B. Han, H. Yang, and G. Liu, “Transient dynamics of atomic spin in the spin-exchange-relaxation-free regime,” Opt. Express 29(6), 8333–8343 (2021). [CrossRef]  

35. Y. Ma, K. Zhang, Y. Wang, K. Yang, Y. Zhai, and J. Lu, “Fast extraction of the electron spin-relaxation rate in the SERF magnetometer from a transient response,” Opt. Express 30(10), 17383–17391 (2022). [CrossRef]  

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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Figures (7)
Fig. 1.
Fig. 1. Experimental setup of single-beam Cs-Ne SERF atomic magnetometer. (a) Magnetometer schematic. MMF, multi-mode fiber; PMF, polarization maintaining fiber; P, fiber port; PCL, planoconvex lens; LP, linear polarizer; QWP, quarter wave plate; PD, photodiode; DD: differential detection system; TIA, transimpedance amplifier; LIA, lock-in amplifier. (b) Nested magnetic shields. (c) The picture of the experimental platform. (d) The photo of Cs miniatured cell with inner dimension of Φ3 mm × 3 mm, the yellow grains are the condensed Cs atoms. (e) Photograph of the as-prepared magnetometer sensor head with the overall size of 50 mm × 18 mm × 18 mm.

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Fig. 2.
Fig. 2. Resonance response of magnetometer to transverse modulation magnetic field at different irradiances fitted by the dispersive resonance functions.

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Fig. 3.
Fig. 3. Relationship between total relaxation rate and irradiance.

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Fig. 4.
Fig. 4. Comparison of spin polarizations of the alkali-metal-vapor atoms as the function of the irradiance based on experimental results and theoretical predictions. The black triangles are the data obtained by the proposed method, the blue line is the fitting curve of experimental data based on y = a*x/(a*x + b) with R-square better than 99.5% (where a and b are free parameters), the red line is the theoretical predication, and the magenta line is the deviation between the experimental and the theoretical results with the maximum value about 4%.

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Fig. 5.
Fig. 5. Noise spectrums density of laser power for differential detection scheme.

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Fig. 6.
Fig. 6. Normalized frequency response of the SERF magnetometer.

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Fig. 7.
Fig. 7. Magnetic field sensitivity of the single-beam Cs-Ne SERF magnetometer under optimal polarization. (a) Noise spectral density at different calibration frequencies with an amplitude of calibration signal 30 pTrms, the black line is electronic noise and dark current noise, and the green line indicate the estimated photon shot noise; (b) Obtained magnetic field sensitivity by scale factor around zero magnetic field without calibration field.

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Equations (10)

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d P d t = D ∇ 2 P + 1 Q ( P ) ( γ e P × B + R o p ( s − P ) − R r e l P ) ,
P Z ( ω ) = P 0 B x 0 Δ B sin ⁡ ( ω t ) Δ B 2 + B x 0 2 J 0 ( γ e B m Q ( P ) ω ) J 1 ( γ e B m Q ( P ) ω ) ,
Δ B = R o p + R r e l γ e = R t o t γ e ,
R t o t ( I ) = R r e l + R o p = R r e l + 2 r e c f I s h ν 0 Γ A ,
P ( I ) = 1 − R r e l R t o t ( I ) .
U = U 0 + k I 0 O D Δ P z e ( − O D ( 1 − P z ) ) + δ N ,
Δ P z = P z γ e B x 0 R t o t .
U = U 0 + k P z γ e B x 0 R t o t I 0 O D e ( − O D ( 1 − P z ) ) + δ N .
φ P z = P z γ e R t o t B x 0 .
R ( f ) = K f s 2 + f 3 d B 2 ,
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