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A measurement method of transverse light-shift in atomic spin co-magnetometer

We disclose a method to obtain the transverse light-shift along the probe light of a single-axis alkali metal-noble gas co-magnetometer. The relationship between transverse compensating field and light-shift is deduced through the steady-state solution of Bloch equations. The variety of probe light intensity is used to obtain the residual magnetic field, and step modulation tests are applied to acquire the total spin-relaxation rate of electron spins and self-compensation point. Finally, the transverse light-shift is reduced from -0.115 nT to -0.039 nT by optimizing the probe light wavelength, and the value of the calibration coefficient can be increased simultaneously.


Introduction
An alkali metal-noble gas co-magnetometer has found a wide range of applications in sensing rotation rate [1][2][3], testing Lorentz and CPT violation [4,5], and searching for anomalous spindependent forces [6,7]. In atomic spin co-magnetometers, the electron spins of alkali-metal are in SERF regime [8], so that the electron spins are ultra-high sensitive to magnetic field [9]. The nuclear spins of noble gas can be hyperpolarized by spin-exchange collisions with the polarized electron spins [10]. The polarized nuclear spins have ability of self-compensation to the external magnetic fields, and meanwhile the ultra-high sensitivity of rotation rate can be maintained [2]. However, the light-shift [11,12] arising from circularly polarized component of non-ideal linearly polarized probe beam can affect the direction and stability of electron spins [13,14]. Thus, the research on measurement and optimization of the transverse light-shift is essential for atomic spin comagnetometers.
Recently, the influence of light-shift caused by the circularly polarized pump light of atomic spin co-magnetometer has been widely studied [15][16][17]. The light-shift interaction appears as a fictitious magnetic field, so that the atomic spins process around the total effective magnetic field [18].
Therefore, the light-shift should be minimized as far as possible. Moreover, the principle of lightshift caused by the pump light of a K-Rb-21Ne co-magnetometer has been analyzed [19], and the light-shift of Rb atoms can be reduced by collision mixing [11]. Furthermore, the light-shift would lead to cross-talk effect for a dual-axis co-magnetometer, which limits the measurement accuracy of the two sensitive axes [2,20]. However, there are few studies on transverse light-shift caused by the probe light of co-magnetometer, which has usually been ignored in the steady-state solution of Bloch equations [21,22]. With the improvement of the accuracy, the existence of the transverse lightshift cannot be neglected.
In this letter, we propose a method to measure the transverse light-shift based on the steady-state solution of Bloch equations through the variety of probe light intensity and transverse compensation magnetic field. The relationship between transverse light-shift and wavelength of the probe light has been studied, and we propose an optimization method for reducing the light-shift. Finally, the transverse light-shift has been reduced from -0.115 nT to -0.039 nT and the light-shift related term has been effectively suppressed. Meanwhile, the calibration coefficient of co-magnetometer has been concurrently increased.

Theory of the measurement method
The behavior of the K-Rb-21 Ne co-magnetometer can be represented by a set of Bloch equations. The evolutions of electron spin polarization e P and nuclear spin polarization n P can be described as below [ is residual magnetic field along z-axis after the coil compensation.
where e r is classical electron radius and c is light velocity. 1   The schematic diagram of the K-Rb-21 Ne co-magnetometer is shown in Fig.2. The sensitive core is a 10mm-diameter spherical cell, which contains a drop of K and Rb alkali metals, 3 atm of 21 Ne and 40 Torr of N2 for quenching. The vapor cell is placed in an oven, which can heat the temperature of the cell to 180 ℃. Three layers of - metal magnetic shields surround the oven to provide a weak magnetic environment for atoms. A set of three-axis magnetic field coils is used to compensate residual fields in the shields.

Experimental setup and results
A circularly polarized pump light along z-axis tuned on the K D1 resonance line is used to polarize the K atoms, and the Rb atoms are polarized through the spin-exchange collision among K atoms. The polarized alkali-metal atoms ultimately hyperpolarize the 21 Ne atoms [23]. A potassium vacuum cell is used to present the absorption spectrum, and the wavelength of pump light can be stabilized to the order of megahertz by saturated absorption. Thus, the influence of pump light wavelength on light-shift can be ignored in our setup.
A non-ideal linearly polarized probe beam detuned to the red side of Rb D2 line, which is orthogonal to the pump beam, is utilized to detect the variety of the transverse polarization of Rb atoms along x-axis. The probe beam contains elliptical polarization component due to the limitation of polarization performance of the polarizer, which can cause transverse light-shift along the probe beam. The relationship between probe light intensity and compensating field yc B is shown in Fig.3.

Conclusion
In conclusion, a method for measuring the transverse light-shift has been examined in a compact K-Rb- 21

Acknowledgement
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