Noise reduction and signal-to-noise ratio improvement of atomic magnetometers with optical gradiometer configurations

An optically pumped magnetic gradiometer for the detection of human biomagnetism

We realise an intrinsic optically pumped magnetic gradiometer based on non-linear magneto-optical rotation. We show that our sensor can reach a gradiometric sensitivity of 18 fT cm - 1 Hz - 1 and can reject common mode homogeneous magnetic field noise with up to 30 dB attenuation. We demonstrate that our magnetic field gradiometer is sufficiently sensitive and resilient to be employed in biomagnetic applications. In particular, we are able to record the auditory evoked response of the human brain, and to perform real-time magnetocardiography in the presence of external magnetic field disturbances. Our gradiometer provides complementary capabilities in human biomagnetic sensing to optically pumped magnetometers, and opens new avenues in the detection of human biomagnetism.

Recent Developments in Fabrication Methods and Measurement Schemes for Optically Pumped Magnetic Gradiometers: A Comprehensive Review

Optically pumped gradiometers have long been utilized in measurement in the International Geomagnetic Reference Field (IGRF). With advancements in technologies such as laser diodes and microfabrication, integrated gradiometers with compact sizes have become available, enabling improvements in magnetoencephalography and fetal magnetocardiography within shielded spaces. Moreover, there is a growing interest in the potential of achieving biomagnetic source detection without shielding. This review focuses on recent developments in optically pumped magnetic field gradiometers, including various fabrication methods and measurement schemes. The strengths and weaknesses of different types of optically pumped gradiometers are also analyzed.

Light-noise suppression method for the single-beam optically-pumped magnetometer arrays

We propose a miniaturized single-beam optically pumped magnetometer (OPM) with a laser power differential structure, along with a dynamically-adjusted detection circuit. This design enables the suppression of optical fluctuation noise and the enhancement of magnetometer sensitivity. For a single-beam OPM, pump light fluctuation noise is a significant contributor to output noise. To address this, we propose an OPM with a laser differential structure that separates the pump light as a part of the reference signal before it enters the cell. The reference current and OPM output current are then subtracted to suppress the noise introduced by pump light fluctuations. To achieve optimal optical noise suppression, we implement balanced homodyne detection (BHD) with real-time current adjustment, which dynamically adjusts the reference ratio between the two currents according to their amplitude. Ultimately, we can reduce the noise introduced by pump light fluctuations by 47% of the original. The OPM with laser power differential achieves a sensitivity of 17.5 fT/Hz^1/2, with the optical fluctuation equivalent noise at 13 fT/Hz^1/2.

Quantum magnetic gradiometer with entangled twin light beams

In the past few decades, optical magnetometry has experienced remarkable development and reached to an outstanding sensitivity. For magnetometry based on optical readout of atomic ensemble, the fundamental limitation of sensitivity is restricted by spin projection noise and photon shot noise. Meanwhile, in practical applications, ambient magnetic noise also greatly limits the sensitivity. To achieve the best sensitivity, it is essential to find an efficacious way to eliminate the noises from different sources, simultaneously. Here, we demonstrate a quantum magnetic gradiometer with sub-shot-noise sensitivity using entangled twin beams with differential detection. The quantum enhancement spans a frequency range from 7 Hz to 6 MHz with maximum squeezing of 5.5 dB below the quantum noise limit. The sensitivity of gradiometer reaches 18 fT/cm[Formula: see text] at 20 Hz. Our study inspires future possibilities to use quantum-enhanced technology in developing sensitive magnetometry for practical applications in noisy and physically demanding environments.

Analysis and Measurement of Differential-Mode Magnetic Noise in Mn-Zn Soft Ferrite Shield for Ultra-Sensitive Sensors

The magnetic noise generated by the ferrite magnetic shield affects the performance of ultra-sensitive atomic sensors. Differential measurement can effectively suppress the influence of common-mode (CM) magnetic noise, but the limit of suppression capability is not clear at present. In this paper, a finite element analysis model using power loss to calculate differential-mode (DM) magnetic noise under a ferrite magnetic shield is proposed. The experimental results confirm the feasibility of the model. An ultrahigh-sensitive magnetometer was built, the single channel magnetic noise measured and the differential-mode (DM) magnetic noise are 0.70 fT/Hz^1/2 and 0.10 fT/Hz^1/2 @30 Hz. The DM magnetic noise calculated by the proposed model is less than 5% different from the actual measured value. To effectively reduce DM magnetic noise, we analyze and optimize the structure parameters of the shield on the DM magnetic noise. When the outer diameter is fixed, the model is used to analyze the influence of the ratio of ferrite magnetic shielding thickness to outer diameter, the ratio of length to outer diameter, and the air gap between magnetic annuli on DM magnetic noise. The results show that the axial DM magnetic noise and radial DM magnetic noise reach the optimal values when the thickness to outer diameter ratio is 0.08 and 0.1. The ratio of length to outer diameter is negatively correlated with DM magnetic noise, and the air gap (0.1-1 mm) is independent of DM magnetic noise. The axial DM magnetic noise is less than that of radial DM magnetic noise. These results are useful for suppressing magnetic noise and breaking through the sensitivity of the magnetometer.

High-sensitivity operation of an unshielded single cell radio-frequency atomic magnetometer

Real-world applications of atomic magnetometers require the ability to operate them with high-sensitivity in the presence of magnetic noise. In the present work, high-sensitivity operation of unshielded atomic magnetometers in a magnetically noisy environment is demonstrated. The distinguishing feature of the demonstrated approach is the implementation of active in-situ bias field stabilization using multiple fluxgate magnetometers. This is combined with the use of a counter-propagating pump and triple-pass probe configuration, to maximize the atomic polarization and the probe rotation respectively, so to reach high-sensitivity. The improvement in sensitivity of the unshielded system with respect to previous realizations is fully characterized, with the contributions of the different modifications of the apparatus individually quantified. The presented set-up is suitable for the detection of long-range magnetic fields, where shielding or differential measurements using multi-sensor set-ups do not constitute viable options.

Gradient Field Detection Using Interference of Stimulated Microwave Optical Sidebands

We demonstrate that stimulated microwave optical sideband generation using parametric frequency conversion can be utilized as a powerful technique for coherent state detection in atomic physics experiments. The technique has advantages over traditional absorption or polarization rotation-based measurements and enables the isolation of signal photons from probe photons. We outline a theoretical framework that accurately models sideband generation using a density matrix formalism. Using this technique, we demonstrate a novel intrinsic magnetic gradiometer that detects magnetic gradient fields between two spatially separated vapor cells by measuring the frequency of the beat note between sidebands generated within each cell. The sidebands are produced with high efficiency using parametric frequency conversion of a probe beam interacting with ^{87}Rb atoms in a coherent superposition of magnetically sensitive hyperfine ground states. Interference between the sidebands generates a low-frequency beat note whose frequency is determined by the magnetic field gradient between the two vapor cells. In contrast to traditional gradiometers the intermediate step of measuring the magnetic field experienced by the two vapor cells is unnecessary. We show that this technique can be readily implemented in a practical device by demonstrating a compact magnetic gradiometer sensor head with a sensitivity of 25  fT/cm/sqrt[Hz] with a 4.4 cm baseline, while operating in a noisy laboratory environment unshielded from Earth's field.

Transforming and comparing data between standard SQUID and OPM-MEG systems

Optically pumped magnetometers (OPMs) have recently become so sensitive that they are suitable for use in magnetoencephalography (MEG). These sensors solve operational problems of the current standard MEG, where superconducting quantum interference device (SQUID) gradiometers and magnetometers are being used. The main advantage of OPMs is that they do not require cryogenics for cooling. Therefore, they can be placed closer to the scalp and are much easier to use. Here, we measured auditory evoked fields (AEFs) with both SQUID- and OPM-based MEG systems for a group of subjects to better understand the usage of a limited sensor count OPM-MEG. We present a theoretical framework that transforms the within subject data and equivalent simulation data from one MEG system to the other. This approach works on the principle of solving the inverse problem with one system, and then using the forward model to calculate the magnetic fields expected for the other system. For the source reconstruction, we used a minimum norm estimate (MNE) of the current distribution. Two different volume conductor models were compared: the homogeneous conducting sphere and the three-shell model of the head. The transformation results are characterized by a relative error and cross-correlation between the measured and the estimated magnetic field maps of the AEFs. The results for both models are encouraging. Since some commercial OPMs measure multiple components of the magnetic field simultaneously, we additionally analyzed the effect of tangential field components. Overall, our dual-axis OPM-MEG with 15 sensors yields similar information to a 62-channel SQUID-MEG with its field of view restricted to the right hemisphere.

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/Hz^1/2 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.

Characterizing atomic magnetic gradiometers for fetal magnetocardiography

Atomic magnetometers (AMs) offer many advantages over superconducting quantum interference devices due to, among other things, having comparable sensitivity while not requiring cryogenics. One of the major limitations of AMs is the challenge of configuring them as gradiometers. We report the development of a spin-exchange relaxation free vector atomic magnetic gradiometer with a sensitivity of 3 fT cm^-1 Hz^-1/2 and common mode rejection ratio >150 in the band from DC to 100 Hz. We introduce a background suppression figure of merit for characterizing the performance of gradiometers. It allows for optimally setting the measurement baseline and for quickly assessing the advantage, if any, of performing a measurement in a gradiometric mode. As an application, we consider the problem of fetal magnetocardiography (fMCG) detection in the presence of a large background maternal MCG signal.

Acousto-optic modulation detection method in an all-optical K-Rb hybrid atomic magnetometer using uniform design method

An acousto-optic modulation (AOM) detection method is demonstrated to detect the atomic Larmor precession frequency in an all-optical K-Rb atomic magnetometer operated in Spin-Exchange Relaxation Free (SERF) regime. Magnetic field sensitivity of 14 fT/Hz^1/2 was achieved by employing the uniform design (UD) [Acta Math Appl Sin.3, 363 (1980)] and subsequently optimizing the AOM modulation conditions. Results were compared to those of Faraday and the balanced polarimetry method in the same magnetometer. The AOM detection method has several advantages, such as small volume, no extra magnetic shielding for the modulator, high measurement signal-to-noise ratio and stability. It has a good prospect for compact and multi-channel atomic magnetometers.

Optimal densities of alkali metal atoms in an optically pumped K-Rb hybrid atomic magnetometer considering the spatial distribution of spin polarization

An optically pumped K-Rb hybrid atomic magnetometer can be a useful tool for biomagnetic measurements due to the high spatial homogeneity of its sensor property inside a cell. However, because the property varies depending on the densities of potassium and rubidium atoms, optimization of the densities is essential. In this study, by using the Bloch equations of K and Rb and considering the spatial distribution of the spin polarization, we confirmed that the calculation results of spin polarization behavior are in good agreement with the experimental data. Using our model, we calculated the spatial distribution of the spin polarization and found that the optimal density of K atoms is 3 × 10¹⁹ m^-3 and the optimal density ratio is n_K/n_Rb ~ 400 to maximize the output signal and enhance spatial homogeneity of the sensor property.

Measurement Sensitivity Improvement of All-Optical Atomic Spin Magnetometer by Suppressing Noises

Quantum manipulation technology and photoelectric detection technology have jointly facilitated the rapid development of ultra-sensitive atomic spin magnetometers. To improve the output signal and sensitivity of the spin-exchange-relaxation-free (SERF) atomic spin magnetometer, the noises influencing on the output signal and the sensitivity were analyzed, and the corresponding noise suppression methods were presented. The magnetic field noises, including the residual magnetic field noise and the light shift noise, were reduced to approximately zero by employing the magnetic field compensation method and by adjusting the frequency of the pump beam, respectively. With respect to the operation temperature, the simulation results showed that the temperature of the potassium atomic spin magnetometer realizing the spin-exchange relaxation-free regime was 180 °C. Moreover, the fluctuation noises of the frequency and the power were suppressed by using the frequency and the power stable systems. The experimental power stability results showed that the light intensity stability was enhanced 10%. Contrast experiments on the sensitivity were carried out to demonstrate the validity of the suppression methods. Finally, a sensitivity of 13 fT/Hz(1/2) was successfully achieved by suppressing noises and optimizing parameters.

Optimal Magnetic Sensor Vests for Cardiac Source Imaging

Magnetocardiography (MCG) non-invasively provides functional information about the heart. New room-temperature magnetic field sensors, specifically magnetoresistive and optically pumped magnetometers, have reached sensitivities in the ultra-low range of cardiac fields while allowing for free placement around the human torso. Our aim is to optimize positions and orientations of such magnetic sensors in a vest-like arrangement for robust reconstruction of the electric current distributions in the heart. We optimized a set of 32 sensors on the surface of a torso model with respect to a 13-dipole cardiac source model under noise-free conditions. The reconstruction robustness was estimated by the condition of the lead field matrix. Optimization improved the condition of the lead field matrix by approximately two orders of magnitude compared to a regular array at the front of the torso. Optimized setups exhibited distributions of sensors over the whole torso with denser sampling above the heart at the front and back of the torso. Sensors close to the heart were arranged predominantly tangential to the body surface. The optimized sensor setup could facilitate the definition of a standard for sensor placement in MCG and the development of a wearable MCG vest for clinical diagnostics.