Spin-exchange Relaxation-free Atomic Magnetometer Research Articles

Ultrasensitive SERF atomic magnetometer with a miniaturized hybrid vapor cell.

The chip-scale hybrid optical pumping spin-exchange relaxation-free (SERF) atomic magnetometer with a single-beam arrangement has prominent applications in biomagnetic measurements because of its outstanding features, including ultrahigh sensitivity, an enhanced signal-to-noise ratio, homogeneous spin polarization and a much simpler optical configuration than other devices. In this work, a miniaturized single-beam hybrid optical pumping SERF atomic magnetometer based on a microfabricated atomic vapor cell is demonstrated. Although the optically thin Cs atoms are spin-polarized, the dense Rb atoms determine the experimental results. The enhanced signal strength and narrowed resonance linewidth are experimentally proven, which shows the superiority of the proposed magnetometer scheme. By using a differential detection scheme, we effectively suppress optical noise with an approximate five-fold improvement. Moreover, the cell temperature markedly affects the performance of the magnetometer. We systematically investigate the effects of temperature on the magnetometer parameters. The theoretical basis for these effects is explained in detail. The developed miniaturized magnetometer has an optimal magnetic sensitivity of 20 fT/Hz1/2. The presented work provides a foundation for the chip-scale integration of ultrahighly sensitive quantum magnetometers that can be used for forward-looking magnetocardiography (MCG) and magnetoencephalography (MEG) applications.

A novel method for multiple cardiovascular disease biomarker detection using a SERF-based microfluidic platform

As cardiovascular diseases (CVDs) are the leading cause of death worldwide, it is of great importance to realize a rapid and sensitive diagnosis. Multiple CVD biomarker detection, which holds higher accuracy and speed of early CVD diagnosis, is becoming a promising alternative to single biomarker analysis. Cardiac troponin I (cTnI), C-reactive protein (CRP), brain-type natriuretic peptide (BNP), and heart fatty acid binding protein (H-FABP) are four significant diagnostic biomarkers for CVDs. Among the several methods for biomarker detection, such as optical, magnetic, mechanical, and electrical methods, the magnetic method stands out because of its stability, low toxicity, noninvasive detection, facile manipulation with an external magnetic field, and immunity to the interference of background light. At present, the lack of multiplexing capability, the imprecision of magnetic signal localization, and the agglomeration and non-specific adsorption of magnetic nanoparticles all limit the clinical application of magnetic detection. This paper presented a novel method for multiple CVD biomarker detection using a spin exchange relaxation-free (SERF)-based microfluidic platform. One or more SERF atomic magnetometers were used to scan the remanent field of magnetic labels to detect four CVD biomarkers in 70 min, with a detection limit of 1.88 pg/mL (cTnI), 1.58 pg/mL (CRP), 1.45 pg/mL (BNP), and 1.71 pg/mL (H-FABP). The results showed two-dimensional magnetic fields with a resolution of submillimeter level and a sensitivity of pT level. The measurement technique provides a new magnetic methodology for applications in clinical diagnosis.

LSA-PINN: A new method based on Physics-Informed Neural Network with lightweight self-attention for solving modified Bloch equation

The Spin-Exchange Relaxation-Free (SERF) atomic magnetometers play an increasingly significant roles in cardiac and brain magnetometry fields, etc. For the SERF atomic magnetometer, the evolution and interaction with the magnetic field of atomic spins can be described by the Bloch equation. However, the traditional Bloch equation does not take into account the transport phenomena caused by the atomic density gradient within the vapor cell, which makes it unable to accurately reflect the polarization distribution in the vapor cell, thereby reducing the accuracy of magnetic field measurement. To achieve a more accurate representation of the evolution characteristics of the spatial distribution of the atomic ensemble, a diffusion term for the polarization strength is introduced into the Bloch equation. Furthermore, a new unsupervised Physics-Informed Neural Network (PINN) model with lightweight self-attention (LSA) module is proposed to solve the modified nonlinear equation. The introduction of LSA enhances the adaptive representational capability of PINN, enabling it to more effectively extract global features and consequently obtain more accurate numerical solutions of the Bloch equation. The experimental results show that LSA-PINN achieves a minimum loss value of 3.98×10-2, which is 62 % lower than the traditional PINN. This study provides new insights and methods to address the limitations of traditional Bloch equation and gain a deeper understanding of system behavior.

Single-beam three-axis SERF atomic magnetometer based on coordinate system rotation

We propose what we believe to be a new single-beam three-axis spin exchange relaxation free (SERF) vector atomic magnetometer scheme based on coordinate system deflection. A theoretical model for the system response under arbitrary angle deflection was established for the first time, and the system response at different angles was simulated and analyzed. The simulation results show that the system response increases in the direction of the non-sensitive axis and decreases in the direction of the sensitive axis as the deflection angle increases, and the two responses tend to be the same when the angle is deflected to 45-degrees. Experimental measurements were carried out at a deflection angle of 45-degrees and the results showed that the sensitivity of the magnetometer was 55fT/Hz1/2 in the x1-axis, 38fT/Hz1/2 in the y1-axis and 60fT/Hz1/2 in the z1-axis. This single-beam magnetometer can be used to construct a miniaturized and low-cost weak magnetic sensor, which is expected to be used for vector measurement of biomagnetism.

Performance optimization of a SERF atomic magnetometer based on flat-top light beam

We explore the impact of pumping beams with different transverse intensity profiles on the performance of the spin-exchange relaxation-free (SERF) atomic magnetometers (AMs). We conduct experiments comparing the traditional Gaussian optically-pumped AM with that utilizing the flat-top optically-pumped (FTOP) method. Our findings reveal that the FTOP-based approach outperforms the conventional method, exhibiting a larger response, a narrower magnetic resonance linewidth, and a superior low-frequency noise performance. Specifically, the use of FTOP method leads to a 16% enhancement in average sensitivity within 1 Hz–30 Hz frequency range. Our research emphasizes the significance of achieving transverse polarization uniformity in AMs, providing insights for future optimization efforts and sensitivity improvements in miniaturized magnetometers.

Comprehensive analysis of the influence of magnetic field gradients on single-beam SERF atomic magnetometer

Magnetic field gradients interfere with the coherence of the atomic ensemble and degrade the performance of the spin-exchange relaxation-free (SERF) atomic magnetometer. In this paper, the influence of magnetic field gradients is incorporated into the response model of single-beam atomic magnetometer, and the theoretical models of transverse relaxation rate, spin polarization and scale factor are established. Based on this model, we find that magnetic field gradients in different directions can cause varying degrees of degradation in the performance parameters of the magnetometer. The magnetic linewidths under different light power and magnetic field gradients are measured using the designed dedicated magnetic field gradients coils, and the spin polarization and magnetic field gradients relaxation rate are obtained through fitting. An unevenness and deviation of the curve are also observed in the experiments, indicating the presence of the magnetic field gradient of approximately 2 nT/cm in the magnetic shields. Furthermore, in a magnetic field gradient environment of 20 nT/cm, the mean of the long-term sensitivity decreased by 3.5 times and the standard deviation increased by 11 times. It shows that the magnetic field gradients will not only affect the signal-to-noise ratio, but also make the magnetometer more vulnerable to external interference when working. The sensitivity and stability of magnetometer will be greatly reduced. The research in this article provides a theoretical and experimental basis for eliminating the influence of magnetic field gradients and improving the accuracy of magnetic field measurements.

Ultra-high consistency multichannel SERF atomic magnetometer based on diffractive optics

Multichannel spin-exchange relaxation-free (SERF) atomic magnetometers (AMs) have broad application prospects in array biomagnetic measurement systems because of their high spatial resolution. This study proposed an efficient and high-quality beam-splitting method based on a diffractive optical element (DOE), which enables multichannel SERF AM to maintain ultrahigh consistency with a channel interval of 3.27 mm. Based on the relaxation rate model under zero-field resonance, the minor differences in the magnetic linewidth of each channel were analyzed. The experimental results demonstrated ultra-high consistency of the magnetic field measurement signals between multiple channels, with a nonlinear error of less than 0.1%. The optimal sensitivity for a single channel was 11.9 fT/Hz1/2 @31.5 Hz, and 9.3 fT/Hz1/2 @31.5 Hz in the first-order gradiometer mode. The structure also satisfied the requirements of long-term high stability and high sensitivity, which are expected to further obtain more measurement channels. This method plays a critical role in improving the accuracy of magnetocardiography (MCG) and magnetoencephalography (MEG) systems.

Femtotesla 87Rb magnetometer based on a coaxial pump-probe beam delivery system

Advancements in highly sensitive and miniaturized spin-exchange relaxation-free atomic magnetometers have attracted significant attention. Although dual-beam magnetometers with high sensitivity have been developed, miniaturization while maintaining sensitivity remains challenging. In this study, we present a novel magnetometer configuration featuring a coaxial pump-probe beam delivery system facilitated by a single polarization-maintaining optical fiber. Utilizing polarized atoms to probe the diffuse central region of a ring pump beam, we achieved optimized performance through parameter adjustments, including the power of the pump and probe beams, modulation index, and other key factors. The magnetometer exhibited a remarkable sensitivity of 15 fT/Hz1/2. In addition, we introduced a novel method for evaluating the polarizability of alkali metals. The proposed magnetometer configuration shows considerable potential for advancing the field of highly sensitive miniaturized atomic magnetometers that are well suited for magnetocardiography (MCG) and magnetoencephalography (MEG) applications.

Response optimization of a three-axis sensitive SERF magnetometer for closed-loop operation

Most triaxial-vectorial magnetic field measurements with spin-exchange relaxation free (SERF) atomic magnetometer (AM) are based on the quasi-steady-state solution of the Bloch equation. However, the responding speed of these methods is greatly limited because the frequency of the modulation signal should be slow enough to ensure the validity of the quasi-steady-state solution. In this work, a new model to describe the response of the three-axis sensitive SERF AM with high modulation frequency is presented and verified. The response of alkali-atomic spin to high-frequency modulation field is further investigated by solving the Bloch equation in a modulation-frequency-dependence manner. This solution is well verified by our experiments and can offer a reference for selection of modulation frequencies. The result shows a potential to achieve a SERF AM operating in a geomagnetic field without heavy aluminum shielding when the modulation frequencies are selected properly.

High-sensitivity atomic magnetometer realized by weak-value-amplification effect

The weak-value-amplification (WVA) effect, which is also called weak measurement, has been developed extensively in various sensing systems. Here, we report the actual realization of the WVA effect in spin-exchange relaxation-free atomic magnetometer system, wherein the slight separation of transverse momentum of the probe light is amplified by introducing orthogonal pre- and post-selection states. A differential detector is used to obtain the transverse position of the probe light accurately in real time. The weak coupling of the magneto-optical interaction with atoms will be reflected in the differential signal. The WVA effect is observed and demonstrated directly and a high sensitivity of 8 fT/Hz is achieved. Also, we obtain the stable and distinct simulated magnetocardiography signal through our system. The present successful implementation of this probe method paves the way for further technical noise suppression and sensitivity improvement of quantum sensors.

Single-Beam Double-Pass Miniaturized Atomic Magnetometer for Biomagnetic Imaging Systems

Miniaturized atomic magnetometers (AMs), particularly spin-exchange relaxation-free (SERF) AMs, have been emerging in clinical imaging applications such as magnetocardiography (MCG) and magnetoencephalography (MEG). Miniaturization, portability, and low cost are primary development targets for biomagnetic imaging technologies, as well as high sensitivity, temporal, and spatial resolution. In this article, we propose a low-cost solution for a biomagnetic imaging system based on AMs, in which one laser source is used for a multichannel AM sensor array. A novel design is demonstrated for a miniaturized SERF AM, consisting of a single-beam double-pass configuration based on an optical fiber circulator. The effects of temperature and laser power on the zero-field magnetic resonance linewidth are characterized, and the experimental results show that the present design achieves better performance, compared with a traditional single-beam single-pass configuration. The magnetic field noise spectrum shows that such single-beam double-pass miniaturized AMs reach a sensitivity of approximately 86 fT/Hz <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{{1}/{2}}$ </tex-math></inline-formula> at a frequency of 10 Hz when operating in the single-channel mode and a sensitivity of approximately 40 fT/Hz <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{{1}/{2}}$ </tex-math></inline-formula> when operating in magnetic differential mode with two sensors sharing one laser source and a 6-mm baseline. A typical adult MCG signal with all the visible P, QRS-complex, and T waves is recorded by the magnetometer in the single-channel mode. This design is especially suitable for AMs operating in arrays as a basic building element for low-cost biomagnetic imaging systems.

A Fast Determination Method for Transverse Relaxation Rate of Minimized SERF Atomic Magnetometer

The sensitivity and bandwidth as the primary criteria of spin-exchange relaxation-free (SERF) atomic magnetometer (AM) are closely related to the transverse relaxation rate of atomic ensemble. In this study, we show an effective method for transverse relaxation rate measurement drawing on golden section algorithm. With no requirement of offline fitting, the measuring time of this method is only 7s. This is especially advantageous for reducing measurement errors due to the drifts of spatial magnetic field and light intensity and employing multiple measurements to better monitor the performance of magnetometers. Moreover, the reset after measuring is optimized as the sensitive axis magnetic field correction, ensuring the integrity of measurement while improving the accuracy of magnetic compensation. Furthermore, we find that the acquired experimental data by using this method can be adopted for the evaluation of magnetic field compensation performance and the monitoring of magnetic anomaly states. This determination method for transverse relaxation rate is anticipated to play a greater important role in multi-channel SERF AMs arrays.

Analysis and suppression of the three-axis crosstalk effect in the modulated SERF atomic magnetometer

In this paper, the effects of modulation fields frequency configuration, modulation fields phase configuration and three-axis direct-current (DC) magnetic fields on the three-axis crosstalk are analyzed in the modulated spin-exchange relaxation-free (SERF) atomic magnetometer. Based on three-axis modulation fields configuration, a method is proposed to suppress the three-axis crosstalk, and the results show that the three-axis crosstalk is lower than 2%. This paper also demonstrates an in-situ magnetic compensation method, and the magnetic compensation accuracy of this method is on the order of pT. Additionally, the three-axis magnetic field closed-loop mode is showed to suppress the effect of the DC magnetic field on the three-axis crosstalk. The three-axis crosstalk is finally reduced by nearly two times compared with that of before crosstalk suppression, and the three-axis sensitivities are better than 30 fT/Hz1/2. The reduction of crosstalk is beneficial to realize the high-precision measurement of the three-axis SERF magnetometer.

Speedy in-situ magnetic field compensation algorithm for multiple-channel single-beam SERF atomic magnetometers

The currently employed algorithms for the magnetic field compensation of single-beam spin-exchange relaxation-free atomic magnetometers are excessively slow and unstable, which limits the use and commercialization of magnetometer arrays for biological magnetic measurement. This study proposes an improved trisection algorithm (ITSA) to compensate for the magnetic field around the vapor cell in an attempt to resolve these limitations. Through the constant monitoring of the intensity of light emitted from a laser, the proposed algorithm reduces the time required to compensate for magnetic fields to 0.85 s in a single magnetometer, which is nine times faster than the traditional algorithm, and to 26 s in 36-channel magnetoencephalography equipment, which is 15.5 times faster than the traditional algorithm. In addition, an approximately 16% increase in measuring sensitivities is achieved based on the ITSA compared with the traditional algorithm. These improvements can promote the usage efficiency and commercialization of biological magnetic measurement instruments. Furthermore, the ITSA is verified using an experimental setup and the mathematical analysis and comparable experimental results demonstrate the effectiveness of the proposed algorithm.

Signal-enhanced spin-exchange relaxation-free atomic magnetometer

Signal-enhanced spin-exchange relaxation-free atomic magnetometer

Quantum‐Based Magnetic Field Sensors for Biosensing

AbstractThe accurate detection of very weak biomagnetic signals with a sensitivity of fT levels and mapping nanoscale magnetic field variations are two of the most significant challenges for biosensing. Compared to the limited sensitivity and spatial resolution of traditional magnetic field sensors, quantum‐based magnetic field sensors are emerging as a promising solution. In this review, the latest developments of three representative quantum‐based magnetic field sensors, including superconducting quantum interference device (SQUID) magnetometers, spin exchange relaxation free (SERF) atomic magnetometers, and nitrogen‐vacancy centers in diamond, are summarized. Both virtues and limitations of these sensors are analyzed systematically, and typical applications in magnetocardiography, magnetoencephalography, detection of neuronal action potentials, magnetic imaging of living cells, biomedical diagnosis, etc., are presented. Furthermore, SQUIDs combined with microfluidics for magnetic immunoassay diagnostics, the chip‐scale SERF atomic magnetometers fabricated by microelectromechanical systems that offer wearable flexibility, and nanodiamonds functionalized with magnetic nanoparticles to improve the sensitivity of nanothermometers are discussed.

A Novel Measurement Method for Spin Polarization Three Axis Spatial Distribution in Spin-Exchange Relaxation Free Atomic Magnetometer

The measurement of atomic spin polarization distribution in spin-exchange relaxation free (SERF) magnetometer is an important topic for improving the sensitivity and consistency of multi-channel magnetic field measurement applications. A novel spin polarization spatial distribution measurement method is presented based on the transient response of the magnetometer after modulating the pumped light with a chopper. Polarization is obtained by a slow-down factor based on the fast spin-exchange interaction effects. Longitudinal and transverse polarization distributions are measured simultaneously without interrupting the operation of the SERF status. Under different oscillating magnetic fields, the spin polarization is measured at the cell centroid. Residual magnetic field inside the magnetometer is obtained from the linear relationship between the precession frequency and the oscillating magnetic field. The one-dimensional polarization distributions in the x, y, and z axes are measured using a digital micromirror device with a resolution of 0.25 cm. The measurement results conform to the Lambert-Bier absorption law and the Gaussian distribution law. Furthermore, 7 × 7 two-dimensional spatial distribution measurements of polarization on the xy and yz planes are performed. Nonuniformity of 1.04 in the xy plane and 1.82 in the yz plane in the built magnetometer. Compared with other measurement methods, the distribution measurement method proposed is independent of optical depth and suitable for low polarization and high polarization applications. Based on the results of the proposed measurement method of spin polarization spatial distribution, further compensation can improve the application consistency of multi-channel magnetic field measurements and improve the sensitivity of single-channel differential measurements.

Dual-beam room-temperature atomic magnetometer with high sensitivity and large dynamic range

We demonstrate a dual-beam high-sensitivity room-temperature atomic magnetometer (AM) with a large dynamic range based on a nonlinear magneto-optical rotation (NMOR) enhancing scheme. Using an inelastic wave-mixing laser, we find significant NMOR signal enhancement compared with a single-beam scheme under the same far-detuned operation conditions. This dual-beam scheme is shown to operate well in the regime of lower laser intensity and off-resonance detuning. The best sensitivity achieved is 20 fT/Hz1/2 with a bandwidth of 2 kHz, substantially greater than common spin-exchange relaxation-free AMs. This provides a way to develop low-power, inexpensive miniaturized AMs for wide application.

A Single-Axis Atomic Magnetometer-Based Mouse Magnetocardiography Measurement System

The mouse Magnetocardiogram’s (MCG) accurate measurement is of the utmost importance for studying heart diseases. However, most of the currently used measuring instruments are Superconducting Quantum Interference Devices (SQUIDs), which are quite problematic. For example, they have a large scale, are expensive, and are difficult to widely promote. To address these issues, we present a mouse MCG measurement system using a Spin-Exchange-Relaxation-Free (SERF) atomic magnetometer. The measurement system mainly consists of a magnetic sensor, a mouse fixation device, a magnetically shielded device, and a data acquisition and processing module. We fabricated a single-axis SERF rubidium atomic magnetometer with a sensitivity of 20 fT/ √ Hz to serve as the system’s magnetic sensor. We also conducted experiments on the mouse MCG signals. Using power line harmonic modeling and wavelet threshold filter processing, we processed the raw signal and obtained an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i> -peak amplitude of 5 pT; moreover, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</i> -, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">QRS</i> -, and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> -waves were clearly visible. We also performed heart rate monitoring on mice at different ambient temperatures. Finally, we conducted a comparative analysis of related systems to illustrate the proposed system’s advantages for mouse MCG signals. This work demonstrates that the SERF atomic magnetometer is compatible with the long-term detection needs of the mouse cardiac magnetic field.

Simultaneous in-situ compensation method of residual magnetic fields for the dual-beam SERF atomic magnetometer

Near-zero magnetic field condition is essential to keep the spin-exchange relaxation-free (SERF) regime for the atomic magnetometer. We analyzed the output response variations of the dual-beam SERF magnetometer under different DC residual magnetic fields. Considering the problem that the gradient coil may introduce an additional DC magnetic field when compensating the gradient field, we propose a novel method of simultaneous in-situ compensation of gradient and DC residual magnetic field with high precision. The sensitivity and effectiveness of the compensation method for residual magnetic fields under 1 nT were verified by simulation and experiment. The precision of the gradient residual magnetic field compensation is better than 2 pT/mm. We built a dual-beam SERF atomic magnetometer platform to validate the proposed method. The magnetic field measurement sensitivity is 7 fT/Hz1/2 after residual magnetic fields compensation by the method mentioned in this paper, which is 4 times higher than the sensitivity of 36 fT/Hz1/2 without residual magnetic fields compensation.