Dynamics of two overlapping spin ensembles interacting by spin exchange

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.

Observation of magnetic amplification using dark spins

Quantum amplification enables the enhancement of weak signals and is of great importance for precision measurements, such as biomedical science and tests of fundamental symmetries. Here, we observe a previously unexplored magnetic amplification using dark noble-gas nuclear spins in the absence of pump light. Such dark spins exhibit remarkable coherence lasting up to 6 min and the resilience against the perturbations caused by overlapping alkali-metal gas. We demonstrate that the observed phenomenon, referred to as "dark spin amplification," significantly magnifies magnetic field signals by at least three orders of magnitude. As an immediate application, we showcase an ultrasensitive magnetometer capable of measuring subfemtotesla fields in a single 500-s measurement. Our approach is generic and can be applied to a wide range of noble-gas isotopes, and we discuss promising optimizations that could further improve the current signal amplification up to [Formula: see text] with [Formula: see text]Ne, [Formula: see text] with [Formula: see text]Xe, and [Formula: see text] with [Formula: see text]He. This work unlocks opportunities in precision measurements, including searches for ultralight dark matter with sensitivity well beyond the supernova-observation constraints.

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.

Optimizing noble gas pressure for enhanced self-compensation in spin-exchange relaxation-free comagnetometers

The coupling of electron spin and nuclear spin through spin-exchange collisions compensates for external magnetic field interference in the spin-exchange relaxation-free (SERF) comagnetometer. However, the compensation ability for magnetic field interference along the detection axis is limited due to the presence of nuclear spin relaxation. This paper aims to enhance the self-compensation capability of the system by optimizing the pressure of the noble gas during cell filling. Models are established to describe the relationships between the nuclear spin polarization, the polarizing magnetic field of nuclei, the magnetic field suppression factors, and the pressure of the noble gas in the K-Rb-21Ne atomic ensemble. Experiments are conducted using five cells with different pressure. The results indicate that in the positive pressure area, the nuclear spin polarization decreases while the equivalent magnetic field experienced by the noble gas increases with increasing pressure. The magnetic field suppression factor for transverse fields increases as the pressure increases, leading to a decrease in the ability to suppress low-frequency magnetic field interference. Moreover, at the cell temperature of 180°C and a transverse residual field gradient of 4.012 nT/cm, the system exhibits its strongest capability to suppress transverse magnetic field interference when the pressure of 21Ne is around 0.7 atm.

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.

Construction and signal analysis of a reflective single-beam spin-exchange relaxation-free comagnetometer for rotation measurement

The single-beam comagnetometer working in the spin-exchange relaxation-free (SERF) state is being developed into a miniaturized atomic sensor with extremely high precision in rotation measurement. In this paper, we propose a reflective configuration for the single-beam SERF comagnetometer. The laser light simultaneously used for optical pumping and signal extraction is designed to pass through the atomic ensemble twice. In the optical system, we propose a structure composed of a polarizing beam splitter and a quarter-wave plate. With this, the reflected light beam can be separated entirely from the forward propagating one and realize a complete light collection with a photodiode, making the least light power loss. In our reflective scheme, the length of interaction between light and atoms is extended, and because the power of the DC light component is attenuated, the photodiode can work in a more sensitive range and has a better photoelectric conversion coefficient. Compared with the single-pass scheme, our reflective configuration has a stronger output signal and performs better signal-to-noise ratio and rotation sensitivity. Our work has an important impact on developing miniaturized atomic sensors for rotation measurement in the future.

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.

Study on the Magnetic Noise Characteristics of Amorphous and Nanocrystalline Inner Magnetic Shield Layers of SERF Co-Magnetometer

With the widespread use of magneto-sensitive elements, magnetic shields are an important part of electronic equipment, ultra-sensitive atomic sensors, and in basic physics experiments. Particularly in Spin-exchange relaxation-free (SERF) co-magnetometers, the magnetic shield is an important component for maintaining the SERF state. However, the inherent noise of magnetic shield materials is an important factor limiting the measurement sensitivity and accuracy of SERF co-magnetometers. In this paper, both amorphous and nanocrystalline materials were designed and applied as the innermost magnetic shield of an SERF co-magnetometer. Magnetic noise characteristics of different amorphous and nanocrystalline materials used as the internal magnetic shielding layer of the magnetic shielding system were analyzed. In addition, the effects on magnetic noise due to adding aluminum to amorphous and nanocrystalline materials were studied. The experimental results show that compared with an amorphous material, a nanocrystalline material as the inner magnetic shield layer can effectively reduce the magnetic noise and improve the sensitivity and precision of the rotation measurement. Nanocrystalline material is very promising for inner shield composition in SERF co-magnetometers. Furthermore, its ultra-thin structure and low cost have significant application value in the miniaturization of SERF co-magnetometers.

Analysis on the effect of electron spin polarization on a hybrid optically pumped K-Rb-21Ne co-magnetometer

In this paper, the effect of longitudinal electron spin polarization under the combined action of alkali metal density ratio and pump laser power density on the hybrid optically pumped co-magnetometer operated in the spin-exchange relaxation-free (SERF) regime is studied. The AC response model of rotation velocity and magnetic noise of the SERF co-magnetometer system is proposed, and the factors of frequency and system bandwidth are considered. Based on the proposed response model, the error equation of the system is obtained, and the relationship between alkali metal density ratio and pump laser power density and the system noise response is theoretically analyzed and experimentally tested. The results show that when the product of pumping rate and alkali metal density ratio is greater than the electron spin relaxation rate, there is a longitudinal electron spin polarization point that minimizes the system error. In addition, the range of minimum error calculated results obtained by changing the pumping rate for the cells with different alkali metal density ratios is within 5% of the average value, that is, their minimum error potential is roughly the same within a certain range. Under the experimental conditions in this paper, due to the limitation of the electron spin relaxation rate and the operating capacity of the pump laser, the optimal alkali metal density ratio range is about 1/100-1/300.

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 .

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.

Analysis and Suppression of Thermal Magnetic Noise of Ferrite in the SERF Co-Magnetometer

The ferrite magnetic shield is widely used in ultra-high-sensitivity atomic sensors because of its low noise characteristics. However, its noise level varies with temperature and affects the performance of the spin-exchange relaxation-free (SERF) co-magnetometer. Therefore, it is necessary to analyze and suppress the thermal magnetic noise. In this paper, the thermal magnetic noise model of a ferrite magnetic shield is established, and the thermal magnetic noise of ferrite is calculated more accurately by testing the low-frequency complex permeability at different temperatures. A temperature suppression method based on the improved heat dissipation efficiency of the ferrite magnetic shield is also proposed. The magnetic noise of the ferrite is reduced by 46.7%. The experiment is basically consistent with the theory. The sensitivity of the co-magnetometer is decreased significantly, from 1.21 × 10-5°/s/Hz1/2 to 7.02 × 10-6°/s/Hz1/2 at 1 Hz. The experimental results demonstrate the effectiveness of the proposed method. In addition, the study is also helpful for evaluating the thermal magnetic noise of other materials.

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

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

Investigation on the pulse response of a spin-exchange relaxation-free comagnetometer

We investigate the magnetic pulse response of the optically pumped comagnetometer operated in the spin-exchange relaxation-free (SERF) regime. The pulse response model describing the evolution of the coupled spin ensemble of alkali metal and noble gas during and after the pulse is established for the first time. A three-beam comagnetometer is created with a circularly and two linearly polarized lasers to detect the responses in the three axes of the comagnetometer simultaneously and independently. The results indicate that the response to the small pulse excitation is dominated by the electron spins, while the response to the large pulse excitation and both responses after the pulse excitation consist of a fast and a slow oscillation, which are dominated by the electron spins and nuclear spins, respectively. We also observe novel dynamics of the coupled spin ensemble when the nuclear spins are tipped far away from equilibrium. The theory and method presented here can not only facilitate the investigation on the dynamics of the optically pumped coupled spin ensemble, but also shed light on the application of the pulse modulation technology in the SERF comagnetometer.

Transverse light-shift in a spin-exchange relaxation-free co-magnetometer: measurement, decoupling, and suppression

The transverse light-shift can induce non-negligible polarization error in the output signal of spin-exchange relaxation-free (SERF) co-magnetometer. In this paper, a novel method for rapid measurement of transverse light-shift based on the error of steady-state response of co-magnetometer is proposed firstly, then the sources of transverse light-shift in a compact SERF co-magnetometer is modeled and analyzed from three aspects: the non-ideal linear polarization of probe laser, the circular dichroism of the atomic spin ensembles, and the stress-induced birefringence effect of the cell wall. Furthermore, the decoupling and suppression methods of transverse light-shift based on a degree of circular polarization (DOCP) regulation scheme is presented, to realize the decoupling measurement of the transverse light-shift introduced by the whole co-magnetometer cell, and cancel it out with the non-ideal linear polarization of the probe laser. Eventually, the DOCP regulation scheme suggested in this paper achieves more than a 67% suppression ratio in transverse light-shift, and the short- and long-term performance of SERF co-magnetometer are improved due to the reduction of the coupling effect between the probe laser power and transverse field. Moreover, the measurement, decoupling and suppression methods provided in this paper also have the potential to be applied to other atomic sensors, such as the SERF magnetometers and nuclear spin co-magnetometers.

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).

Optimized Design of a Pump Laser System for a Spin Exchange Relaxation Free Inertial Measurement Device

In order to improve the precision and beam quality of a pump laser for a spin exchange relaxation free inertial measurement device, we applied one scheme to achieve the square wave modulation and power stability control of the pump laser and another one to obtain the uniform intensity distribution of the laser beam, in which the acousto-optic modulator (AOM) and proportion integration differentiation (PID) controller were used to achieve the former, and the freeform surface lens was designed and optimized to achieve the latter based on the TracePro software. In experiments, the first-order diffraction light beam coming through the AOM had a spot size of about 1.1×0.7 mm², and a spherical vapor cell with a radius of 7 mm was placed behind the freeform surface lens. Results show that the uniformity of the reshaped intensity distribution is higher than 90% within the target area with a radius of 7 mm both in the simulation and the experiment, which ensure that the uniform laser beam covers the area of cell. On the other hand, the power stability of the pump laser is controlled to be less than 0.05%. Compared with traditional methods, the complicated calculation process in optical design is better solved, and a higher uniformity with slight energy loss is achieved.

Coupling light to a nuclear spin gas with a two-photon linewidth of five millihertz

Nuclear spins of noble gases feature extremely long coherence times but are inaccessible to optical photons. Here, we realize a coherent interface between light and noble-gas spins that is mediated by alkali atoms. We demonstrate the optical excitation of the noble-gas spins and observe the coherent back action on the light in the form of high-contrast two-photon spectra. We report on a record two-photon linewidth of 5 ± 0.7 mHz above room temperature, corresponding to a 1-min coherence time. This experiment provides a demonstration of coherent bidirectional coupling between light and noble-gas spins, rendering their long-lived spin coherence accessible for manipulations in the optical domain.

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.

Search for topological defect dark matter with a global network of optical magnetometers

Ultralight bosons such as axion-like particles are viable candidates for dark matter. They can form stable, macroscopic field configurations in the form of topological defects that could concentrate the dark matter density into many distinct, compact spatial regions that are small compared with the Galaxy but much larger than the Earth. Here we report the results of the search for transient signals from the domain walls of axion-like particles by using the global network of optical magnetometers for exotic (GNOME) physics searches. We search the data, consisting of correlated measurements from optical atomic magnetometers located in laboratories all over the world, for patterns of signals propagating through the network consistent with domain walls. The analysis of these data from a continuous month-long operation of GNOME finds no statistically significant signals, thus placing experimental constraints on such dark matter scenarios.

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.

Investigation on magnetic field response of a 87Rb-129Xe atomic spin comagnetometer

The magnetic field response of a ⁸⁷Rb-¹²⁹Xe atomic spin comagnetometer operated in the spin-exchange relaxation-free (SERF) regime was investigated. The response model of the comagnetometer to the transverse magnetic fields along the y-axis and the x-axis considering the couple of electron spin and nuclear spin is presented. In the experiment, a high hybrid resonance peak near low-frequency was observed. By fitting the hybrid resonance with the presented response model, a pair of poles at 0.62 Hz and 1.8 Hz were obtained which correspond to the nuclear spin resonance and the electron spin resonance, respectively. The magnetic field response characteristic of the ⁸⁷Rb-¹²⁹Xe comagnetometer with different nuclear magnetic fields and electronic magnetic fields was simulated and analyzed. The simulation results indicate that the hybrid resonance frequency can be right-shifted by the larger nuclear magnetic field while the magnetic field suppression factor can be decreased by the larger electron magnetic field. This study is helpful to improve the performance of the atomic spin gyroscope based on the ⁸⁷Rb-¹²⁹Xe comagnetometer.

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

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

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.

Long-Lived Entanglement Generation of Nuclear Spins Using Coherent Light

Nuclear spins of noble-gas atoms are exceptionally isolated from the environment and can maintain their quantum properties for hours at room temperature. Here we develop a mechanism for entangling two such distant macroscopic ensembles by using coherent light input. The interaction between the light and the noble-gas spins in each ensemble is mediated by spin-exchange collisions with alkali-metal spins, which are only virtually excited. The relevant conditions for experimental realizations with ^{3}He or ^{129}Xe are outlined.

Effects of pump laser power density on the hybrid optically pumped comagnetometer for rotation sensing

We investigate the effects of pump laser power density on the hybrid optically pumped comagnetometer operated in the spin-exchange relaxation-free (SERF) regime. The analytic steady-state output model for the comagnetometer considering two alkali metal species and one nuclear species is presented for the first time. And the effects of pump laser power density on the rotation sensitivity, suppression of low-frequency magnetic noise and long-term stability of the comagnetometer are studied experimentally. The results indicate that when the product of pumping rate and density ratio of pumped atom to probed atom is equal to the spin relaxation rate of the probed atom, the maximum response and highest sensitivity of the comagnetometer are achieved. However, the suppression of low-frequency magnetic noise and long-term stability improve with the increasing of pump laser power density due to the increasing of nuclear spin polarization. Our focus is to optimize the performance of the comagnetometer for rotation sensing, but the theory and method presented here are relevant to all applications of the hybrid optical pumping technique.

"Radiation Damping" in gas spin comagnetometers

We report a new kind of interaction between overlapping Rb-Xe spin ensembles polarized by spin-exchange optical pumping. The Rb acts as both a medium to optically polarize the Xe spins and as a magnetometer to probe the precession of Xe spins. When Xe spins precess, they result in the precession of Rb spins. Like the radiation damping effect caused by the coil in conventional NMR systems, the precessing Rb spins lead to damping and a frequency-shift for the precessing Xe spins. When Xe spins are operated in a free-induction decay mode, the transverse relaxation time and oscillating frequency of Xe spins change due to the "radiation damping" effect of Rb spins. When Xe spins are operated in the self-oscillating mode, its transverse relaxation time and oscillating frequency will also be changed. These effects will influence the accuracy of NMR probes, which are widely used in the search for CPT- and Lorentz-invariance violations, the fifth force, etc. If this problem is solved or compensated for, the limit of the aforementioned search may be improved.

Light storage for one second in room-temperature alkali vapor

Light storage, the controlled and reversible mapping of photons onto long-lived states of matter, enables memory capability in optical quantum networks. Prominent storage media are warm alkali vapors due to their strong optical coupling and long-lived spin states. In a dense gas, the random atomic collisions dominate the lifetime of the spin coherence, limiting the storage time to a few milliseconds. Here we present and experimentally demonstrate a storage scheme that is insensitive to spin-exchange collisions, thus enabling long storage times at high atomic densities. This unique property is achieved by mapping the light field onto spin orientation within a decoherence-free subspace of spin states. We report on a record storage time of 1 s in room-temperature cesium vapor, a 100-fold improvement over existing storage schemes. Furthermore, our scheme lays the foundations for hour-long quantum memories using rare-gas nuclear spins.

Storing quantum memories for a long time is important and challenging for quantum communication. Here the authors demonstrate a storage time of about 1 s using spin exchange relaxation free resonance in cesium vapor.

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.

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.

Precision measurement of magnetic field based on the transient process in a K-Rb-21Ne co-magnetometer

We demonstrate a novel method of measuring magnetic field based on the transient signal of the K-Rb-²¹Ne co-magnetometer operating in nuclear spin magnetization self-compensation magnetic field regime. The operation condition for self-compensation magnetic field by nuclear spin magnetization of ²¹Ne in steady state is presented. We characterize the dynamics of the coupled spin ensembles by a set of Bloch equations, and formulate the expression of transient output signal. After verifying the stability of this method, the measurement range and error are studied. This method is also verified to be valid in various temperature and pumping light power density.

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.

Synchronous Spin-Exchange Optical Pumping

We demonstrate a new approach to precision NMR with hyperpolarized gases designed to mitigate NMR shifts due to the alkali spin-exchange field. The NMR bias field is implemented as a sequence of alkali (Rb) 2π pulses, allowing the Rb polarization to be optically pumped transverse to the bias field. When the Rb polarization is modulated at the noble-gas (Xe) NMR resonance, spin-exchange collisions buildup a precessing transverse Xe polarization. We study and mitigate novel NMR broadening effects due to the oscillating spin-exchange field. Spin-exchange frequency shifts are suppressed 2500×, and Rb magnetometer gain measurements project photon shot-noise limited NMR frequency uncertainties below 10  nHz/sqrt[Hz].

Advances in atomic gyroscopes: a view from inertial navigation applications

With the rapid development of modern physics, atomic gyroscopes have been demonstrated in recent years. There are two types of atomic gyroscope. The Atomic Interferometer Gyroscope (AIG), which utilizes the atomic interferometer to sense rotation, is an ultra-high precision gyroscope; and the Atomic Spin Gyroscope (ASG), which utilizes atomic spin to sense rotation, features high precision, compact size and the possibility to make a chip-scale one. Recent developments in the atomic gyroscope field have created new ways to obtain high precision gyroscopes which were previously unavailable with mechanical or optical gyroscopes, but there are still lots of problems that need to be overcome to meet the requirements of inertial navigation systems. This paper reviews the basic principles of AIG and ASG, introduces the recent progress in this area, focusing on discussing their technical difficulties for inertial navigation applications, and suggests methods for developing high performance atomic gyroscopes in the near future.

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

We performed a search for neutron spin coupling to a Lorentz- and CPT-violating background field using a magnetometer with overlapping ensembles of K and ³He atoms. The comagnetometer is mounted on a rotary platform for frequent reversal of its orientation. We measure sidereal oscillations in the signal to search for anomalous spin coupling of extra-solar origin. We determine the equatorial components of the background field interacting with the neutron spin to be b˜Xn=(0.1 ± 1.6) × 10⁻³³ GeV and b˜Yn=(2.5 ± 1.6) × 10⁻³³ GeV, improving on the previous limit by a factor of 30. This measurement represents the highest energy resolution of any spin anisotropy experiment.

Limits on new long range nuclear spin-dependent forces set with a K-3He comagnetometer

A magnetometer using spin-polarized K and 3He atoms occupying the same volume is used to search for anomalous nuclear spin-dependent forces generated by a separate 3He spin source. We measure changes in the 3He spin precession frequency with a resolution of 18 pHz and constrain anomalous spin forces between neutrons to be less than 2x10(-8) of their magnetic or less than 2x10(-3) of their gravitational interactions on a length scale of 50 cm. We present new limits on neutron coupling to light pseudoscalar and vector particles, including torsion, and constraints on recently proposed models involving unparticles and spontaneous breaking of Lorentz symmetry.

Push-pull laser-atomic oscillator

A vapor of alkali-metal atoms in the external cavity of a semiconductor laser, pumped with a time-independent injection current, can cause the laser to self-modulate at the "field-independent 0-0 frequency" of the atoms. Push-pull optical pumping by the modulated light drives most of the atoms into a coherent superposition of the two atomic sublevels with an azimuthal quantum number m=0. The atoms modulate the optical loss of the cavity at the sharply defined 0-0 hyperfine frequency. As in a maser, the system is not driven by an external source of microwaves, but a very stable microwave signal can be recovered from the modulated light or from the modulated voltage drop across the laser diode. Potential applications for this new phenomenon include atomic clocks, the production of long-lived coherent atomic states, and the generation of coherent optical combs.

Nuclear spin gyroscope based on an atomic comagnetometer

We describe a nuclear spin gyroscope based on an alkali-metal-noble-gas comagnetometer. Optically pumped alkali-metal vapor is used to polarize the noble-gas atoms and detect their gyroscopic precession. Spin precession due to magnetic fields as well as their gradients and transients can be cancelled in this arrangement. The sensitivity is enhanced by using a high-density alkali-metal vapor in a spin-exchange relaxation free regime. With a K-3He comagnetometer we demonstrate rotation sensitivity of 5 x 10(-7) rad s(-1) Hz(-1/2), equivalent to a magnetic field sensitivity of 2.5 fT/Hz(1/2). The rotation signal can be increased by a factor of 10 using 21Ne with a smaller magnetic moment. The comagnetometer is also a promising tool in searches for anomalous spin couplings beyond the standard model.

NMR detection with an atomic magnetometer

We demonstrate detection of NMR signals using a noncryogenic atomic magnetometer and describe several novel applications of this technique. A nuclear spin-precession signal from water is detected using a spin-exchange-relaxation-free potassium magnetometer. We also demonstrate detection of less than 10(13) 129Xe atoms whose NMR signal is enhanced by a factor of 540 due to Fermi-contact interaction with K atoms. The possibility of using a multichannel atomic magnetometer for fast 3D magnetic resonance imaging is also discussed.

Nonlinear amplification of small spin precession using long-range dipolar interactions

In measurements of small signals using spin precession the precession angle usually grows linearly in time. We show that a dynamic instability caused by spin interactions can lead to an exponentially growing spin-precession angle, amplifying small signals and raising them above the noise level of a detection system. We demonstrate amplification by a factor of greater than 8 of a spin-precession signal due to a small magnetic field gradient in a spherical cell filled with hyperpolarized liquid 129Xe. This technique can improve the sensitivity in many measurements that are limited by the noise of the detection system, rather than the fundamental spin-projection noise.