Gradient phase and amplitude errors in atomic magnetic gradiometers for biomagnetic imaging systems.

The cross-axis projection error (CAPE) caused by residual magnetic fields has recently attracted widespread attention. In this study, we propose a more specific theoretical model and expand the CAPE in gradient measurements. We first report that differences in relaxation rate and residual magnetic field between optically pumped magnetometers (OPMs) introduce a significant error term in the output of OPM gradiometers, referred to as the gradient phase error. Furthermore, when the longitudinal field compensation is inadequate, the interaxial response interference of a single OPM is prominent, resulting in an amplitude distortion of the signal. This is further amplified in the gradiometer configuration, introducing the gradient amplitude error. Our experiments demonstrated that the efficacy of mitigating common-mode noise of OPM gradiometers was significantly impaired when existing the gradient errors. In addition, a simulation with a magnetoencephalography (MEG) system illustrated an induced source localization error of exceeding 2 cm, severely compromising the localization accuracy of OPM-MEG systems.

In-situ measurement and cancellation of the light-shift in fiber-coupled atomic magnetometers.

In optical atomic magnetometers (AMs), the light-shift caused by the circularly polarized pumping beam have a significant impact on the response and is also one of the non-negligible sources of the noise. In this paper, we develop a novel method whereby utilizing the symmetry of the frequency response in an AM to measure and cancel the light-shift. Furthermore, we theoretically analyze and experimentally verify a rapid method of magnetic field compensation and the approach is convenient to measure and cancel of the light-shift. Moreover, the influence of intensity and frequency of the pumping beam is also investigated. The proposed method of in - situ measurement and cancellation of light-shift will be particularly profitable to other optical systems based on AMs.

Spin polarization characteristics of hybrid optically pumped comagnetometers with different density ratios.

We investigate the effects of the density ratio of K-Rb hybrid cells on the alkali metal-noble gas comagnetometers. Bloch equations simplified with the density ratio and average-pumping-rate model are presented for numerical simulation, which simplifies equations of complete hybrid spin ensemble and problem of polarization gradient. The spin polarizations of electron and nucleon, total electronic relaxation rates, and the spin-exchange efficiencies are measured with cells of different density ratios. The results are in good agreement with our equivalent model. Based on our theoretical analysis, the K-Rb-21Ne comagnetometer achieves maximum output signal by optimizing the combination of density ratio and optical power density. The density ratio is critical to the homogeneity of spin polarization and efficiency of hyperpolarization. The method in this work finds a way to optimize the sensitivity of comagnetometers, which is significant for angular-rotation sensors and new physics research.

A High-Performance Magnetic Shield with MnZn Ferrite and Mu-Metal Film Combination for Atomic Sensors.

This study proposes a high-performance magnetic shielding structure composed of MnZn ferrite and mu-metal film. The use of the mu-metal film with a high magnetic permeability restrains the decrease in the magnetic shielding coefficient caused by the magnetic leakage between the gap of magnetic annuli. The 0.1-0.5 mm thickness of mu-metal film prevents the increase of magnetic noise of composite structure. The finite element simulation results show that the magnetic shielding coefficient and magnetic noise are almost unchanged with the increase in the gap width. Compared with conventional ferrite magnetic shields with multiple annuli structures under the gap width of 0.5 mm, the radial shielding coefficient increases by 13.2%, and the magnetic noise decreases by 21%. The axial shielding coefficient increases by 22.3 times. Experiments verify the simulation results of the shielding coefficient of the combined magnetic shield. The shielding coefficient of the combined magnetic shield is 16.5%. It is 91.3% higher than the conventional ferrite magnetic shield. The main difference is observed between the actual and simulated relative permeability of mu-metal films. The combined magnetic shielding proposed in this study is of great significance to further promote the performance of atomic sensors sensitive to magnetic field.

Fast extraction of the electron spin-relaxation rate in the SERF magnetometer from a transient response.

The magnitude of the electron spin-relaxation rate Rrel of the atomic ensemble directly affects the sensitivity of the spin-exchange relaxation-free (SERF) atomic magnetometer (AM). The rapid and in-situ characterization of Rrel is of great importance. In this work, a fast extraction method of Rrel is proposed with a measurement period shorten to 0.5 s, merely detecting the transient response of SERF AM to a transverse DC excitation magnetic field after switching off the pump beam. In contrast to the conventional methods based on the measurement of the magnetic resonance linewidth, this method circumvents the involvement of optical pumping rate, and enables monitoring Rrel under arbitrary polarization, which is expected to improve the authenticity of Rrel measurement in a more convenient way.

Hybrid algorithm for predicting the temperature-variation-induced wavelength drift of DBR semiconductor lasers.

In this paper, a hybrid algorithm to predict the wavelength drift induced by ambient temperature variation in distributed Bragg reflector semiconductor lasers is proposed. This algorithm combines the global search capability of a genetic algorithm (GA) and the supermapping ability of an extreme learning machine (ELM), which not only avoids the randomness of ELM but also improves its generalization performance. In addition, a tenfold cross-validation method is employed to determine the optimal activation function and the number of hidden layer nodes for ELM to construct the most suitable model. After applying multiple sets of test data, the results demonstrate that GA-ELM can quickly and accurately predict the wavelength drift, with an average rms error of 4.09×10-4nm and average mean absolute percentage error of 0.21 %. This model is expected to combine the temperature and current tuning models for a wavelength in follow-up research to achieve rapid tuning and high stability of a wavelength without additional devices.

Suppression of ambient temperature-caused drift in a laser power stabilization system with a liquid crystal variable retarder in atomic gyroscopes.

Laser power stabilization systems with liquid crystal variable retarders have been employed in miniaturized atomic gyroscopes for the merits of low power consumption and easy integration. However, the long-term power drift of the system output with ambient temperature significantly decreases the long-term performance of atomic gyroscopes. Here, we demonstrated a method of dynamic closed-loop control based on the combination of optical power drift and ambient temperature modeling. For a continuous 45 min operation within an ambient temperature variation range of 23.7-25.3 °C, the relative Allan deviation of the output optical power was decreased by one order of magnitude from 2.29 × 10-4 to 3.35 × 10-5 after 100 s averaging time. The long-term stability of the system was significantly improved. In addition, the scheme requires no additional thermal control device, preventing the introduction of extra electromagnetic interference, which is desirable in a miniaturized atomic gyroscope.

Magnetic field sensing based on multi-order resonances of atomic spins.

Broad-dynamic-range magnetometers are demanded in practical applications and fundamental research. We experimentally demonstrate a parametrically modulated atomic magnetometer with a large dynamic range by taking advantage of the high-order resonance effects. With the increase of the strength of the modulation field, both low-order and high-order resonances are well resolved and used to measure the DC or AC magnetic fields. The experimentally demonstrated sensitivity of the magnetometer based on the zeroth-order resonance is 1.5 pT/Hz, and those based on the high-order resonances are below 3 pT/Hz, making the measurement of high magnetic fields feasible under an open-loop operation. Moreover, we also demonstrated the measurement of high-frequency large AC magnetic field with the high-order resonances, and the sensitivity for the AC magnetic field based on the first-order resonance is 7 pT/Hz. Our scheme provides a new path for the development of broad-dynamic-range and miniaturized atomic magnetometers.

Optimization of beam shaping for ultrasensitive inertial measurement using a phase-only spatial light modulator.

This study proposes an approach to generate a uniform flat-top beam with a liquid crystal spatial light modulator (LC-SLM) to optimize ultrasensitive inertial measurement. The random incomplete Gaussian beam is modulated into a flat-top beam by uploading a beam shaping optimization algorithm on an LC-SLM. Simulation results verify the effectiveness of the proposed method. The beam obtained from the experimental results with the 4f filter system optimization also conforms to the properties of the generated flat-top beam. Compared to existing beam shaping algorithms for simulation and experimental analysis, the beam shaping design based on the LC-SLM to optimize the ultrasensitive inertial measurement is realized. This method has also been verified to be effective in beam shaping in various beam situations. The application of this method in ultrahigh-sensitivity inertial measurement should prove significant.

Pulsed light power stabilization of a semiconductor laser using a mixed analog-digital method with an acousto-optic modulator.

Diffraction beams produced by an acousto-optic modulator are widely used in various optical experiments, some of which need to modulate the radio-frequency drive signal to change the diffraction beams from continuous light to pulsed light. The generation of such pulsed light is open-loop, and long-term stability of the power is disregarded. In this paper, we introduce a method to suppress the pulsed light power drift of a semiconductor laser. By using the servo system, the low frequency power drift of 1-60 kHz pulsed light can be suppressed. This pulsed light power stabilization method can be applied to optical rotation detection and pulse pumping.

Analysis of effects of magnetic field gradient on atomic spin polarization and relaxation in optically pumped atomic magnetometers.

The magnetic field gradient within optical pumping magnetometers (OPMs) suppresses sensitivity improvement. We investigated the effects of the magnetic field gradient along the x-, y-, and z-axes on the limiting factors of magnetometers under extremely low magnetic field conditions. We modified the magnetic field gradient relaxation model such that it can be applied to atoms in the spin exchange relaxation free (SERF) regime. The gradient relaxation time and spin polarizations, combined with fast spin-exchange interaction, were determined simultaneously using the oscillating cosine magnetic field excitation and amplitude spectrum analysis method. During the experiments, we eliminated the errors caused by the temperature and pumping power, and considered different isotope spin exchange collisions in naturally abundant Rb during the data analysis to improve the fitting accuracy. The experimental results agreed well with those of theoretical calculations and confirmed the accuracy of the improved model. The contribution of the transverse magnetic field gradient to the relaxation of the magnetic field gradient cannot be ignored in the case of small static magnetic fields. Our study provides a theoretical and experimental basis for eliminating magnetic gradient relaxation in atomic sensors in the SERF region.

High-sensitivity operation of a single-beam atomic magnetometer for three-axis magnetic field measurement.

We demonstrate a single-beam atomic magnetometer (AM) capable of measuring a three-axis magnetic field with high-sensitivity, achieved by applying a small DC offset field and a high frequency modulation field. To satisfy the miniaturization demand of AMs, an elliptically polarized light detuned by 50 GHz from the resonance transition center is employed. The circularly polarized component is used to polarize the alkali-metal atoms, while the linearly polarized light is used to detect the dynamics of the polarized spin under a magnetic field. Based on theoretical analysis, parameters that significantly affect the performance are optimized, and a sensitivity of 20 fT/Hz1/2 in x-axis, 25 fT/Hz1/2 in y-axis, 30 fT/Hz1/2 in z-axis is achieved with a miniature 4 × 4 × 4 mm 87Rb vapor cell. Moreover, we also verify that the operation principle of AMs can be used to null background magnetic fields in-situ with isotropic compensation resolution of 6.7 pT, which provides an effectively precise method for zeroing ambient magnetic field. The high-sensitivity operating of an elliptically-polarized-laser-based magnetometer provides prospective futures for constructing a compact, low-cost AM, which is particularly applicable for non-invasive bio-magnetic imaging such as array-based magnetoencephalography (MEG) and magnetocardiography (MCG).

Transient dynamics of atomic spin in the spin-exchange-relaxation-free regime.

In this paper, we experimentally study transient dynamics of spin polarized atoms in the spin-exchange-relaxation-free (SERF) regime with a single-beam configuration. We pumped atoms with a weak detuning pumping beam, along with a sequence of magnetic field pulses orthogonal to the pumping beam were applied. The dynamics of atomic spin, which experiences Larmor precession under the perturbation of magnetic field, is detected by the transmitted pumping beam. Benefited from the long coherence time of atomic spin in the SERF regime, the dependence of precession frequency and decay rate, which is equal to the magnetic resonance linewidth of atomic spin, on magnetic fields is studied with the transient dynamics of atomic spin in the limit of low spin polarization. Moreover, we demonstrate that coil constants can be calibrated by analyzing the precession frequency of the transient dynamics of atomic spin. And the experimental results show that the coil constants are 114.25 ± 0.02 nT/mA and 114.12 ± 0.04 nT/mA in x- and y-axis, respectively. This method is particularly applicable to study the atomic spin dynamics and calibrate the coil constant in situ of a miniature single-beam SERF magnetometer.

Double-loop control and intelligent parameter tuning for the temperature control system of a DBR semiconductor laser.

Aiming at lower startup power consumption, stronger thermal load adaptability, easier parameters adjustment, and higher parameter tuning efficiency for the temperature control system of a distributed Bragg reflector (DBR) semiconductor laser, this paper employs the double-loop control and intelligent parameter tuning methods. First, the thermal equivalent circuit model is established for the laser temperature control system, which has stronger thermal load adaptability than the traditional transfer function model. In order to improve the modeling speed and accuracy, a mean impact value (MIV) quantum particle swarm optimization (QPSO) intelligent algorithm is proposed to tune the model parameters. A double-loop temperature control system is set up on this basis. Then, the MIV-QPSO intelligent algorithm is used to tune the control parameters, which shortens the settling time, increases the tuning efficiency, and improves the temperature control effect. The feasibility and effectiveness of the proposed methods are verified through the MATLAB/Simulink simulation of the laser temperature control process.

A Review of Polarization-Sensitive Materials for Polarization Holography.

Polarization holography has the unique capacity to record and retrieve the amplitude, phase, and polarization of light simultaneously in a polarization-sensitive recording material and has attracted widespread attention. Polarization holography is a noteworthy technology with potential applications in the fields of high-capacity data storage, polarization-controlled optical elements, and other related fields. The choice of its high-performance materials is particularly important. To further develop polarization holography applications and improve the quality of the information recorded (i.e., material sensitivity and resolution), a deeper understanding of such materials is needed. We present an overview of the polarization-sensitive materials, which introduced polarization holographic technology and the development of polarization holographic materials. The three main types of polarization holographic materials are described, including azopolymer materials, photopolymer material, and photorefractive polymer material. We examine the key contributions of each work and present many of the suggestions that have been made to improve the different polarization-sensitive photopolymer materials.

Broadening of magnetic linewidth by spin-exchange interaction in the K-Rb-21Ne comagnetometer.

The elimination of relaxation resulting from spin-exchange (SE) interaction is crucial for ultrasensitive atomic comagnetometers. In this study, we demonstrate the SE relaxation is only partially suppressed and significantly broadens the magnetic linewidth in the K-Rb-21Ne comagnetometer. The SE relaxation arises from the compensation magnetic field when operating in the self-compensation regime. We propose a new method to measure the SE relaxation in the self-compensation regime where the alkali-metal and noble-gas spin ensembles are coupled. In the presence of SE relaxation, we find the optimal alkali-metal polarization for maximizing the sensitivity is shifted from the typical value. Under various conditions, we present a detailed study of the SE relaxation and the scale factor as a function of alkali-metal polarization, which are further verified by the theoretical models. The reduction of SE relaxation and improvement of scale factor by using 87Rb atoms is also studied.

High spatial resolution multi-channel optically pumped atomic magnetometer based on a spatial light modulator.

Ultra-sensitive multi-channel optically pumped atomic magnetometers based on the spin-exchange relaxation-free (SERF) effect are powerful tools for applications in the field of magnetic imaging. To simultaneously achieve ultra-high spatial resolution and ultra-high magnetic field sensitivity, we proposed a high-resolution multi-channel SERF atomic magnetometer for two-dimensional magnetic field measurements based on a digital micro-mirror device (DMD) as the spatial light modulator for a single vapor cell. Under the optimal experimental conditions obtained via spatial and temporal modulation of the probe light, we first demonstrated that the average sensitivity of the proposed 25-channel magnetometer was approximately 25fT/Hz1/2 with a spatial resolution of 216µm. Then, we measured the magnetic field distribution generated by a gradient coil and compared the experimentally obtained distributions with those calculated via finite element simulation. The obtained g value of 99.2% indicated good agreement between our experimental results and the theoretical calculations, thereby confirming that our proposed multi-channel SERF magnetometer was effective at measuring magnetic field distributions with an ultra-high spatial resolution.

Nuclear magnetic field measurement of the spin-exchange optically pumped noble gas in a self-compensated atomic comagnetometer.

We demonstrate a new method to determine the nuclear magnetic field of the spin-exchange optically pumped noble gas in a self-compensated atomic comagnetometer based on the steady-state AC response. The result shows that it has higher resolution and precision than a previous method based on the transient process. Furthermore, a convergence frequency is observed in the low-frequency region and its parameter dependence is studied simulatively, which may inspire further research into its relationship with the strong suppression mechanism of the self-compensation ability for the low-frequency magnetic field. We also prove that this method can be developed for suppression of residual main magnetic field to improve the systematic stability of the comagnetometer.

Miniaturized optical rotation detection system based on liquid crystal variable retarder in a K-Rb-21Ne gyroscope.

A novel method to control the light intensity stability and modulate the probe light polarization using a liquid crystal variable retarder (LCVR) to detect atomic spin precession simultaneously in a K-Rb-21Ne gyroscope is reported. A sinusoidal driving voltage is applied to drive the LCVR and is skillfully used to produce a high-frequency modulation for the probe light. The modulation helps to avoid electronic detection noise appearing at low frequencies and allows for phase-sensitive detection. The coefficient of rate ramp can be reduced from 1.31 (deg/h)/h to 0.05 (deg/h)/h (Allan deviation), and the bias instability of about 0.08 deg/h at the averaging time of 200 s is achieved. Therefore, the long-term stability of the angular velocity measurement can be improved and other optical modulators can be replaced to facilitate the miniaturization of the gyroscope by using this intensity modulation detection method. This optical rotation detection method also can be applied to other miniaturized atomic sensors, such as atomic magnetometers.

In-situ measurement of the density ratio of K-Rb hybrid vapor cell using spin-exchange collision mixing of the K and Rb light shifts.

We investigate a new method that enables the direct measurement of the density ratio of a K-Rb hybrid vapor cell, using the spin-exchange collision mixing of the K and Rb light shifts. The densities for each alkali metals can be further determined using Raoult's law. The mixture of the light shifts in both magnetometers and comagnetometers is formulated using Bloch equations and explained by considering the fast spin-exchange interaction. The relationship between the density ratio and the mixed light shifts is both formulated and simulated. The method was performed on several K-Rb magnetometer- and K-Rb-21Ne comagnetometer-cells at different temperatures, pump light powers, and mole fractions of K. The method was further verified by the conventional laser-absorption-spectroscopy method. The new approach has the advantage to measure the density ratio of the optically-thick hybrid alkali atoms, while requiring no additional magnetic field necessary for conventional magnetic-field induced Faraday-rotation techniques. It also has the advantage of in-situ measuring the density ratio under exactly the normal operation of the devices, which means that the errors caused by the heating-effect of the strong pump light and the temperature drift during long-term operation can be real-time monitored.