New limit on Lorentz- and CPT-violating neutron spin interactions

New Classes of Magnetic Noise Self-Compensation Effects in Atomic Comagnetometer

Precision measurements of anomalous spin-dependent interactions are often hindered by magnetic noise and other magnetic systematic effects. Atomic comagnetometers use the distinct spin precession of two species and have emerged as important tools for effectively mitigating the magnetic noise. Nevertheless, the operation of existing comagnetometers is limited to very low-frequency noise commonly below 1 Hz. Here, we report a new type of atomic comagnetometer based on a magnetic noise self-compensation mechanism originating from the destructive interference between alkali-metal and noble-gas spins. Our comagnetometer employing K-^{3}He system remarkably suppresses magnetic noise exceeding 2 orders of magnitude at higher frequencies up to 160 Hz. Moreover, we discover that the capability of our comagnetometer to suppress magnetic noise is spatially dependent on the orientation of the noise and can be conveniently controlled by adjusting the applied bias magnetic field. Our findings open up new possibilities for precision measurements, including enhancing the search sensitivity of spin-dark matter particles interactions into unexplored parameter space.

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.

Calibration of the coil constants and nonorthogonal angles of triaxial NMR coils based on in-situ EPR magnetometers

Triaxial magnetic field coils are one of the most important components of magnetic resonance sensors. Traditional measurement methods for coil constants and non-orthogonal angles using fluxgate magnetometers are no longer suitable for small-volume nuclear magnetic resonance sensors. This study presents a method for measuring the coil constants and nonorthogonal angles of triaxial nuclear magnetic resonance coils using the dynamics of the electron paramagnetic resonance magnetometer without requiring any additional calibration equipment. After constructing the in-situ magnetometer, we measured the coil constants of the z- and the x-axes as 1189 nT/mA and 45.53 nT/mA, respectively. We obtained the nonorthogonal angle of approximately 0.18° between the z-axis and the x-y plane with a standard deviation of about 0.03° by solving the relevant trigonometric function. Additionally, the non-orthogonal angle between the x- and y-axes is approximately 1.70° with a standard deviation of about 0.17°. This study is significant for evaluating and reducing signal crosstalk errors and improving the accuracy of NMR sensors.

Fractional Exponential Feedback Control for Finite-Time Stabilization and its Application in a Spin-Exchange Relaxation-Free Comagnetometer

This article is the first work to propose a series of control strategies for the longitudinal electron spin polarization of the spin-exchange relaxation-free comagnetometer system to ensure its ultrastable measurement. Two types of finite-time control strategies are presented for a nonlinear system with affine input. The first control strategy is finite-time fractional exponential feedback control (FEFC), which ensures that the trajectories of an autonomous system converge to an equilibrium state in a finite time that can be specified. The second control strategy is finite-time robust FEFC, which provides a finite-time stability of a nonautonomous system with unknown structures under disturbance and perturbations, and its upper bound of the settling time can be estimated. The theoretical results are supported by numerical simulations.

In Situ Study of the Magnetic Field Gradient Produced by a Miniature Bi-Planar Coil for Chip-Scale Atomic Devices

The miniaturization of quantum sensors is a popular trend for the development of quantum technology. One of the key components of these sensors is a coil which is used for spin modulation and manipulation. The bi-planar coils have the advantage of producing three-dimensional magnetic fields with only two planes of current confinement, whereas the traditional Helmholtz coils require three-dimensional current distribution. Thus, the bi-planar coils are compatible with the current micro-fabrication process and are quite suitable for the compact design of the chip-scale atomic devices that require stable or modulated magnetic fields. This paper presents a design of a miniature bi-planar coil. Both the magnetic fields produced by the coils and their inhomogeneities were designed theoretically. The magnetic field gradient is a crucial parameter for the coils, especially for generating magnetic fields in very small areas. We used a NMR (Nuclear Magnetic Resonance) method based on the relaxation of 131Xe nuclear spins to measure the magnetic field gradient in situ. This is the first time that the field inhomogeneities of the field of such small bi-planar coils have been measured. Our results indicate that the designed gradient caused error is 0.08 for the By and the Bx coils, and the measured gradient caused error using the nuclear spin relaxation method is 0.09±0.02, suggesting that our method is suitable for measuring gradients. Due to the poor sensitivity of our magnetometer under a large Bz bias field, we could not measure the Bz magnetic field gradient. Our method also helps to improve the gradients of the miniature bi-planar coil design, which is critical for chip-scale atomic devices.

Constraints on axion-like dark matter from a SERF comagnetometer

Ultralight axion-like particles are well-motivated relics that might compose the cosmological dark matter and source anomalous time-dependent magnetic fields. We report on terrestrial bounds from the Noble And Alkali Spin Detectors for Ultralight Coherent darK matter (NASDUCK) collaboration on the coupling of axion-like particles to neutrons and protons. The detector uses nuclei of noble-gas and alkali-metal atoms and operates in the Spin-Exchange Relaxation-Free (SERF) regime, achieving high sensitivity to axion-like dark matter fields. Conducting a month-long search, we cover the mass range of 1.4 × 10-12 eV/c2 to 2 × 10-10 eV/c2 and provide limits which supersede robust astrophysical bounds, and improve upon previous terrestrial constraints by over two orders of magnitude for many masses within this range for protons, and up to two orders of magnitude for neutrons. These are the sole reliable terrestrial bounds reported on the coupling of protons with axion-like dark matter, covering an unexplored terrain in its parameter space.

New Limits on Exotic Spin-Dependent Interactions at Astronomical Distances

Exotic spin-dependent interactions involving new light particles address key questions in modern physics. Interactions between polarized neutrons (n) and unpolarized nucleons (N) occur in three forms: g_{S}^{N}g_{P}^{n}σ·r, g_{V}^{N}g_{A}^{n}σ·v, and g_{A}^{N}g_{A}^{n}σ·v×r, where σ is the spin and g's are the corresponding coupling constants for scalar, pseudoscalar, vector, and axial-vector vertexes. If such interactions exist, the Sun and Moon could induce sidereal variations of effective fields in laboratories. By analyzing existing data from laboratory measurements on Lorentz and CPT violation, we derive new experimental upper limits on these exotic spin-dependent interactions at astronomical ranges. Our limits on g_{S}^{N}g_{P}^{n} surpass the previous combined astrophysical-laboratory limits, setting the most stringent experimental constraints to date. We also report new constraints on vector-axial-vector and axial-axial-vector interactions at astronomical scales, with vector-axial-vector limits improved by ∼12 orders of magnitude. We extend our analysis to Hari Dass interactions and obtain new constraints.

BASE-high-precision comparisons of the fundamental properties of protons and antiprotons

Abstract

The BASE collaboration at the antiproton decelerator/ELENA facility of CERN compares the fundamental properties of protons and antiprotons with ultra-high precision. Using advanced Penning trap systems, we have measured the proton and antiproton magnetic moments with fractional uncertainties of 300 parts in a trillion (p.p.t.) and 1.5 parts in a billion (p.p.b.), respectively. The combined measurements improve the resolution of the previous best test in that sector by more than a factor of 3000. Very recently, we have compared the antiproton/proton charge-to-mass ratios with a fractional precision of 16 p.p.t., which improved the previous best measurement by a factor of 4.3. These results allowed us also to perform a differential matter/antimatter clock comparison test to limits better than 3 %. Our measurements enable us to set limits on 22 coefficients of CPT- and Lorentz-violating standard model extensions (SME) and to search for potentially asymmetric interactions between antimatter and dark matter. In this article, we review some of the recent achievements and outline recent progress towards a planned improved measurement of the antiproton magnetic moment with an at least tenfold improved fractional accuracy.

Graphic Abstract

Combined Polarization/Magnetic Modulation of a Transverse NMR Gyroscope

In this paper, we describe a new approach to the continuous operation of a transverse spin-exchange optically pumped NMR gyroscope that utilizes modulation of both the applied bias field and the optical pumping. We demonstrate the simultaneous, continuous excitation of 131Xe and 129Xe using this hybrid modulation approach and the real-time demodulation of the Xe precession using a custom least-squares fitting algorithm. We present rotation rate measurements with this device, with a common field suppression factor of ∼1400, an angle random walk of 21 μHz/Hz, and a bias instability of ∼480 nHz after ∼1000 s.

Ultrasensitive Atomic Comagnetometer with Enhanced Nuclear Spin Coherence

Achieving high energy resolution in spin systems is important for fundamental physics research and precision measurements, with alkali-noble-gas comagnetometers being among the best available sensors. We found a new relaxation mechanism in such devices, the gradient of the Fermi-contact-interaction field that dominates the relaxation of hyperpolarized nuclear spins. We report on precise control over spin distribution, demonstrating a tenfold increase of nuclear spin hyperpolarization and transverse coherence time with optimal hybrid optical pumping. Operating in the self-compensation regime, our ^{21}Ne-Rb-K comagnetometer achieves an ultrahigh inertial rotation sensitivity of 3×10^{-8}  rad/s/Hz^{1/2} in the frequency range from 0.2 to 1.0 Hz, which is equivalent to the energy resolution of 3.1×10^{-23}  eV/Hz^{1/2}. We propose to use this comagnetometer to search for exotic spin-dependent interactions involving proton and neutron spins. The projected sensitivity surpasses the previous experimental and astrophysical limits by more than 4 orders of magnitude.

Atomic spin precession detection method based on the Mach-Zehnder interferometer in an atomic comagnetometer

A new method for the detection of atomic spin precession based on the Mach-Zehnder interferometer (MZI) is proposed and experimentally demonstrated. Different from the conventional polarization detection methods which obtain the atomic spin precession signal by measuring the change of the probe laser power, the proposed method uses the laser modulated by an electro-optic phase modulator (EOM) as the source of the interferometer, and obtains the atomic spin precession signal by measuring the phase difference between the two arms of the MZI. The output of interferometer is independent of the probe laser power, which avoids the system error caused by the fluctuation of the probe laser power, and the long-term stability of the system is effectively improved. At the same time, the method adopts high-frequency electro-optic modulation, which can effectively suppress low-frequency noise, such as 1/f noise, and can significantly improve the detection sensitivity. The rotation sensitivity and long-term stability of the atomic comagnetometer were tested using the MZI detection method and a typical detection method, respectively. The comparison results show that the proposed method has the highest low frequency sensitivity and the potential to improve the long-term stability of the system.

Improved bounds on Lorentz violation from composite pulse Ramsey spectroscopy in a trapped ion

In attempts to unify the four known fundamental forces in a single quantum-consistent theory, it is suggested that Lorentz symmetry may be broken at the Planck scale. Here we search for Lorentz violation at the low-energy limit by comparing orthogonally oriented atomic orbitals in a Michelson-Morley-type experiment. We apply a robust radiofrequency composite pulse sequence in the 2F7/2 manifold of an Yb+ ion, extending the coherence time from 200 μs to more than 1 s. In this manner, we fully exploit the high intrinsic susceptibility of the 2F7/2 state and take advantage of its exceptionally long lifetime. We match the stability of the previous best Lorentz symmetry test nearly an order of magnitude faster and improve the constraints on the symmetry breaking coefficients to the 10−21 level. These results represent the most stringent test of this type of Lorentz violation. The demonstrated method can be further extended to ion Coulomb crystals.

Spin exchange optically pumped nuclear spin self compensation system for moving magnetoencephalography measurement

Recording moving magnetoencephalograms (MEGs ), in which a person's head can move freely as the brain's magnetic field is recorded, has been a key subject in recent years. Here, we describe a method based on an optically pumped atomic co-magnetometer (OPACM) for recording moving MEGs. In the OPACM, hyper-polarized nuclear spins produce a magnetic field that blocks the background fluctuation low-frequency magnetic field noise while the rapidly changing MEG signal is recorded. In this study, the magnetic field compensation was studied theoretically, and we found that the compensation is closely related to several parameters such as the electron spin magnetic field, nuclear spin magnetic field, and holding magnetic field. Furthermore, the magnetic field compensation was optimized based on a theoretical model . We also experimentally studied the magnetic field compensation and measured the responses of the OPACM to different magnetic field frequencies. We show that the OPACM clearly suppresses low-frequency (under 1 Hz) magnetic fields. However, the OPACM responses to magnetic field frequencies around the band of the MEG. A magnetic field sensitivity of 3 fT/Hz^1/2 was achieved. Finally, we performed a simulation of the OPACM during utilization for moving MEG recording. For comparison, the traditional compensation system for moving MEG recording is based on a coil that is around 2 m in dimension , while our compensation system is only 2 mm in dimension .

The Rb-Xe coupling effect in optically pumped NMR gyroscopes

Optically pumped nuclear magnetic resonance (NMR) gyroscope has been widely concerned as a future gyroscope with great development potential. In this study, the Rb-Xe coupling effect in this gyroscope between the alkali metal magnetometer and the noble gas NMR is investigated. The theoretical formulae about this effect are obtained based on Bloch equation and demonstrated by experiments. In order to see the influence of this effect on the gyro signal, the Xe NMR frequency changes with the carrier frequency and demodulation phase of the Rb magnetometer are studied with the deduced formulae. More importantly, theoretical analysis shows that this coupling effect can also significantly reduce the efficiency of the dual species scheme, which is used to suppress the influence of magnetic fluctuation. Therefore, to remove the Rb-Xe coupling effect, a simple and preliminary decoupling scheme operated by locking the phase difference to zero is proposed and demonstrated. All this work is of great significance to the improvement of the NMR gyro performance and future applications.

Single-beam comagnetometer using elliptically polarized light for dual-axis rotation measurement

We have developed a single-beam spin-exchange relaxation-free comagnetometer using elliptically polarized light for dual-axis rotation measurement. The light beam propagating through the glass cell is simultaneously used for optical pumping and signal extraction. Combined with transverse magnetic field modulation, the rotation information can be collected through a balanced polarimeter module and a lock-in amplifier. Also, we propose a decoupling method by adjusting the phase shift of the reference signal, allowing the device to realize biaxial signal decoupling while still maintaining its self-compensation state. Compared to those without decoupling, our method improves the performance of our device in its signal-to-noise ratio and rotation sensitivity. The single-beam comagnetometer scheme and the decoupling method have a positive impact on the development of miniaturized atomic sensors for high-precision inertial measurement.

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.

Analysis and suppression of the misalignment error for the pumping laser in the atomic comagnetometer

The misalignment error of the pumping laser in the atomic comagnetometer (ACM) dramatically diminishes the efficiency of the optical pumping process (characterized by the polarization of the hybrid atomic spin ensembles containing electron spins and nuclear spins) and deteriorates the performance of the ACM (characterized by the Allan standard deviation). In this work, a steady-state response model considering the misalignment error of the pumping laser is established and an in-situ evaluation method for this error is proposed. Based on the evaluation method, the influence of this misalignment error on the pumping efficiency and the performance of the ACM is quantitatively analyzed. Furthermore, a pumping laser alignment method based on the second harmonic of a single-beam magnetometer is then proposed, whose effectiveness is verified by experiments. The experimental results show that compared to the original ACM with the severely misaligned pumping laser, the polarization of the hybrid atomic spin ensembles of the ACM with the pumping laser aligned by the proposed method is increased by about 19%, and the corresponding Allan variance at 100s is reduced by about 40%.

New constraints on axion-like dark matter using a Floquet quantum detector

Dark matter is one of the greatest mysteries in physics. It interacts via gravity and composes most of our universe, but its elementary composition is unknown. We search for nongravitational interactions of axion-like dark matter with atomic spins using a precision quantum detector. The detector is composed of spin-polarized xenon gas that can coherently interact with a background dark matter field as it traverses through the galactic dark matter halo. Conducting a 5-month-long search, we report on the first results of the Noble and Alkali Spin Detectors for Ultralight Coherent darK matter (NASDUCK) collaboration. We limit ALP-neutron interactions in the mass range of 4 × 10^-15 to 4 × 10^-12 eV/c² and improve upon previous terrestrial bounds by up to 1000-fold for masses above 4 × 10^-13 eV/c². We also set bounds on pseudoscalar dark matter models with quadratic coupling.

Response of atomic spin-based sensors to magnetic and nonmagnetic perturbations

Searches for pseudo-magnetic spin couplings require implementation of techniques capable of sensitive detection of such interactions. While Spin-Exchange Relaxation Free (SERF) magnetometry is one of the most powerful approaches enabling the searches, it suffers from a strong magnetic coupling, deteriorating the pseudo-magnetic coupling sensitivity. To address this problem, here, we compare, via numerical simulations, the performance of SERF magnetometer and noble-gas-alkali-metal co-magnetometer, operating in a so-called self-compensating regime. We demonstrate that the co-magnetometer allows reduction of the sensitivity to low-frequency magnetic fields without loss of the sensitivity to nonmagnetic couplings. Based on that we investigate the responses of both systems to the oscillating and transient spin perturbations. Our simulations reveal about five orders of magnitude stronger response to the neutron pseudo-magnetic coupling and about three orders of magnitude stronger response to the proton pseudo-magnetic coupling of the co-magnetometer than those of the SERF magnetometer. Different frequency responses of the co-magnetometer to magnetic and nonmagnetic perturbations enables differentiation between these two types of interactions. This outlines the ability to implement the co-magnetometer as an advanced sensor for the Global Network of Optical Magnetometer for Exotic Physics searches (GNOME), aiming at detection of ultra-light bosons (e.g., axion-like particles).

Active stabilization of terrestrial magnetic field with potassium atomic magnetometer

This paper introduces a magnetically quiet environment where the magnetic-field noise is actively suppressed using an optically pumped potassium magnetometer. In a large dynamic range of Earth's magnetic fields, the magnetic-resonance signals of potassium are completely separated in frequency, and we experimentally demonstrate that one of them could be used to measure and compensate magnetic-field noise. The magnetic-field noise floor after stabilization is ∼100 fT/Hz under a bias field ranging from 20 to 100 μT. This method could be useful for fundamental-physics experiments and biomedical sciences where a large dynamic range of quiet magnetic fields is needed.

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/Hz^1/2 in x-axis, 25 fT/Hz^1/2 in y-axis, 30 fT/Hz^1/2 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.

Analysis and suppression of the polarization error for the optical rotation detection system in an atomic comagnetometer

This paper investigates the laser polarization error in the optical rotation detection system (ORDS) of an atomic comagnetometer (ACM), which will seriously degrade the long-term performance of the ORDS. We first establish an optical transmission model of the ORDS by using Jones matrix concerning the optical imperfection of polarizers. Then, we analyze the polarization error based on this model and propose a novel error suppression method. Finally, we experimentally test the long-term performance of the ORDS and the ACM before and after the polarization error suppression to verify the effectiveness of the proposed method. The experimental results show that the long-term performance of the ORDS and the ACM can be improved by approximately 3.4 times with the proposed polarization error suppression method.

New Limits on Anomalous Spin-Spin Interactions

We report the results of a new search for long-range spin-dependent interactions using a Rb-^{21}Ne atomic comagnetometer and a rotatable electron spin source based on a SmCo_{5} magnet with an iron flux return. By looking for signal correlations with the orientation of the spin source we set new constraints on the product of the pseudoscalar electron and neutron couplings g_{p}^{e}g_{p}^{n}/ℏc<1.7×10^{-14} and on the product of their axial couplings g_{A}^{e}g_{A}^{n}/ℏc<5×10^{-42} to a new particle with a mass of less than about 1  μeV. Our measurements improve by about 2 orders of magnitude previous constraints on such spin-dependent interactions.

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.

Active Magnetic-Field Stabilization with Atomic Magnetometer

A magnetically-quiet environment is important for detecting faint magnetic-field signals or nonmagnetic spin-dependent interactions. Passive magnetic shielding using layers of large magnetic-permeability materials is widely used to reduce the magnetic-field noise. The magnetic-field noise can also be actively monitored with magnetometers and then compensated, acting as a complementary method to the passive shielding. We present here a general model to quantitatively depict and optimize the performance of active magnetic-field stabilization and experimentally verify our model using optically-pumped atomic magnetometers. We experimentally demonstrate a magnetic-field noise rejection ratio of larger than ∼800 at low frequencies and an environment with a magnetic-field noise floor of ∼40 fT/Hz1/2 in unshielded Earth's field. The proposed model provides a general guidance on analyzing and improving the performance of active magnetic-field stabilization with magnetometers. This work offers the possibility of sensitive detections of magnetic-field signals in a variety of unshielded natural environments.

Single-Species Atomic Comagnetometer Based on ^{87}Rb Atoms

The comagnetometer has been one of the most sensitive devices with which to test new physics related to spin-dependent interactions, but the comagnetometers based on overlapping ensembles of multiple spin species usually suffer from systematic errors due to magnetic field gradients. Here, we propose a comagnetometer based on the Zeeman transitions of the dual hyperfine levels in ground-state ^{87}Rb atoms, which shows nearly negligible sensitivity to variations of laser power and frequency, magnetic field, and magnetic field gradients. We measured the hypothetical spin-dependent gravitational energy of the proton with the comagnetometer, which is smaller than 4×10^{-18}  eV, comparable to the most stringent existing constraint. Through optimizing the system parameters such as cell temperature, laser power, amplitude of driving magnetic field, as well as choosing better current source, it is possible to improve the sensitivity of the comagnetometer further.

Bose-Einstein Condensate Comagnetometer

We describe a comagnetometer employing the f=1 and f=2 ground state hyperfine manifolds of a ^{87}Rb spinor Bose-Einstein condensate as colocated magnetometers. The hyperfine manifolds feature nearly opposite gyromagnetic ratios and thus the sum of their precession angles is only weakly coupled to external magnetic fields, while being highly sensitive to any effect that rotates both manifolds in the same way. The f=1 and f=2 transverse magnetizations and azimuth angles are independently measured by nondestructive Faraday rotation probing, and we demonstrate a 44.0(8) dB common-mode rejection in good agreement with theory. We show how the magnetometer coherence time can be extended to ∼1  s, by using spin-dependent interactions to inhibit hyperfine relaxing collisions between f=2 atoms. The technique could be used in high sensitivity searches for new physics on submillimeter length scales, precision studies of ultracold collision physics, and angle-resolved studies of quantum spin dynamics.

A Fast and Efficient Measurement System for Nuclear Spin Relaxation Times in Atomic Vapors

With the rapid progress of cutting-edge research such as quantum measurement technology, nuclear magnetic resonance (NMR) gyroscopes represent a major development direction of high-precision micro-miniature gyroscopes, which have significant advantages such as high precision, small size, and low power consumption. It is meaningful to measure the relaxation times of noble-gas atoms which are crucial indicators to accurately and quickly characterize the vapor cell performance as a core component of gyroscopes. In this paper, a test platform for relaxation time is built and an automatic relaxation time test system based on free induction decay (FID) and the π pulse method is designed to accelerate the relaxation time test. Firstly, the formula of the atomic dynamic process based on the Bloch equation was deduced, a GUI (Graphical User Interface) simulation based on the derived differential equation was conducted, and the moving process of the magnetic moment was visually described. Then, the virtual instrument was used to integrate multiple test instruments into an auto-test system, and LabVIEW programming was used for control to realize the automation of the test process on the test platform. Finally, the test results in different conditions were compared. The results show that the test system is stable and reliable with excellent man–machine interaction, and the measurement efficiency was increased by about 185%, providing an effective test scheme for vapor cell performance.

Static weak magnetic field measurements based on low-field nuclear magnetic resonance

To measure the residual magnetic field, which is a kind of static magnetic fields in the magnetic shields, is a tough task in the design of the cylindrical magnetic shields. Here, we demonstrate a method to measure static weak magnetic fields based on low-field nuclear magnetic resonance (NMR), where the static magnetic field's strength can be obtained by measuring nuclear spin precession's frequency. Atomic magnetometers can be adopted to sense the nuclear spin precession, and the nuclear spin can be adopted to measure the static magnetic field through this indirect method to obtain the static magnetic field's strength. With this method, some adverse factors that can make atomic magnetometers yield fluctuations, such as fluctuations in the light intensity and misalignment of the pump and probe beams, can be avoid. We also measure the axial residual magnetic field in the magnetic shields, where the magnetic field's strength is about 235 pT in the direction along the pump beam. By monitoring NMR signals from protons and fluorine nuclei, we realize a nuclear-spin comagnetometer, which can be used to detect static weak magnetic fields. The possibility of using a miniaturized atomic magnetometer sensor (MAMS) for static field measurements is also discussed.

Dispersion of the Retardation of a Photoelastic Modulator

Recently, ellipsometry and polarization imaging using photoelastic modulators (PEMs) have been applied to a wide spectral range, from vacuum ultraviolet to the mid-infrared wavelengths. To ensure high accuracy polarization performance, the accurate calibration of the retardation of PEM is crucial. In this report, the dispersion of the retardation of the PEM is studied. According to the operational principle of PEM, their retardation can be separated into independent dispersion and driving terms. The effect attributed to the dispersion on PEM retardation calibration is experimentally explored. These experiments indicate that the dispersion term can be defined in advance using the refractive index of the photoelastic crystal under incident light, and that the driving term is directly proportional to the amplitude of the driving voltage. The calibration method for the retardation amplitude of the PEM, which considers dispersion, is also demonstrated. The results show that the relative deviation between the calibration and actual measurement values of PEM retardation amplitude are less than 1%. This study presents an accurate way to calibrate the PEM retardation and supports the application of PEMs in a wide range of wavelengths.

Nuclear-Spin Comagnetometer Based on a Liquid of Identical Molecules

Atomic comagnetometers are used in searches for anomalous spin-dependent interactions. Magnetic field gradients are one of the major sources of systematic errors in such experiments. Here we describe a comagnetometer based on the nuclear spins within an ensemble of identical molecules. The dependence of the measured spin-precession frequency ratio on the first-order magnetic field gradient is suppressed by over an order of magnitude compared to a comagnetometer based on overlapping ensembles of different molecules. Our single-species comagnetometer is capable of measuring the hypothetical spin-dependent gravitational energy of nuclei at the 10^{-17}  eV level, comparable to the most stringent existing constraints. Combined with techniques for enhancing the signal such as parahydrogen-induced polarization, this method of comagnetometry offers the potential to improve constraints on spin-gravity coupling of nucleons by several orders of magnitude.

Next Generation of Phonon Tests of Lorentz Invariance Using Quartz BAW Resonators

We demonstrate technological improvements in phonon sector tests of the Lorentz invariance that implement quartz bulk acoustic wave oscillators. In this experiment, room temperature oscillators with state-of-the-art phase noise are continuously compared on a platform that rotates at a rate of order of a cycle per second. The discussion is focused on improvements in noise measurement techniques, data acquisition, and data processing. Preliminary results of the second generation of such tests are given, and indicate that standard model extension coefficients in the matter sector can be measured at a precision of order 10^-16 GeV after taking a year's worth of data. This is equivalent to an improvement of two orders of magnitude over the prior acoustic phonon sector experiment.

Response of a Bell⁻Bloom Magnetometer to a Magnetic Field of Arbitrary Direction

The Bell–Bloom magnetometer in response to a magnetic field of arbitrary direction is observed theoretically and experimentally. A theoretical model is built from a macroscopic view to simulate the magnetometer frequency response to an external magnetic field of arbitrary direction. Based on the simulation results, the magnetometer characteristics, including the signal phase and amplitude at resonance, the linewidth, and the magnetometer sensitivity, are analyzed, and the dependencies of these characteristics on the external magnetic field direction are obtained, which are verified by the experiment.

Improved Limits on Spin-Mass Interactions

Very light particles with CP-violating couplings to ordinary matter, such as axions or axionlike particles, can mediate long-range forces between polarized and unpolarized fermions. We describe a new experimental search for such forces between unpolarized nucleons in two 250 kg Pb weights and polarized neutrons and electrons in a ^{3}He-K comagnetometer located about 15 cm away. We place improved constraints on the products of scalar and pseudoscalar coupling constants, g_{p}^{n}g_{s}^{N}<4.2×10^{-30} and g_{p}^{e}g_{s}^{N}<1.7×10^{-30} (95% C.L.) for axionlike particle masses less than 10^{-6}  eV, which represents an order of magnitude improvement over the best previous neutron laboratory limit.

^{3}He-^{129}Xe Comagnetometery using ^{87}Rb Detection and Decoupling

We describe a ^{3}He-^{129}Xe comagnetometer using ^{87}Rb atoms for noble-gas spin polarization and detection. We use a train of ^{87}Rb π pulses and σ^{+}/σ^{-} optical pumping to realize a finite-field Rb magnetometer with suppression of spin-exchange relaxation. We suppress frequency shifts from polarized Rb by measuring the ^{3}He and ^{129}Xe spin precession frequencies in the dark, while applying π pulses along two directions to depolarize Rb atoms. The plane of the π pulses is rotated to suppress the Bloch-Siegert shifts for the nuclear spins. We measure the ratio of ^{3}He to ^{129}Xe spin precession frequencies with sufficient absolute accuracy to resolve Earth's rotation without changing the orientation of the comagnetometer. A frequency resolution of 7 nHz is achieved after integration for 8 h without evidence of significant drift.

Nuclear Matrix Elements for Tests of Local Lorentz Invariance Violation

The nuclear matrix elements for the spin operator and the momentum quadrupole operator are important for the interpretation of precision atomic physics experiments that search for violations of local Lorentz and CPT symmetry and for new spin-dependent forces. We use the configuration-interaction nuclear shell model and self-consistent mean-field theory to calculate the momentum matrix elements for ^{21}Ne, ^{23}Na, ^{133}Cs, ^{173}Yb, and ^{201}Hg. We show that these momentum matrix are strongly suppressed by the many-body correlations, in contrast to the well-known enhancement of the spatial quadrupole nuclear matrix elements.

Optically polarized 3He

This article reviews the physics and technology of producing large quantities of highly spin-polarized 3He nuclei using spin-exchange (SEOP) and metastability-exchange (MEOP) optical pumping. Both technical developments and deeper understanding of the physical processes involved have led to substantial improvements in the capabilities of both methods. For SEOP, the use of spectrally narrowed lasers and K-Rb mixtures has substantially increased the achievable polarization and polarizing rate. For MEOP nearly lossless compression allows for rapid production of polarized 3He and operation in high magnetic fields has likewise significantly increased the pressure at which this method can be performed, and revealed new phenomena. Both methods have benefitted from development of storage methods that allow for spin-relaxation times of hundreds of hours, and specialized precision methods for polarimetry. SEOP and MEOP are now widely applied for spin-polarized targets, neutron spin filters, magnetic resonance imaging, and precision measurements.

The polarization and the fundamental sensitivity of 39K (133Cs)-85Rb-4He hybrid optical pumping spin exchange relaxation free atomic magnetometers

The hybrid optical pumping spin exchange relaxation free (SERF) atomic magnetometers can realize ultrahigh sensitivity measurement of magnetic field and inertia. We have studied the ⁸⁵Rb polarization of two types of hybrid optical pumping SERF magnetometers based on ³⁹K-⁸⁵Rb-⁴He and ¹³³Cs-⁸⁵Rb-⁴He respectively. Then we found that ⁸⁵Rb polarization varies with the number density of buffer gas ⁴He and quench gas N₂, pumping rate of pump beam and cell temperature respectively, which will provide an experimental guide for the design of the magnetometer. We obtain a general formula on the fundamental sensitivity of the hybrid optical pumping SERF magnetometer due to shot-noise. The formula describes that the fundamental sensitivity of the magnetometer varies with the number density of buffer gas and quench gas, the pumping rate of pump beam, external magnetic field, cell effective radius, measurement volume, cell temperature and measurement time. We obtain a highest fundamental sensitivity of 1.5073 aT/Hz ^1/2 (1 aT = 10^-18 T) with ³⁹K-⁸⁵Rb-⁴He magnetometer between above two types of magnetometers when ⁸⁵Rb polarization is 0.1116. We estimate the fundamental sensitivity limit of the hybrid optical pumping SERF magnetometer to be superior to 1.8359 × 10^-2 aT/Hz ^1/2, which is higher than the shot-noise-limited sensitivity of 1 aT/Hz ^1/2 of K SERF atomic magnetometer.

Reduction of far off-resonance laser frequency drifts based on the second harmonic of electro-optic modulator detection in the optically pumped magnetometer

The frequency drifts of the probe laser could be coupled into the calibrated scale factor of the optically pumped magnetometer (OPM) and induce an error of the measurement accuracy. We propose a method to reduce the far off-resonance laser frequency drifts based on the second harmonic of the electro-optic modulator (EOM) detection system in the all-optical K-Rb hybrid pumping magnetometer. Adopting the closed-loop feedback by monitoring the second-harmonic component in real time, the frequency drift of the probe laser has been effectively reduced by about five times to ∼30  MHz/0.5  h at the detuning of 130 GHz and the cell temperature of 443 K. Besides, this technique has been demonstrated to be helpful for reducing the frequency drifts at different detuning points and temperatures. This method is not only suitable for the development of more compact, high-sensitivity OPMs due to the long-term stability improvement with no extra optical path, but also can be applied to other atomic devices and EOM detection systems for reducing the influence of the laser.

Elliptical polarization of near-resonant linearly polarized probe light in optically pumped alkali metal vapor

Optically pumped alkali metal atoms currently provide a sensitive solution for magnetic microscopic measurements. As the most practicable plan, Faraday rotation of linearly polarized light is extensively used in spin polarization measurements of alkali metal atoms. In some cases, near-resonant Faraday rotation is applied to improve the sensitivity. However, the near-resonant linearly polarized probe light is elliptically polarized after passing through optically pumped alkali metal vapor. The ellipticity of transmitted near-resonant probe light is numerically calculated and experimentally measured. In addition, we also analyze the negative impact of elliptical polarization on Faraday rotation measurements. From our theoretical estimate and experimental results, the elliptical polarization forms an inevitable error in spin polarization measurements.

Spin exchange broadening of magnetic resonance lines in a high-sensitivity rotating K-Rb-21Ne co-magnetometer

Atomic co-magnetometers can be utilized for high-precision angular velocity sensing or fundamental physics tests. The sensitivity of a co-magnetometer determines the angle random walk of an angular velocity sensor and the detection limit for a fundamental physics test. A high-sensitivity K-Rb-²¹Ne co-magnetometer, which is utilized for angular velocity sensing, is presented in this paper. A new type of spin relaxation of Rb atom spins, which can broaden the zero-field magnetic resonance lines of the co-magnetometer, is discovered. Further studies show that the spin relaxation of Rb atoms is caused by a high Rb electron magnetization field. With this discovery, the total relaxation rate of Rb atoms is optimized to improve the sensitivity of the co-magnetometer. Moreover, its sensitivity is optimized by suppressing various noises. Especially, to suppress laser-related noises, the co-magnetometer is designed such that the sensitive axis of the co-magnetometer can be fixed to the direction in which the projection input of the earth’s rotation is 0. This is called a rotating co-magnetometer. A magnetic field sensitivity of 1.0 fT/Hz^−1/2@5 Hz, which is equal to an angular velocity sensitivity of 2.1 × 10⁻⁸ rad s⁻¹ Hz^−1/2@5 Hz, is demonstrated using a spherical vapour cell with a diameter of 14 mm.

45° double-drive photoelastic modulation

In this report, a new type of double-drive photoelastic modulation effect is studied. Two piezoelectric actuators are connected to a symmetric photoelastic crystal at an angle of 45°. The actuators and crystal have the same resonant frequency. By adjusting the amplitude and phase difference between the driving voltages of the two piezoelectric actuators, two special forms of photoelastic modulation can be realized, namely, a pure standing wave form and a pure traveling wave form. The retardation magnitude and the azimuth angle of the modulation fast axis can be regulated in the pure standing wave, and the modulation axis moves circumferentially in the pure traveling wave. We have experimentally observed the two special photoelastic modulation modes, and the test and calibration methods are also reported.

New classes of systematic effects in gas spin comagnetometers

Atomic comagnetometers are widely used in precision measurements searching for spin interactions beyond the standard model. We describe a new (3)He-(129)Xe comagnetometer probed by Rb atoms and use it to identify two general classes of systematic effects in gas comagnetometers, one associated with diffusion in second-order magnetic-field gradients and another due to temperature gradients. We also develop and confirm experimentally a general and practical approach for calculating spin relaxation and frequency shifts due to arbitrary magnetic-field gradients.

Limiting P-odd interactions of cosmic fields with electrons, protons, and neutrons

We propose methods for extracting limits on the strength of P-odd interactions of pseudoscalar and pseudovector cosmic fields with electrons, protons, and neutrons, by exploiting the static and dynamic parity-nonconserving amplitudes and electric dipole moments they induce in atoms. Candidates for such fields are dark matter (including axions) and dark energy, as well as several more exotic sources described by Lorentz-violating standard model extensions. Atomic calculations are performed for H, Li, Na, K, Rb, Cs, Ba(+), Tl, Dy, Fr, and Ra(+). From these calculations and existing measurements in Dy, Cs, and Tl, we constrain the interaction strengths of the parity-violating static pseudovector cosmic field to be 7 × 10(-15) GeV with an electron, and 3 × 10(-8) GeV with a proton.

A magnetically shielded room with ultra low residual field and gradient

A versatile and portable magnetically shielded room with a field of (700 ± 200) pT within a central volume of 1 m × 1 m × 1 m and a field gradient less than 300 pT/m, achieved without any external field stabilization or compensation, is described. This performance represents more than a hundredfold improvement of the state of the art for a two-layer magnetic shield and provides an environment suitable for a next generation of precision experiments in fundamental physics at low energies; in particular, searches for electric dipole moments of fundamental systems and tests of Lorentz-invariance based on spin-precession experiments. Studies of the residual fields and their sources enable improved design of future ultra-low gradient environments and experimental apparatus. This has implications for developments of magnetometry beyond the femto-Tesla scale in, for example, biomagnetism, geosciences, and security applications and in general low-field nuclear magnetic resonance (NMR) measurements.

What do we know about Lorentz invariance?

The realization that Planck-scale physics can be tested with existing technology through the search for spacetime-symmetry violation brought about the development of a comprehensive framework, known as the gravitational standard-model extension (SME), for studying deviations from exact Lorentz and CPT symmetry in nature. The development of this framework and its motivation led to an explosion of new tests of Lorentz symmetry over the past decade and to considerable theoretical interest in the subject. This work reviews the key concepts associated with Lorentz and CPT symmetry, the structure of the SME framework, and some recent experimental and theoretical results.

New limit on Lorentz-invariance- and CPT-violating neutron spin interactions using a free-spin-precession He3-Xe129 comagnetometer

We report on the search for a CPT- and Lorentz-invariance-violating coupling of the He3 and Xe129 nuclear spins (each largely determined by a valence neutron) to posited background tensor fields that permeate the Universe. Our experimental approach is to measure the free precession of nuclear spin polarized He3 and Xe129 atoms in a homogeneous magnetic guiding field of about 400 nT using LTC SQUIDs as low-noise magnetic flux detectors. As the laboratory reference frame rotates with respect to distant stars, we look for a sidereal modulation of the Larmor frequencies of the colocated spin samples. As a result we obtain an upper limit on the equatorial component of the background field interacting with the spin of the bound neutron b(⊥)(n)<8.4 × 10(-34)  GeV (68% C.L.). Our result improves our previous limit (data measured in 2009) by a factor of 30 and the world's best limit by a factor of 4.