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Abstract
An all-optical self-oscillating 4He atomic magnetometer with a large dynamic range of the magnetic field is demonstrated. This device has the advantage of the fast response of the self-oscillating magnetometer and is not affected by the systematic errors originated from the radio-frequency field. It is also free from the nonlinear Zeeman effect in large magnetic fields. We use a liquid crystal to adjust the phase shift, which is independent of frequency. Results show that our self-oscillating 4He magnetometer exhibits a response time of 0.2 ms for a step signal of 3600 nT, and the noise floor reaches 1.7 pT / Hz1/2 for frequencies from 2 Hz to 500 Hz. It can work stably in magnetic fields ranging from 2500 nT to 103000 nT. Compared with the commercial self-oscillating cesium atomic magnetometer (Scintrex, CS-3), the self-oscillating 4He atomic magnetometer has shown a better gradient tolerance in larger magnetic field. This magnetometer is ideally suited in magnetic observatories to monitor geomagnetic field requiring large dynamic range and high bandwidth.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In recent years, the optically pumped atomic magnetometers (OPAMs) with high sensitivity and accuracy have attracted increasing attention [1–5] and are widely used in geomagnetic exploration [6], planetary magnetic-field measurement [7], earthquake prediction [8], bio-magnetic field detection [9–12], and tests of fundamental physics [13–16]. Different applications have different requirements for the OPAMs. For geomagnetic exploration, fast response time, large dynamic range and robustness are especially important [2,17,18].
The OPAMs are based on detecting the Larmor frequency of the macroscopic magnetic moment of the atomic ensemble (the ground state alkali metals or metastable helium) under the influence of the external magnetic field. According to the different frequency tracking methods, the OPAMs can be generally divided into two types: servo-OPAM and self-oscillating OPAM. Self-oscillating atomic magnetometers (SOAMs) generate magnetic resonance by the self oscillation of the atomic ensemble. The closed-loop gain should be unity and the phase shift in the whole loop should be $2n\pi$ ($n$ is an integer). Compared to other OPAMs, the SOAMs generally have a simpler structure and faster response to the variation of magnetic field [19,20]. Self-oscillating $^{87}$Rb atomic magnetometers with both single-cell and double-cell structure originally proposed by Bloom, have been used in space exploration missions [20]. A self-oscillating $^{4}$He atomic magnetometer (HAM) with lamp as the light source has been constructed and has demonstrated excellent performances for measuring geomagnetic field ranging from $25000$ nT to $75000$ nT [21]. From then on, the self-oscillating alkali-metal atomic magnetometers have been well developed and commercialized [22–25].
Most of the earlier SOAMs are based on magneto-optical double resonance driven by radio-frequency (RF) fields generated with RF coils. However, RF coils cause systematic errors due to their imperfect alignments relative to the direction of the optical axis [20]. In addition, the cross-talk between coils of different magnetometers degrades the performance in multi-sensor scenarios such as bio-magnetic detection [26]. Alternatively, precessing macroscopic spin polarization is achieved with amplitude-, frequency-, or polarization-modulated pumping laser [27,28]. The phase shifters, amplifiers and digital or analog filters utilized in these magnetometers cause frequency-dependent phase shift [29]. It is difficult to shift the phase accurately in a large frequency range [30]. In addition, the electronic phase shift needs to be carefully and fast calibrated to avoid the parametric shifts of the magnetic resonance and the errors exist in determination of the resonance line center [31]. An all-optical self-oscillating rubidium atomic magnetometer based on optical phase shift has been demonstrated [32]. The phase shift is adjusted by manually changing the relative polarization direction between the probe light and the pump light. The advantage is that the optical phase has no frequency dependence, which guarantees a stable phase condition for self-oscillation within a wide dynamic range of magnetic field. However, few works have been done about all-optical self-oscillating HAM. Compared with alkali-metal atoms, $^{4}$He is free from the nonlinear Zeeman effect in large magnetic fields [25]. The sensitivity of the HAM is immune to temperature variations because the density of $^{4}$He atoms is nearly independent of temperature. Because of these advantages, the HAM investigated in the early stage [33–41] were widely used in applications of geomagnetic exploration and detecting the magnetic field of other planets [42]. Here we introduce and demonstrate an all-optical self-oscillating HAM. A liquid crystal rotator is used to compensate the phase shift to satisfy the self-oscillating condition. Results show clearly that the method of optical phase shift can effectively improve the sensitivity and extend the dynamic range of the self-oscillating $^{4}$He atomic magnetometer.
2. Experimental setup and the principle
The experimental setup of the all-optical self-oscillating HAM is shown in Fig. 1. The light emitted from a fiber laser with a wavelength of $1083$ nm, is split into the pump ($70\%$) and probe ($30\%$) beams with a polarization-maintaining optical fiber splitter. The intensity of the pump light is modulated with an acousto-optic modulator (AOM). In order to increase the number of atoms interacting with the laser and improve the signal-to-noise ratio, a beam expander (BE) is added to expand the waist diameter to $10$ mm ($1/e^{2}$). A half-wave plate (HWP) and a polarized beam splitter (PBS) are used to adjust the pump-light intensity. The linearly-polarized resonant pump light is reflected and enters a $45$ mm long $^{4}$He atomic cell with the diameter of $35$ mm, with the pressure of $0.7$ Torr, and discharged by a $33$ MHz power source to populate the metastable state. The cell is placed in the center of a three-dimensional coils which can provide a magnetic field in an arbitrary direction. To decrease the fluctuation from external magnetic field, both the cell and the coils are located in a $7$-layer magnetic shield with a shielding factor of $10^{5}$. In the probe light path, a HWP and a PBS are used to split a fraction of the laser beam for frequency stabilization to the $D_0$ line of the $^{4}$He ($2^3$S$_1-2^3$P$_0$) using the polarization spectroscopy method [43]. The propagating direction of the probe light is perpendicular to that of the pump light. A bias magnetic field, of which the direction is along the propagating direction of the probe beam, is generated in a three-dimensional coils inside the magnetic shield. For our self-oscillating HAM, the macroscopic magnetic moment is built up by aligning the metastable $^{4}$He atoms with the intensity modulated linearly-polarized pump light, whose direction is parallel to the linear polarization direction of the pump light. The macroscopic magnetic moment precesses around the bias magnetic field and the maximum absorption of probe light occurs twice in a period. The magnetic resonance occurs when the modulation frequency is equal to twice the Larmor frequency, i.e., $\omega _{m} = 2\omega _{L}=2 \gamma B$, where $\omega _m$ is magnetic resonance frequency, $\omega _L$ is the Larmor frequency, $\gamma$ is the gyromagnetic ratio of the metastable $^{4}$He and $B$ is the external magnetic field.
Fig. 1. Schematics of the self-oscillating $^{4}$He atomic magnetometer (HAM). There are two separate beams, one is the linearly-polarized pump light, and the other one is the linearly-polarized probe light. Both of the two laser beams transmit through a polarization maintaining fiber. The intensity of the pump light is modulated with an acoustic-optical modulator (AOM), from which the zero-order output laser beam is used in the experiment. A beam expander (BE) is used to increase the spot size of the pump light. A polarizer (P) is used to increase the extinction ratio. A half wave plate (HWP) and a polarization beam splitter (PBS) are used to adjust the pump light intensity. The probe light passes through a coupler, a polarizer (P) and a liquid crystal rotator, and then is detected with a photodiode (PD). The structure of the liquid crystal rotator is shown in the figure, which can rotate the polarization direction of linearly polarized light [38], QWP is a quarter wave plate. A zero-crossing circuit, which is integrated to an amplifier (AMP), is used to change the sinusoidal signal to a square signal. In the feedback loop, the switch between the driver (D) and the AMP output is on, while the one between the generator (G) and the driver is off. The magnetic shield is used to decrease the fluctuation from external magnetic field. The coils are used to generate a bias magnetic field inside the magnetic shield, which is measured with the self-oscillating HAM.
According to Bloch equations, a $\pi /2$ phase shift is needed for the feedback signal [20]. In our system, the phase shift $\phi$ in the feedback loop can be expressed as
where $\phi _0$ is $\pi /2$ when the pump-light polarization is parallel to the probe-light polarization, and $\phi _1(\Delta \omega )$ is phase shift related to the pump modulation, $\phi _1(\Delta \omega ) =~$tan$^{-1}(\Delta \omega /\Gamma )$ is the phase shift caused by the frequency detuning, where $\Delta \omega = \omega _m - 2\omega _L$ and $\Gamma$ is the atomic relaxation rate, $\phi _2(\omega _m)$ is the phase shift caused by the devices, such as the amplifier, the filter or the optical modulation devise in our experiment, and is sensitive to modulation frequency. $\phi _3(\theta )$ depends on the angle $\theta$ between the pump-light polarization and the probe-light polarization. The optical-rotation signal undergoes two cycles as the atomic alignment rotates by $360 ^{\circ }$, so the phase shift $\phi _3(\theta ) = 2\theta$ [32,44]. Such a special relationship between optical phase shift and probe angle holds only for the condition where the propagation direction of the linearly-polarized laser is parallel to the direction of the bias magnetic field. Thus, to keep the phase shift $\phi$ zero, one should have When $-2\theta = \pi /2 + \phi _2(\omega _m)$, the magnetic resonance frequency $\omega _m$ is exactly twice the Larmor frequency $\omega _L$.In the open loop, a square wave modulation signal is used to drive the AOM driver to modulate the pump light. A sinusoidal oscillation signal is generated in the photodiode (PD), when the modulation frequency is twice the resonance frequency. In order to make the amplitude of the magnetic resonance signal stable in the closed loop, the sinusoidal oscillation signal passes through a zero-crossing circuit, and is converted into a square wave signal with amplitude of $0 \sim 5$V for driving the AOM driver. A maximum signal amplitude is achieved with a duty cycle of about $30\%$ [45].
Previously, we have researched on an all-optical self-oscillating HAM using a half-wave plate to adjust $\phi _3(\theta )$ [44]. However, when we want to extend the dynamic range of the magnetometer, the devices used to modulate the amplitude of the pump beam bring phase shift $\phi _2(\omega _m)$, which depends on the modulation frequency. Even though the pioneering work had realized the all-optical self-oscillating $^{87}$Rb atomic magnetometer for the first time [32], the issue that the AOM device with phase shift has the difficulty of achieving the larger dynamic range has not been mentioned. Because of smaller gyromagnetic ratio and Larmor frequency for the alkali atoms, this issue may not be significant and $\phi _2(\omega _m)$ needs not to be considered. However, in the metastable $^4$He atoms with the larger gyromagnetic ratio of $28.025$ Hz/nT, realizing a large dynamic range of measured magnetic field needs a broad modulation frequency range and has to compensate the phase shift $\phi _2(\omega _m)$ from optical modulation device. Results show that after the $\phi _3(\theta )$ has been optimized by the liquid crystal rotator, the noise floors remain almost unchanged in the dynamic range.
As shown in Fig. 2(a), when the modulation frequency increasing from $100$ kHz to $4000$ kHz, the relative phase changes linearly with the modulation frequency. The experimental data in Fig. 2(a) are linearly fitted with respect to modulation frequency. This linear model is substituted into Eq. (2) to obtain the relationship between the frequency shift and the modulation frequency as shown in Fig. 2(b). There are "break points" where the self oscillation of $^{4}$He cannot be maintained at all, making magnetic field measurement impossible. There are also frequency shifts near the breakpoints as shown in Fig. 2(b). The frequency shifts cause systematic errors, which affect the sensitivity and accuracy of the self-oscillating HAM. To solve these problems, the phase shift caused by the optical components should be compensated, which could be achieved by adjusting the angle between the polarization direction of the pump and probe beams. However, changing the relative polarization manually is rather laborious and time-consuming, which makes it impossible to measure fast-varying field and difficult to integrate. Therefore, a liquid crystal rotator has been used to rotate the polarization direction of the probe light. The liquid crystal utilizes the birefringence effect to change the polarization direction of linearly polarized light. In our experiment, we use a liquid crystal rotator which can rotate the polarization direction of linearly polarized light [38,46]. A square wave signal with the $4$ kHz repetition rate is applied to the liquid crystal to control the rotation angle of polarization of probe light by adjusting the amplitude of the square wave. In the closed-loop operation of the magnetometer, the rotation of probe light polarization generates a phase shift $\phi _3(\theta )$ and causes a change of the amplitude of the magnetic resonance signal. When the whole phase shift $\phi$ in the closed loop is zero, the signal amplitude can reach the maximum.
Fig. 2. (a) Using two AOMs (circles and triangles ) and an electro-optic modulator (EOM, squares) to investigate the relationship between modulation frequency and phase shift $\phi _2(\omega _m)$. In the open loop, the phase shift in the whole loop is between the modulation signal and the signal from AMP output. (b) The relationship between frequency shift of the self-oscillating HAM and modulation frequency of different AOMs and EOM. It is shown that the measured magnetic field results with using these devices are sensitive to modulation frequency, which causes systematic errors.
3. Results and discussions
One of the advantages of the SOAM is its fast response, even though the amplitude change of the magnetic field is beyond several times of the line width of magnetic resonance [29]. As shown in the Fig. 3, the bias magnetic field changes about $3600$ nT with a step signal beyond the line width of magnetic resonance signal ($\sim$ $200$ nT), and the self-oscillating HAM set up again within $0.2$ ms.
Fig. 3. The response of the self-oscillating HAM with a step change in the bias magnetic field. The magnetic field step is larger than the line width ($\sim 200$ nT) of the magnetic resonance signal. The response time is about $200$ $\mu$s.
Figure 4 shows the sensitivity of the self-oscillating HAM in different magnetic fields. In Fig. 4(a), the DC current is set to $35$ mA equivalent to magnetic field of $4335$ nT and $\phi _3(\theta )$ is optimized to get a maximum signal amplitude. The noise floor (sensitivity) of the self-oscillating HAM is about $1.7$ pT/Hz$^{1/2}$ (black line). The current is increased from $35$ mA to $60$ mA with a step of $5$ mA. The magnetic resonance signal is recorded by a frequency counter with a sampling rate of $1$ kHz, and a total time duration of $600$ s. Keeping the angle $\theta$ fixed, different magnetic fields are obtained as shown in Fig. 4(a). The sensitivity of the self oscillating HAM gradually decreases as the current in the magnetic filed coils increasing. When the current is set to $60$ mA (the carmine line), the noise floor of the self-oscillating HAM increases to about $10$ pT/Hz$^{1/2}$. If the polarization direction of the probe light is optimized by the liquid crystal rotator, as is shown in Fig. 4(b), the noise floor, within the frequency range of $2\sim 500$ Hz or higher, remains almost unchanged when the magnetic field varies over large dynamic range. In order to test the dynamic range of our self-oscillating HAM, we test the results semi-continuously, in comparison with a commercial self-oscillating cesium atomic magnetometer (Scintrex, CS-3) [23]. As shown in Fig. 5, a DC current is scanned from $20$ mA to $840$ mA to generate a bias magnetic field from $2500$ nT to $103000$ nT. The self-oscillating HAM records the magnetic field value (squares) with an optimized $\phi _3(\theta )$ at each magnetic field point (step by $2500$ nT). There is no break point in the measured magnetic field. The slopes of the curves are basically equal to the coils constant ($123.7$ nT/mA). When the measured magnetic field is about $69272$ nT ($560$ mA), the amplitude of the CS-3 magnetometer has decreased greatly and the atomic resonance linewidth has been widely broadened due to the nonlinear Zeeman effect [25] and the magnetic field gradient [2,47]. As shown in Fig. 5 (circles), the self-oscillating HAM has more tolerance to magnetic field gradients than the CS-3 magnetometer.
Fig. 4. (a) The noise floors with fixed $\phi _3(\theta )$ as measuring different bias values of magnetic field. (b) The noise floors with adaptively optimizing $\phi _3(\theta )$ as measuring the same bias values. The results show that after $\phi _3(\theta )$ has been optimized by the liquid crystal rotator for various magnetic fields, the noise floors remain almost unchanged.
Fig. 5. A larger dynamic range of measured magnetic field of the self-oscillating HAM is acquired. The current is increasing from $20$ mA to $840$ mA by a step of $20$ mA, which can produce bias magnetic fields ranging from $2500$ to $103000$ nT. The results demonstrate that the self-oscillating HAM (squares) has a larger dynamic range than the CS-3 (triangles) in our experiment. The gradient along the direction of the probe beam increases with the bias magnetic field, which is proportional to the strength of the current. The increased magnetic field gradient tends to broaden the linewidth and reduce the amplitude of the resonance signal of the CS-3 magnetometer, which stops working at a bias field around $69272$ nT.
4. Conclusion
We have demonstrated an all-optical self-oscillating HAM with optical phase shift using a liquid crystal rotator. Compared with self-oscillating magnetometers with electronic phase shift, we have shown experimentally that our magnetometer can effectively solve the breakdown problems and can work stably within a large range of magnetic fields from $2500$ nT to $103000$ nT. Our magnetometer has also shown fast response time of less than $0.2$ ms for severe magnetic field variations, of which the amplitude is far beyond the line width of the magnetic resonance signal. The noise floor of the self-oscillating HAM reaches $1.7$ pT/Hz$^{1/2}$@ $2\sim 500$ Hz using the optical phase shift and remains almost unchanged when the magnetic field changes within a large range. Compared with the commercial self-oscillating cesium atomic magnetometer (Scintrex, CS-3) [23], our magnetometer shows a better gradient tolerance and is unaffected by nonlinear Zeeman effect broadening. Combined with parameter optimization and system integration, together with some existing techniques to remove the dead zones and heading error of the magnetometer, our system provides a very efficient and accurate method for tracking the geomagnetic field.
Funding
National Natural Science Foundation of China (61531003, 61571018).
Acknowledgments
The authors would like to thank Z. Chen, B. Luo, Z. Lin, Y. Zhan and C. Yang for useful discussions.
Disclosures
The authors declare no conflicts of interest.
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