Spin-exchange Relaxation-free Regime Research Articles

Two-dimensional biaxial magnetic field imaging with millisecond resolution

Multi-axial dynamic magnetic field imaging with femto-Tesla sensitivity paves a promising route for acquiring comprehensive information of the extremely-weak magnetic source. Here we propose a two-dimensional (2D) scanning imaging configuration that can realize rapid biaxial magnetic field measurement. Based on the Bragg diffraction, the configuration utilizes two orthogonally-arranged acousto-optic modulators to scan the probe laser temporally and spatially, realizing a 2D (7 × 7 pixels) magnetic field detection. To solve the multi-axial dynamic magnetic field imaging problem, a non-modulated time-sharing technique is theoretically and experimentally verified. Profiting from the non-modulated biaxial working mode that avoids long demodulation time, the magnetometer realizes millisecond temporal resolution (17.15 ms) for each sensitive axis. Operation in the spin-exchange relaxation-free regime, the single-pixel measurement sensitivity reaches around 2.6 fT/Hz1/2 (y-axis) and 7.5 fT/Hz1/2 (z-axis). Furthermore, weak pump and probe lasers power (500 μW and 350 μW) make it a low-power imaging device.

An Integrated Single-Beam Three-Axis High-Sensitivity Magnetometer

Three-axis atomic magnetometers have great advantages for interpreting information conveyed by magnetic fields. Here, we demonstrate a compact construction of a three-axis vector atomic magnetometer. The magnetometer is operated with a single laser beam and with a specially designed triangular 87Rb vapor cell (side length is 5 mm). The ability of three-axis measurement is realized by reflecting the light beam in the cell chamber under high pressure, so that the atoms before and after reflection are polarized along two different directions. It achieves a sensitivity of 40 fT/Hz in x-axis, 20 fT/Hz in y-axis, and 30 fT/Hz in z-axis under spin-exchange relaxation-free regime. The crosstalk effect between different axes is proven to be little in this configuration. The sensor configuration here is expected to form further values, especially for vector biomagnetism measurement, clinical diagnosis, and field source reconstruction.

Design of a Fiber Alkali Vapor Cell for Atomic Magnetometer for Magnetoencephalography Applications

Spin exchange relaxation free (SERF) atomic magnetometer (AM), based on the Larmor precession of alkali atoms, is considered a promising candidate for magnetoencephalography (MEG) systems with the advantages of high sensitivity and no need for cryogenic devices. The footprint of the sensor header contains alkali vapor cell and bulk optical elements determining the spatial resolution of the MEG system. Optical fiber could separate the vapor cell far from other parts of the sensor header to improve the spatial resolution. However, coupling between glass cell and fibers limits the coupling loss of the light. Here, we describe the design of a fiber-based alkali vapor cell that could alleviate these issues. A pair of fiber cables combining a polarization maintaining fiber (PMF) and hollow-core photonic crystal fibers (HC-PCFs) are enclosed in a vacuum-sealed T-shape glass tube filled with alkali atoms. The fiber cell ensures a flexible integration with most fiber systems. The fiber structure, with an air gap between HC-PCFs, provides a large interaction volume between light and atoms. The vapor of the alkali atoms diffuses into the air core of the HC-PCF from the glass tube by heating. The alkali atoms still contained in SERF regime are within the wall relaxation rates of 12,764 s−1 in the coating fiber cell. The insertion loss due to fiber coupling is analyzed. The coupling efficiency could be 91%, with the fiber structure consisting of a 40 μm diameter HC-PCF and a 1 mm air gap. The limit sensitivity under this condition is simulated at 14.7 fT/Hz1/2. The fabrication technique and the light insertion loss are discussed. The fiber alkali vapor cell is of compact size and has flexible integration with the fiber atomic spin precession detection system.

Femtotesla 4He magnetometer with a multipass cell.

In this Letter, we propose a single-beam nonlinear magneto-optical rotation (NMOR) magnetometer with a multipass 4He gas-discharged cell. In contrast to the single-pass cell, the multipass cell allowed laser beams to pass through the metastable-state atomic ensemble 22 times, which directly increases the optical path length and significantly enhances magneto-optical rotation in the 4He gas sample. Based on nonlinear Faraday rotation, the 4He magnetometer with the multipass cell demonstrates a noise floor of 9 fT/Hz1/2, which approaches the photon-shot noise floor limit of 6.4 fT/Hz1/2. In addition, the wider linewidth in metastable-state atoms realizes an NMOR 4He magnetometer with a 3 dB bandwidth of 4.3 kHz, in contrast to the ultranarrow linewidth in the antirelaxation-coated cells or spin-exchange relaxation-free regime alkali-metal cells with buffer gas. Since the 4He cell functions without heating or cryogenic cooling, the femtotesla sensitivity and kilohertz-bandwidth 4He magnetometer exhibits potential in biomagnetic applications such as magnetocardiography and magnetoencephalography.

Rabi oscillation of spin-polarized rubidium in the spin-exchange relaxation-free regime.

The transient dynamics of atomic spins under oscillating and static magnetic fields have been studied in the spin-exchange relaxation-free (SERF) regime with a dual-beam configuration. The spin-relaxation rate can be accurately measured by detecting the transient response signal of the free induction decay (FID) process within several milliseconds. Leveraging this convenient method for measuring a large relaxation rate in a small cell volume, the dependence of the spin-relaxation rate on the probe intensity and ambient magnetic field was studied in the limit of low spin polarization. Moreover, by theoretical analysis of the dynamic evolution of the Rabi oscillation generated by a consecutive oscillating field and a small static magnetic field, we experimentally demonstrate that the amplitude of the Rabi oscillation is affected by the amplitude of the oscillating field in the SERF regime. According to the retrieved frequency of the FID signal and amplitude of relevant Rabi oscillation, the coil constants were 75.55 ± 0.78~nT/mA, 151.5 ± 0.9~nT/mA, and 116.6 ± 0.3~nT/mA along the x-, y-, and z-axes, respectively.

Level-crossing resonances on open atomic transitions in a buffered Cs vapor cell: Linewidth narrowing, high contrast, and atomic magnetometry applications

The ground-state Hanle effect (GSHE) in alkali-metal atomic vapors using a single circularly polarized wave underlies one of the most robust and simplest techniques in atomic magnetometry. This effect causes a narrow (subnatural-width) resonance in the light wave intensity transmitted through a vapor cell. Usually, GSHE-based sensors operate in the spin-exchange-relaxation-free (SERF) regime. However, this regime requires a relatively high temperature of vapors (150 C or higher), leading to a relatively large heat release and power consumption of the sensor head. Besides, without applying special measures, SERF regime significantly limits a dynamic range of measurements. Here, we study a pump-probe scheme involving a single elliptically polarized wave and a polarimetric detection technique. The wave is in resonance with two adjacent optical transitions in the cesium D1 line (894.6 nm) owing to their overlapping in presence of a buffer gas (Ne, 130 Torr). Using a small (0.1 cm$^3$) glass vapor cell, we demonstrate a possibility of observing subnatural-width resonances with a high contrast-to-width ratio (up to 45 %/mG) under a low-temperature (60 C) regime of operation thanks to a strong light-induced circular dichroism. Basing on a $\Lambda$ scheme of atomic energy levels, we obtain explicit analytical expressions for the line shape. The model reveals a linewidth narrowing effect due to openness of the scheme. This result is unusual for magneto-optical atomic spectroscopy because the openness is commonly considered as a undesirable effect, degrading the resonance characteristics. We estimate a sensitivity of 1.8 pT/$\surd$Hz with a 60 fT/$\surd$Hz sensitivity in the photon-shot-noise limit. The results contribute to the theory of GSHE resonances and can be applied to development of a low-temperature high-sensitivity miniaturized magnetic field sensor with an extended dynamic range.

Design of real time magnetic field compensation system based on fuzzy PI control algorithm for comagnetometer

Alkali-metal-noble-gas comagnetometers operating in the spin exchange relaxation free regime have been widely used in frontier science research and navigation technology. Under normal circumstances, the comagnetometer operates at the compensation point so that any interfering external magnetic field is tracked and suppressed by the nuclear spin. This in turn can greatly diminish the comagnetometer’s sensitivity to the magnetic field; however, its sensitivity to rotations and to anomalous fields is still maintained. The compensation point is typically adjusted manually, which leads to low accuracy and compensation speed, in addition to only allowing short-term magnetic field stability. In order to account for these problems, we designed a three-axis magnetic field compensation system in real time based on LabVIEW, and employed it to a K−RbNe comagnetometer. Our study shows that by using a fuzzy proportional-integral (PI) controller, the compensation point can be tracked in real time and with higher precision when compared with manually adjusted methods, therefore improving the magnetic field stability and sensitivity of the comagnetometer.

A nanocrystalline shield for high precision co-magnetometer operated in spin-exchange relaxation-free regime

Spin-exchange relaxation-free (SERF) co-magnetometer presents promising applications in both inertial navigation and basic physical experiments because of its ultrahigh rotation measurement sensitivity and magnetic field disturbance cancellation capacity. Magnetic shielding system is an essential part of the co-magnetometer, and the intrinsic magnetic noise of shielding material is one of the main factors limiting the sensitivity of co-magnetometer. This paper presents a low-noise nanocrystalline magnetic shield for SERF co-magnetometer. The transfer function model of SERF co-magnetometer to transverse magnetic noise was established based on Bloch equation. The amplitude and frequency band of the co-magnetometer signal noise caused by transverse magnetic noise were quantitatively obtained, and the magnetic noise characteristics of nanocrystalline and other shielding materials were analyzed by theoretical calculation and experimental measurement in the obtained frequency band. The superiority of nanocrystalline in low magnetic noise was verified. Experimental results show that the signal noise and bias instability of the SERF co-magnetometer can be considerably decreased by using the nanocrystalline shield as the inner shield.

Bandwidth Expansion Through Large-Amplitude Modulation and Proportional Feedback for Single-Beam Atomic Magnetometers

Atomic magnetometers are widely acknowledged as one of the most sensitive devices for magnetic field measurement. Our study presents a novel method that enables bandwidth expansion of single-beam magnetometers in the spin-exchange relaxation-free regime. This method bases on increasing the modulation amplitude of magnetic field combining with negative feedback with proportional gain. Through our method, the magnetometer&#x2019;s total relaxation rate is moderately increased by elevating modulation amplitude and frequency, and correspondingly, the detection bandwidth experiences dramatic improvement from 230 Hz to 1380 Hz. The application of negative feedback with proportional gain further increases this bandwidth to higher than 4 kHz, which is over 17 times of its original value. The sensitivity of the magnetometer under this condition is measured as 25 fT/<inline-formula> <tex-math notation="LaTeX">$\text {Hz}^{\text {1/2}}$ </tex-math></inline-formula> for open-loop scheme and 35 fT/<inline-formula> <tex-math notation="LaTeX">$\text {Hz}^{\text {1/2}}$ </tex-math></inline-formula> for closed-loop scheme. Comparatively, the sensitivity measured on conventional conditions in our experiment is 12 fT/<inline-formula> <tex-math notation="LaTeX">$\text {Hz}^{\text {1/2}}$ </tex-math></inline-formula>. This approach offers a profitable trade-off that extraordinary expansion of detection bandwidth can be acquired with the price of a little sensitivity loss. Our method is advantageous for miniaturization of atomic magnetometers as no extra hardware is added, which is of special interest for applications including biomagnetic measurement where large detection bandwidth is sometimes in need.

Ultra-sensitive all-optical comagnetometer with laser heating

Ultra-sensitive comagnetometers, which are designed to detect nuclear- and electron-spin-dependent interaction, have important applications ranging from basic research to inertial navigation systems (INSs). Unfortunately, electric heating, which is typically used in comagnetometers, introduces noise and instability because of the unavoidable generation of a modulated magnetic field. In this study, we investigate and introduce a K-Rb-21Ne comagnetometer that uses laser heating for the first time, when operated in the spin exchange relaxation free regime. The performance of the comagnetometer, which is equipped with both laser heating and electric heating, is investigated, and the two heating modes are compared. The temperature characteristics of the comagnetometer are studied theoretically and experimentally. By optimizing the operating temperature and power density of the pump-light, an equivalent rotation sensitivity of rad−1 s−1 Hz@1 Hz is achieved in laser heating mode. The improvement of laser-heating technology could prove essential to reduce electron relaxation and increase the low-frequency sensitivity of comagnetometers. Our results indicate that laser heating can make comagnetometers more suitable for applications in basic research (fifth forces, dark matter, etc), INSs, and other accurate measurements of electronic and nuclear precession.

Effects of Probe Laser Intensity on Co-Magnetometer Operated in Spin-Exchange Relaxation-Free Regime

The probe laser intensity working point optimization of the co- magnetometer operated in the spin-exchange relaxation-free (SERF) regime is studied theoretically and experimentally in this article. Based on the steady-state solution of the Bloch equation, the error equation of output signal considering the probe laser pumping effect is established. A method for real-time measuring the pumping rate of the probe laser on SERF co- magnetometer is presented. Combined with the measurement results, a method for quickly finding the optimal working point for the probe laser intensity is presented. The signal noise and long-term stability of the co- magnetometer under different probe laser intensities are measured experimentally to verify the accuracy of the law deduced from the theory. The results show that the pumping effect of the probe laser significantly reduces the signal-to-noise ratio of the co- magnetometer, which verifies the necessity of supplementing to error equation in this article. In addition, selecting an appropriate probe laser intensity working point can effectively reduce signal noise and bias instability of the SERF co- magnetometer.

Measuring Spin Polarization of a Spin-Exchange Relaxation-Free Atomic Magnetometer at Extremely Large Optical Depths

This paper presents a method for measuring the spin polarization of spin-exchange relaxation-free (SERF) atomic magnetometers at extremely large optical depths. Owing to the slowing-down effect, the spin polarization can be extracted by measuring the slowing-down factor extracted from the precession frequency. However, this technique is limited by a significant error in the regime of extremely large optical depths, where the pump beam intensity for achieving the optimized spin polarization of alkali atoms is significantly increased. We observed that the instantaneous precession frequency measured in the regime where the spin-exchange rate is not much larger than the Larmor frequency was no longer a constant but varied with the pump beam intensity. Thus, a method for measuring spin polarization based on the ratio of the precession frequency to the measured instantaneous precession frequency is proposed. Based on the proposed method, the spin polarization at a temperature of 473K and optical depth of 64 is measured. The measurement results were accordant with theoretical analysis. The expanded uncertainties of the experimental results varied between 1.8% and 9.6%. The proposed method is also applicable to other atomic devices operated in the SERF regime with extremely large optical depths, such as co-magnetometers and atomic spin gyroscopes.

Cross-Axis projection error in optically pumped magnetometers and its implication for magnetoencephalography systems

Optically pumped magnetometers (OPMs) developed for magnetoencephalography (MEG) typically operate in the spin-exchange-relaxation-free (SERF) regime and measure a magnetic field component perpendicular to the propagation axis of the optical-pumping photons. The most common type of OPM for MEG employs alkali atoms, e.g. 87Rb, as the sensing element and one or more lasers for preparation and interrogation of the magnetically sensitive states of the alkali atoms ensemble. The sensitivity of the OPM can be greatly enhanced by operating it in the SERF regime, where the alkali atoms’ spin exchange rate is much faster than the Larmor precession frequency. The SERF regime accommodates remnant static magnetic fields up to ±5 nT. However, in the presented work, through simulation and experiment, we demonstrate that multi-axis magnetic signals in the presence of small remnant static magnetic fields, not violating the SERF criteria, can introduce significant error terms in OPM's output signal. We call these deterministic errors cross-axis projection errors (CAPE), where magnetic field components of the MEG signal perpendicular to the nominal sensing axis contribute to the OPM signal giving rise to substantial amplitude and phase errors. Furthermore, through simulation, we have discovered that CAPE can degrade localization and calibration accuracy of OPM-based magnetoencephalography (OPM-MEG) systems.

Miniature Wide-Range Three-Axis Vector Atomic Magnetometer

A miniature wide-range three-axis vector atomic magnetometer under spin-exchange relaxation-free regime has been developed. With a cylindrical vapor cell of size 10 mm in diameter and length, we have constructed a single-beam configuration through a polarization-maintaining fiber carrying the laser beam to the sensor and a multimode fiber guiding the transmitted light field to the photodiode. A rotating field on the plane perpendicular to the direction of propagation of the laser and another modulation field in the pump direction, which are generated in the field programmable gate array using direct digital synthesis to measure the three components of the magnetic field simultaneously. The spin-exchange relaxation is suppressed in zero field controlled by a feedback system, thus a wide range and excellent accuracy of three-axis vector atomic magnetometer response is obtained. Consequently, the transverse magnetic field sensitivity of 350 fT/Hz <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/2</sup> and longitudinal field sensitivity of 3pT/Hz <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/2</sup> are achieved with a dynamic range of 60000 nT. This sensor with compact size, wide range and high sensitivity is particularly suitable for geomagnetic observatory and space exploration.

A new wearable multichannel magnetocardiogram system with a SERF atomic magnetometer array

In this study, a wearable multichannel human magnetocardiogram (MCG) system based on a spin exchange relaxation-free regime (SERF) magnetometer array is developed. The MCG system consists of a magnetically shielded device, a wearable SERF magnetometer array, and a computer for data acquisition and processing. Multichannel MCG signals from a healthy human are successfully recorded simultaneously. Independent component analysis (ICA) and empirical mode decomposition (EMD) are used to denoise MCG data. MCG imaging is realized to visualize the magnetic and current distribution around the heart. The validity of the MCG signals detected by the system is verified by electrocardiogram (ECG) signals obtained at the same position, and similar features and intervals of cardiac signal waveform appear on both MCG and ECG. Experiments show that our wearable MCG system is reliable for detecting MCG signals and can provide cardiac electromagnetic activity imaging.

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.

Reducing crosstalk in optically-pumped magnetometer arrays

Optically pumped magnetometers (OPMs) operating in the spin-exchange relaxation-free regime are emerging as alternative sensors to superconducting quantum interference devices (SQUIDs) for magnetoencephalography (MEG). As the number of OPMs in a single imaging system increases to rival SQUID MEG systems, cross-talk between nearby sensors limits the measurement accuracy. We experimentally demonstrate a coil geometry, which generates an order of magnitude less cross-talk (less than 0.5%) than a Helmholtz coil (8%). The new coil design is simple and compact, requiring two coaxial coil pairs that add 1 mm to the 6 mm radius and is driven by a single current driver. The new design maintains a magnetic field homogeneity over the volume of the magnetometer of more than 94%, which is sufficient for the zero-field OPM to operate in a 200 nT ambient field environment. Our result increases the feasibility of high-spatial resolution OPM-based bio-magnetic imaging technology due to the reduction of cross-talk at high sensor density.

Closed-Loop Control of Compensation Point in the K−Rb−21Ne Comagnetometer

We investigate the real-time closed-loop control of compensation point in the K-Rb-$^{21}$Ne comagnetometer operated in the spin-exchange relaxation-free regime. By locking the electron resonance, the alkali metal electrons are free from the fluctuations of the longitudinal ambient magnetic field and nuclear magnetization, which could improve the systematic stability, enlarge the linear measuring range, and suppress the cross-talk error of the comagnetometer. This is the first demonstration of closed-loop control of magnetic field in the single nuclear species comagnetometer, which will be of great significance for rotation sensing as gyroscopes and other high precision metrology applications of the comagnetometer.

Characterization of noise sources in a microfabricated single-beam zero-field optically-pumped magnetometer.

We present an experimental noise characterization of a miniature single-beam absorption-based optically-pumped magnetometer with a noise floor of 7 fT/Hz1/2 operating in the spin-exchange relaxation-free regime. We experimentally evaluate noise arising from the laser intensity, laser frequency, laser polarization, cell temperature, and magnetic field coils used for the phase-sensitive detection of the magnetometer signal. We find that noise in the range between DC and 30 Hz is a result of noise sources coupling to the atoms in a manner similar to a magnetic field, while the noise at frequencies above 30 Hz is mainly due to laser intensity noise. Our results place an upper limit on the noise sources for our system that matches well with the noise spectrum of the magnetometer at frequencies above 5 Hz.

Ultra-sensitive single-beam atom-optical magnetometer using weak measurement method

Ultra-sensitive measurement of the magneto-optical rotation, due to interaction of linearly-polarized light passing through room-temperature Rb85 atoms, in response to change in longitudinal magnetic field (δBz) is demonstrated using the weak measurement method. The polarization rotation angle measurement sensitivity (δϕ) of 16 μrad and hence of the magnetometer of 1 nT, achieved using the weak measurement method is better than the balanced optical polarimetry results by a factor of three. The improvement in the measurement sensitivity is realized via optical amplification of the polarization rotation angle via spin-orbit coupled light beam-field. The method is devoid of external rf(/ac) modulation, allows for optimal tunability of sensitivity depending on the dynamic range of the applied magnetic field and the sensitivity can be further enhanced by operating in the spin exchange relaxation free regime of alkali spin polarization.