Effects of pump laser power density on the hybrid optically pumped comagnetometer for rotation sensing

Liwei Jiang; Wei Quan; Wei Quan; Yixiang Liang; Jiali Liu; Lihong Duan; Jiancheng Fang; Jiancheng Fang

doi:10.1364/OE.27.027420

1. Introduction

The alkali metal-noble gas comagnetometers use optically pumped alkali metal vapor operated in the spin-exchange relaxation-free (SERF) regime [1,2] to polarize the noble gas atoms and detect their precession with high sensitivity. In this arrangement, slow changes in the ambient magnetic field can be automatically compensated by interactions between alkali metal and noble gas, leaving only a signal proportional to rotations and other anomalous fields [3]. Thus, the SERF comagnetometer can implement high-precision rotation sensing as gyroscope and is a promising rotation sensor for next generation inertial navigation applications in the future [4–7]. Furthermore, the SERF comagnetometer can also be used for fundamental physics experiments, including tests of Lorentz and CPT symmetries [8,9] and searches for spin-dependent forces [10,11].

A SERF comagnetometer based on K-³He used for rotation sensing was first demonstrated by Romalis group in 2005, achieving a rotation sensitivity of 5.0×10⁻⁷ rad s⁻¹ Hz^−1/2 and a bias drift of 0.04 deg/h [4]. Subsequently, the comagnetometers based on Cs-¹²⁹Xe and Rb-¹²⁹Xe pair were also investigated for rotation sensing [12,13]. In the earlier studies on the SERF comagnetometer, a single alkali metal species is used. A polarization gradient would be introduced due to the attenuation of pump laser along the pumping direction, especially when the density of the alkali metal is high and the pump laser power density is not large enough. In order to achieve more homogeneous polarization of alkali metal and higher pumping efficiency of the noble gas, the hybrid optical pumping technique is adopted [14, 15]. Two alkali metal species are utilized and the density of one species is much lower than the other. The alkali metal species with lower density is optically thin and can be homogeneously polarized via optical pumping, which then homogeneously polarizes the optically thick alkali metal species through spin-exchange interactions. Based on the hybrid optical pumping K-Rb-²¹Ne comagnetometer, a rotation sensitivity of 2.1 ×10⁻⁸ rad s⁻¹ Hz^−1/2 and a bias drift on the order of 10⁻² deg/h have been achieved by our group [16–18]. However, the present performance of the SERF comagnetometer is far low from the theoretical estimate [4,5,19], thus the exquisite optimization is required.

The polarization of alkali metal and noble gas have a significant impact on the performance of the comagnetometer and are mainly determined by the pump laser power density and spin relaxation rates. The effect of pump laser power density on the sensitivity of the single alkali metal species comagnetometer has been investigated based on the analytic solution of the Bloch equations for electron and nuclear spin ensembles [20, 21]. In terms of the hybrid optically pumped comagnetometer, a simple experimental result about the effect of pump laser power density on the output signal has been reported on by our group previously [16]. Therein, we innocently concluded that when the pumping rate is equal to the relaxation rate of probed atoms, the signal reaches the maximum according to model of the single alkali metal species comagnetometer as usual. The lack of the specific output model limits the research on the hybrid optically pumped comagnetometer. Furthermore, the above studies only focus on the effect of pump laser power density on the sensitivity of the comagnetometer, and other effects have not yet been considered.

In this paper, we study the dynamic equations of spin evolution with two alkali metal species and one nuclear species and obtain the analytic steady-state output model for the hybrid optically pumped comagnetometer for the first time. Based on this, the effects of pump laser power density on the rotation sensitivity, suppression of low-frequency magnetic noise and long-term stability of the comagnetometer are investigated. The theory and method presented here can not only shed light on the way to improve the performance of the SERF comagnetometer, but also have significance for other applications using the hybrid optical pumping technique [22,23].

2. Principle of the hybrid optically pumped comagnetometer

The coupled dynamics of the SERF comagnetometer can be described by a complete set of Bloch equations [3,24,25]. In the hybrid optically pumped comagnetometer, the optically thin alkali metal species (K, in our setup) called A is directly polarized by the pump laser, while the optically thick alkali metal species (Rb, in our setup) called B is polarized by spin-exchange with A and measured by the probe laser. The evolution of the electron spin polarization P^A and P^B, as well as nuclear spin polarization Pⁿ can be expressed as follows:

\frac{\partial P^{A}}{\partial t} = Ω \times P^{A} + \frac{γ_{e} (B + λ_{A} M^{n} P^{n} + L^{A}) \times P^{A}}{Q (P^{A})} + \frac{R_{p} s_{p} + R_{se}^{An} P^{n} + R_{se}^{AB} P^{B} - Γ^{A} P^{A} - R_{se}^{AB} P^{A}}{Q (P^{A})},

\frac{\partial P^{B}}{\partial t} = Ω \times P^{B} + \frac{γ_{e} (B + λ_{B} M^{n} P^{n} + L^{B}) \times P^{B}}{Q (P^{B})} + \frac{R_{m} s_{p r} + R_{se}^{Bn} P^{n} + R_{se}^{BA} P^{A} - Γ^{B} P^{B} - R_{se}^{BA} P^{B}}{Q (P^{B})},

\frac{\partial P^{n}}{\partial t} = Ω \times P^{n} + γ_{n} (B + λ_{A} M^{A} P^{A} + λ_{B} M^{B} P^{B}) \times P^{n} + R_{s e}^{n A} P^{A} + R_{se}^{n B} P^{B} - Γ^{n} P^{n} .

Here, Ω is the input rotation velocity vector. γ_e and γ_n are the gyromagnetic ratios of the electron and nuclear spins, respectively. Q is the electron slowing-down factor and is a function of the electron polarization [26]. B is the ambient magnetic field vector, while L^A and L^B are the fictitious magnetic fields of ac-Stark shifts. λ_A and λ_B are the geometrical factors containing the Fermi contact enhancement factor [27]. M^A, M^B and Mⁿ are the magnetizations of electron and nuclear spins corresponding to full spin polarization, respectively. R_p and R_m are the pumping rates of the pump and probe laser, while s_p and s_pr give the degree of circular polarization.

R_{se}^{A B}

is the spin-exchange rate from B to A, defined as

R_{se}^{A B} = n_{B} σ_{se} \bar{v}

, where n_B is the density of atom B, σ_se is the effective spin-exchange cross section between A and B, and v̄ is the relative thermal velocity.

R_{se}^{B A}

is the spin-exchange rate from A to B, defined as

R_{se}^{B A} = n_{A} σ_{se} \bar{v}

, where n_A is the density of atom A. Thus

R_{se}^{B A} = D_{r} R_{se}^{A B}

, where D_r is the density ratio of A to B. The same definition holds for

R_{se}^{An}

,

R_{se}^{nA}

,

R_{se}^{Bn}

and

R_{se}^{nB}

. Γ^A is the total spin relaxation rate for electron of A, defined as

Γ^{A} = R_{p} + R_{se}^{An} + R_{sd}^{A}

, where

R_{sd}^{A}

is the electron spin-destruction rate. Similarly,

Γ^{B} = R_{m} + R_{se}^{Bn} + R_{sd}^{B}

and

Γ^{n} = R_{se}^{nA} + R_{se}^{n B} + R_{sd}^{n}

.

A series of approximations are adopted to derive the steady-state solution, remaining the main features that determine high accuracy behavior of the coupled dynamics. The steady-state solution of the Bloch equations can be obtained by setting the left-hand side of Eqs. (1)–(3) to 0. As the electron spins and nuclear spins are polarized along the z axis, for small transverse excitation of the spins, the angles of polarization vectors P^A, P^B and Pⁿ with respect to the z axis are small enough, so that we approximately assume the longitudinal polarization components $P_{z}^{A}$ , $P_{z}^{B}$ and $P_{z}^{n}$ as constants [17, 20]. Since the spin-exchange rate $R_{se}^{A B}$ is usually on the order of 10⁵ s⁻¹, it is much larger than the other relaxation rate of atom B in the SERF regime, which is typically on the order of several hundred s⁻¹, and R_p dominates the total spin relaxation rate of atom A, the equilibrium polarization values for $P_{z}^{A}$ , $P_{z}^{B}$ and $P_{z}^{n}$ can be simplified to

P_{z}^{A} = P_{z}^{B} = \frac{D_{r} R_{p}}{Γ^{B} + D_{r} R_{p}},

P_{z}^{n} = \frac{R_{s e}^{n B}}{Γ^{n}} P_{z}^{B} .

An interesting result is obtained that though the density of atom B is much higher than that of atom A, the longitudinal polarization components $P_{z}^{A}$ and $P_{z}^{B}$ are approximately equal, as shown in Eq. (4). This is because that the rapid spin-exchange collisions between the A and B atoms transfer the A polarization to the B atoms with little loss. The A and B atoms are hybridized together as if they were one alkali metal species [28]. The property of the hybrid atoms leans on the spin relaxation rate of alkali metal B, Γ^B. Therefore, we establish the Bloch equation for the electron polarization of the hybrid alkali metal atoms based on the Bloch equation for atom B, Eq. (2), which is modified by the Bloch equation for atom A, Eq. (1). The Bloch equation for the “new atom” can be expressed by

\begin{array}{l} \frac{\partial P^{B}}{\partial t} & = (1 + D_{r}) Ω \times P^{B} + \frac{γ_{e} [(1 + D_{r}) B + λ M^{n} P^{n} + L] \times P^{B}}{Q (P^{B})} \\ + \frac{D_{r} R_{p} s_{p} + R_{m} s_{p r} + R_{se}^{en} P^{n} - Γ^{e} P^{B}}{Q (P^{B})}, \end{array}

where λ=λ_B + D_rλ_A, L = L^B+D_rL^A,

R_{se}^{en} = R_{se}^{Bn} + D_{r} R_{se}^{An}

, Γ^e = Γ^A + D_rΓ^B.

Equation (6) is the complete description of the evolution of the electron spin ensemble considering both B and A atoms, which is different from previous studies, only considering the optically thick alkali metal species in the hybrid optically pumped comagnetometer [18]. Compared to the Bloch equation for single alkali metal species, the effective rotation rate and magnetic field experienced by the probed atom B are increased by a factor of density ratio D_r. The geometrical factor, light shift and electron relaxation rate of the probed atom B are modified by that of the pumped atom A multiplied by D_r. Detailed modeling the evolution of the electron spin polarization considering both pumped atom and probed atom is of great significance for error allocation and parameter determination in the hybrid optically pumped system.

Combining Eq. (6) and Eq. (3), the steady-state solution of the Bloch equations can be acquired by complex-field transformation and elaborate simplification [17]. A bias field B_c = −B_n/(1 + D_r) − B_e referred as the compensation point is applied along the pumping direction to cancel the field from nuclear magnetization $B_{n} = λ M^{n} P_{z}^{n}$ and the field from electron magnetization $B_{e} = λ M^{B} P_{z}^{B}$ , unlike B_c = −B_n − B_e in the single alkali metal species comagnetometer [3, 4]. δB_z is the magnetic field with respect to the compensation point and approaches 0 when the residual magnetic field of the magnetic shields compensated by coils. The leading terms of the electron polarization along x axis, $P_{x}^{B}$ , are simplified to

\begin{array}{l} P_{x}^{B} & = \frac{- γ_{e} P_{z}^{B} (1 + D_{r}) (Γ^{B} + D_{r} R_{p})}{{(Γ^{B} + D_{r} R_{p})}^{2} + {γ_{e}}^{2} {[(1 + D_{r}) δ B_{z} + L_{z}]}^{2}} [\frac{Ω_{y}}{γ} + γ_{e} Ω_{x} \frac{(1 + D_{r}) δ B_{z} + L_{z}}{γ (Γ^{B} + D_{r} R_{p})} \\ + \frac{(1 + D_{r}) δ B_{z}}{B_{n}} B_{y} + γ_{e} (1 + D_{r}) δ B_{z} B_{x} \frac{(1 + D_{r}) δ B_{z} + L_{z}}{B_{n} (Γ^{B} + D_{r} R_{p})}], \end{array}

where γ = γ_eγ_n/(γ_e − Qγ_n).

The transverse electron polarization $P_{x}^{B}$ can be monitored by measuring the rotation of the polarization plane of a linearly polarized probe beam caused by the Faraday effect [29]. Then Ω_y can be extracted after the scale factor calibrated, which is the coefficient of Ω_y. A cross-talk effect from Ω_x can be introduced by the nonzero ac-Stark shift field L_z [18], and the response to the transverse magnetic field B_y and B_x can be suppressed by the field from nuclear magnetization B_n. According Eq. (4) and Eq. (7), the scale factor of Ω_y sensing approaches to the extremum when D_rR_p equals to Γ^B, therein the highest sensitivity can be achieved.

3. Experimental setup

The experiment is performed in our compact K-Rb-²¹Ne comagnetometer which is shown in Fig. 1. An 8-mm-diameter spherical cell made from GE180 aluminosilicate glass is used, which contains a mixture of K and Rb alkali metals in natural abundance, 2 atm of ²¹Ne (70% isotope enriched), and 33 Torr N₂ for quenching. The cell is placed in a boron nitride ceramic oven and heated to 190°C by twisted-pair wires using AC currents at 300 kHz to reduce the low-frequency magnetic noise. At the operating temperature, the density ratio D_r of K to Rb is approximately 1: 34, which is carefully calibrated by a method combining alkali metal absorption spectroscopy and Raoult’s law [30]. The oven is enclosed by two layers cylindrical high permeability μ-metal magnetic shields and an inner MnZn ferrite barrel for shielding the ambient magnetic field. The residual magnetic field is further compensated by a set magnetic coil system, consisting of two pairs of saddle coils along x and y axis respectively and a pair of Lee-Whiting coil along z axis.

Fig. 1 Schematic of our compact SERF comagnetometer using K-Rb hybrid optical pumping. BE, beam expander; P, linear polarizer; LCVR, liquid crystal variable retarder; GT, Glan-Taylor polarizer; PD, photodiode; M, reflection mirror; PBS, polarizing beamsplitter; LIC, laser intensity controller.

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The measurements are performed using a pump and probe configuration. A circularly polarized laser emitted from a distributed Bragg reflector (DBR) diode laser, propagating along the z axis is used for polarizing the K atoms, centered on K D1 resonance line. The Gaussian beam is expanded by a set of beam expander to 8-mm diameter to cover the whole cell, to improve the homogeneity of the atomic polarization. The optically thick Rb atoms are polarized by K atoms through rapid spin-exchange collisions. Then they hyperpolarize the ²¹Ne atoms. After several hours polarizing, the polarization of the atomic ensembles reaches the equilibrium. With the residual magnetic field compensated and the compensation point enforced, the high-sensitivity comagnetometer begins to work.

When sensing rotations or other anomalous fields, the polarization vectors of electron and nuclear spins will slightly precess away from the z axis and produce the transverse components. The transverse component of the electron spin polarization $P_{x}^{B}$ is measured by optical rotation of a linearly polarized probe laser propagating along the x axis, which is emitted from a distributed feedback (DFB) diode laser and tuned by 0.2 nm to the blue side of the Rb D1 resonance line. The probe beam is expanded to 3-mm diameter by the beam expander. The transmitted laser from the cell is analyzed by a polarizing beamsplitter cube set at 45° to the initial polarization direction by the half-wave plate. The output signal can be extracted from the difference between the two photodiodes (PD1 and PD2).

A homemade laser intensity controller sampling the signals of the photodiodes (PD3 and PD4) stabilizes the power of the pump laser and probe laser using the liquid crystal variable retarder (LCVR) as actuators [31]. The polarization axis of the linear polarizers before and after the LCVR are orthogonal to each other, and the fast axis of the LCVR is oriented at 45° to the polarization axis of the linear polarizer. The laser power entering the cell can be controlled by adjusting the modulation amplitude of the LCVR.

4. Results and discussion

The experimental comagnetometer is self-contained and can be calibrated on a rotating platform which can provide stable rotation input with an accuracy of 0.001 deg/s. The y axis of the comagnetometer is mounted vertically and aligned with the rotating axis of the platform. The calibration results of the scale factor of Ω_y sensing at different pump laser power density are depicted in Fig. 2, plotted against the left axis. The error bars of the experimental data are smaller than the data markers, and thus they are not plotted. The experimental data are fitted with coefficient of Ω_y in Eq. (7). The result shows that when the pump laser power density is 16.4 mW/cm², the scale factor approaches the maximum. The pumping rate R_p as a function of the pump laser power density P with the approximation of Lorentzian shape of the absorption curve is shown below [32]

R_{p} = \frac{P c r_{e} f}{h ν} \frac{Γ / 2}{{(ν - ν_{0} - Δ ν_{0})}^{2} + {(Γ / 2)}^{2}},

where c is the speed of light, and r_e is the classical electron radius. f is the oscillator strength, for alkali atoms, the oscillator strengths are approximately given by f_D1 ≈ 1/3 and f_D2 ≈ 2/3. h is the Planck constant. ν is the frequency of the pump laser and ν₀ is the natural resonant frequency of the pumped atoms. Γ and Δν₀ are the pressure broadening (full width at half maximum, FWHM) and shift of the optical absorption curve [33].

Fig. 2 Scale factor of Ω_y sensing and polarization of the alkali metal atoms as a function of the pump laser power density. The scale factor approaches the maximum at 16.4 mW/cm² by fitting with the coefficient of Ω_y in Eq. (7), while the polarization of the alkali metal atoms increases with the pump laser power density.

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Therefore, the pumping rate R_p of the K atoms corresponding to the maximum scale factor is 33889 s⁻¹. According to Eq. (7), the total spin relaxation rate for Rb electron Γ^Rb can be inferred by D_rR_p, which is 1000 s⁻¹. This is an improvement over our previous model considering only one alkali metal species, which predicts that the maximum response is when the total spin relaxation rate for Rb is equal to the pumping rate. The theoretical total spin relaxation rate for Rb electron Γ^Rb in the SERF regime can be simplified to the sum of the spin-exchange rate from the noble gas ²¹Ne and the spin-destruction rates from itself, K, ²¹Ne and N₂, as follows:

Γ^{Rb} = R_{se}^{RbNe} + R_{sd}^{Rb} + R_{sd}^{RbK} + R_{sd}^{RbNe} + R_{sd}^{{RbN}_{2}} .

According to the spin-exchange and spin-destruction parameters in [2, 19, 34], Γ^Rb can be calculated, which is 569 s⁻¹. The theoretical total spin relaxation rate Γ^Rb is smaller than the total spin relaxation rate obtained from the experiment. This is reasonable for the theoretical total spin relaxation rate Γ^Rb neglecting the spin-exchange relaxation rate of alkali metal atoms, which is often not completely eliminated in the comagnetometer with the large field from electron magnetization [35]. Based on the pumping rate and the spin relaxation rate, the polarization of the alkali metal atoms can be calculated by Eq. (4) and shown in Fig. 2. The polarization of the alkali metal electron increases with the pump laser power density.

The rotation sensitivity of the comagnetometer operated at different pump laser power density are compared and the typical five curves as well as the probe background noise are shown in Fig. 3. The output signal of the comagnetometer is acquired by a National Instrument 24-bit data acquisition system with the sampling rate of 200 Hz. The voltage signal is converted to the rotation rate by the scale factor shown in Fig. 2. Then the power spectral density is calculated and averaged for each 0.05-Hz bin. Above 0.2 Hz, the highest rotation sensitivity is achieved at the pump laser power density corresponding to the largest scale factor. Larger or smaller than this pump laser power density, the rotation sensitivity decreases. And the rotation sensitivity decreases faster with the decreasing of the pump laser power density than the increasing of it. A sensitivity of 3.8×10⁻⁷ rad s⁻¹ Hz^−1/2 @ 1 Hz is achieved at 18.5 mW/cm². The probe background noise equivalent sensitivity is much higher than the rotation sensitivity, which dose not limit the sensitivity. The pump laser intensities are monitored by PD3 at different pump laser power density and the noise spectrums are collected in Fig. 4. Below 2 Hz, the pump laser power noises are almost identical. The pump laser power noises also do not limit the sensitivity of the comagnetometer, expect for the jitters introduced by the electronic noise of the homemade laser intensity controller in the higher frequency domain. We believe that though the low noise MnZn ferrite shield is utilized, the rotation sensitivity of our comagnetometer is still limited by noises from the ambient magnetic fields as well as their gradients [18]. In the frequency domain below 0.2 Hz, the rotation sensitivity increases with the increasing of the pump laser power density, which is owing to the self-compensation effect of the nuclear spins. The electron spin polarization increases with the pump laser power density as shown in Fig. 2, and the nuclear spin polarization will increase accordingly referring to Eq. (5). The larger magnetization from the higher nuclear spin polarization can cancel transverse slowly changing ambient magnetic fields more efficiently, which is addressed by the magnetic field dependence terms in Eq. (7).

Fig. 3 Rotation sensitivity of the comagnetometer operated at different pump laser power density. The probe background noise obtained in the absence of the pump laser is also shown. Above 0.2 Hz, the highest rotation sensitivity is achieved at the pump laser power density corresponding to the largest scale factor. Below 0.2 Hz, the rotation sensitivity improves with the pump laser power density.

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Fig. 4 Spectral density of pump laser intensity monitored by PD3 at different pump laser power density. Below 2 Hz, the pump laser intensity noises are almost identical. The jitters in the higher frequency domain are mainly introduced by the electronic noise of the homemade laser intensity controller.

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To further validate the effect of the pump laser power density on the suppression of low-frequency magnetic noise, a series of oscillating fields with different frequencies and the same amplitude are applied to the comagnetometer along y and x axis respectively, and the suppression factors are obtained and shown in Fig. 5 and Fig. 6. The suppression factor is defined as the ratio of the scale factor of rotation sensing to the magnetic response amplitude of the comagnetometer [4,36], which can characterize the ability of the magnetic-noise suppression. In Fig. 5, below 0.2 Hz, the suppression factor increases with the increasing of the pump laser power density, indicating that the ability of the magnetic-noise suppression increases with the pump laser power density. The same result holds for the B_x suppression factor below 0.1 Hz in Fig. 6. The suppression ability gets worse for higher frequencies because the magnetic responses of the comagnetometer increase when close to the nuclear resonance [35]. Moreover, the results obtained here are consistent with the low-frequency rotation sensitivity in Fig. 3.

Fig. 5 Suppression factor of the comagnetometer to the low-frequency oscillating fields in the y direction at different pump laser power density. Below 0.2 Hz, the suppression ability increases with pump laser power density.

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Fig. 6 Suppression factor of the comagnetometer to the low-frequency oscillating fields in the x direction at different pump laser power density. Below about 0.1 Hz, the suppression ability increases with pump laser power density.

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The long-term stability of the comagnetometer is vital important in its applications, which is overwhelmingly limited by the low-frequency noises. In order to evaluate the effect of pump laser power density on the long-term stability, the Allan deviation analysis is implemented and shown in Fig. 7. When the comagnetometer kept stationary, the output signals of the comagnetometer are collected by the data acquisition system for 2 h at different pump laser power density. Then the Allan deviation plots are drawn. The flat line’s corresponding σ-value divided by a factor of 0.664 can represent the bias instability at the averaging time of about 10 s. The bias instability improves with the pump laser power density and a bias instability of 0.07 deg/h is achieved at 75.6 mW/cm².

Fig. 7 Allan deviation plots of the comagnetometer output. The bias instability improves with the pump laser power density.

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The larger pump laser power density can strengthen the ability of low-frequency magnetic-noise suppression, and then improve the long-term stability of the comagnetometer. However, with the increasing of the pump laser power density, this effect will become unobvious gradually, due to the saturation of the nuclear spin polarization. Further improvement may be obtained by optimizing the design of the shielding system and adopting new shielding materials such as NiZn ferrite to decrease the magnetic noise. Meanwhile, the real-time method to closed-loop control magnetic field of the comagnetometer is still needed to be investigated [35].

5. Conclusion

In conclusion, we have elaborated the dynamic equations of the hybrid optically pumped comagnetometer considering two alkali metal species and one noble gas species. Due to the rapid spin-exchange collisions, the two alkali metal species are hybridized together as if they were one alkali metal species and their Bloch equations can be merged into one. By solving the set of Bloch equations, the analytic steady-state output model for the hybrid optically pumped comagnetometer is presented for the first time. According to this model, the effects of pump laser power density on the rotation sensitivity, suppression of low-frequency magnetic noise and long-term stability of the comagnetometer are investigated experimentally. The results indicate that when the product of pumping rate and density ratio of pumped atom to probed atom equals to the spin relaxation rate of the probed atom, the maximum response and highest sensitivity of the comagnetometer are achieved. However, the suppression of low-frequency magnetic noise and long-term stability improve with the increasing of pump laser power density due to the increasing of nuclear spin polarization. The theory and method presented here will be significant for optimizing the performance of the comagnetometer and other high-precision metrology applications using the hybrid optical pumping technique.

Funding

National Key R&D Program of China (2016YFB0501600); National Natural Science Foundation of China (NSFC) (61773043, 61473268, 61503353); Academic Excellence Foundation of BUAA for PhD Students.

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Effects of pump laser power density on the hybrid optically pumped comagnetometer for rotation sensing

Abstract

1. Introduction

2. Principle of the hybrid optically pumped comagnetometer

3. Experimental setup

4. Results and discussion

5. Conclusion

Funding

References

Cited By

Figures (7)

Equations (9)

Optics Express