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

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

A compact and closed-loop spin-exchange relaxation-free atomic magnetometer for wearable magnetoencephalography

Atomic magnetometers operated in the spin-exchange relaxation-free(SERF)regime are the promising sensor to replace superconducting quantum interference devices(SQUIDs)in the biomagnetism field.The SERF magnetometer with compact size and good performance is crucial to the new generation of wearable magnetoencephalography(MEG)system.In this paper,we developed a compact and closed-loop SERF magnetometer with the dimensions of 15.0×22.0×30.0 mm^(3)based on a single-beam configuration.The bandwidth of the magnetometer was extended to 675 Hz while the sensitivity was maintained at 22 f T/Hz^(1/2).A nearly 3-fold enhancement of the bandwidth was obtained in comparison with the open-loop control.The implementation of the closed-loop control also greatly improved the dynamic range,enabling the magnetometer to be robust against the disturbance of the ambient field.Moreover,the magnetometer was successfully applied for the detection of humanα-rhythm and auditory evoked fields(AEFs),which demonstrated the potential to be extended to multi-channel MEG measurements for future neuroscience studies.

A miniaturized spin-exchange relaxation-free atomic magnetometer based on uniform light field

We experimentally study the dynamic characteristics of a miniaturized spin-exchange relaxation-free(SERF) magnetometer based on uniform light field. The ceramic ferrule is used to expand the Gaussian beam to improve light intensity uniformity, while the volume of the sensor is also reduced. This scheme makes the magnetometer have better sensitivity when the detected light intensity is less than 3.16 m W/cm^(2) at 120℃. When the temperature rises to 150℃ the sensitivity under the action of uniform light field is 18.5 f T/Hz^(1/2). The bandwidth of the sensor remains at the original level and meets application needs. The proposed structure improves transverse polarization uniformity within the miniaturized sensor, which is ideal for the magnetoencephalography and magnetocardiography imaging systems.

High contrast atomic magnetometer based on coherent population trapping

We present an experimental and theoretical investigation of the coherent population trapping （CPT） resonance excited on the D1 line of 87Rb atoms by bichromatic linearly polarized laser light. The experimental results show that a lin｜｜lin tran- sition scheme is a promising alternative to the conventional circular-circular transition scheme for an atomic magnetometer. Compared with the circular light transition scheme, linear light accounts for high-contrast transmission resonances, which makes this excitation scheme promising for high-sensitivity magnetometers. We also use linear light and circular light to detect changes of a standard magnetic field, separately.

Dynamic range and linearity improvement for zero-field single-beam atomic magnetometer

Zero-field single-beam atomic magnetometers with transverse parametric modulation for ultra-weak magnetic field detection have attracted widespread attention recently.In this study,we present a comprehensive response model and propose a modification method of conventional first harmonic response by introducing the second harmonic correction.The proposed modification method gives improvement in dynamic range and reduction of linearity error.Additionally,our modification method shows suppression of response instability caused by optical intensity and frequency fluctuations.An atomic magnetometer with single-beam configuration is built to compare the performance between our proposed method and the conventional method.The results indicate that our method’s magnetic field response signal achieves a 5-fold expansion of dynamic range from 2 nT to 10 nT,with the linearity error decreased from 5%to 1%.Under the fluctuations of 5%for optical intensity and±15 GHz detuning of frequency,the proposed modification method maintains intensityrelated instability less than 1%and frequency-related instability less than 8%while the conventional method suffers 15%and 38%,respectively.Our method is promising for future high-sensitive and long-term stable optically pumped atomic sensors.

A modified analytical model of the alkali-metal atomic magnetometer employing longitudinal carrier field

Alkali-metal atomic magnetometers employing longitudinal carrier magnetic field have ultrahigh sensitivity to measure transverse magnetic fields and have been applied in a variety of precise-measurement science and technologies.In practice,the magnetometer response is not rigorously proportional to the measured transverse magnetic fields and the existing fundamental analytical model of this magnetometer is effective only when the amplitudes of the measured fields are very small.In this paper,we present a modified analytical model to characterize the practical performance of the magnetometer more definitely.We find out how the longitudinal magnetization of the alkali metal atoms vary with larger transverse fields.The linear-response capacity of the magnetometer is determined by these factors:the amplitude and frequency of the longitudinal carrier field,longitudinal and transverse spin relaxation time of the alkali spins and rotation frequency of the transverse fields.We give a detailed and rigorous theoretical derivation by using the perturbation-iteration method and simulation experiments are conducted to verify the validity and correctness of the proposed modified model.This model can be helpful for measuring larger fields more accurately and configuring a desirable magnetometer with proper linear range.

A laser pump-re-pump atomic magnetometer

We demonstrate experimentally an atomic magnetometer based on optical pumping theory, a magnetic resonance that is induced by a radio frequency field and dependent on the magnetic field strength. Compared with the conventional method using one radiation field, which is used not only as the probe beam but also as a pump beam, the additional re-pump beam can increase remarkably the amplitude of the signal. It is shown that the amplitude of the magnetic field resonance signal can increase more than 55% by using an additional re-pump beam, which makes the sensitivity of the magnetometer higher. Finally, we investigate the relation between amplitude of the signal and re-pump laser power, and calculate the atomic population in the trapping states with rate equations.

Atomic magnetometer with microfabricated vapor cells based on coherent population trapping

An atomic magnetometer based on coherent population trapping(CPT) resonances in microfabricated vapor cells is demonstrated. Fabricated by the micro-electro-mechanical-system(MEMS) technology, the cells are filled with Rb and Ne at a controlled pressure. An experimental apparatus is built for characterizing properties of microfabricated vapor cells via the CPT effects. The typical CPT linewidth is measured to be about 3 k Hz(1.46 k Hz with approximately zero laser intensity) for the rubidium D1 line at about 90℃. The effects of pressure, temperature and laser intensity on CPT linewidth are studied experimentally. A closed-loop atomic magnetometer is finally finished with a sensitivity of 210.5 p T/Hz1/2 at 1 Hz bandwidth. This work paves the way for developing an integrated chip-scale atomic magnetometer in the future.

Fast In-Situ Triaxial Remanent Magnetic Field Measurement for Single-Beam SERF Atomic Magnetometer Based on Trisection Algorithm

We demonstrate a method for quickly and automatically detecting all three components of a remanent magnetic field around a shielded spin-exchange relaxation-free(SERF)atomic magnetometer(AM)using the trisection algorithm(TSA)for zero-field resonance(ZFR).To satisfy the measurement of AMs,a resonance light of the ^(87)Rb D1 line with a spectral width of less than 1 MHz is converted to circular polarization by a linear polarizer and a quarter-wave plate.After the light beam has passed through the alkali metal vapor cell,the residual magnetic field can be measured by searching for triaxial ZFR optical peaks.The TSA stably reduces the measurement time to 2.41 s on average and improves the measurement accuracy,significantly outpacing existing methods.The weighted averages of all measurements with corresponding uncertainties are(–15.437±0.022)nT,(6.062±0.021)nT,and(–14.158±0.052)nT on the x-,y-,and z-axes,respectively.These improvements could facilitate more extremely weak magnetic studies in real time,such as magnetoencephalography(MEG)and magnetocardiography(MCG)measurements.

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

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

Search for topological defect of axionlike model with cesium atomic comagnetometer

Many terrestrial experiments have been designed to detect domain walls composed of axions or axionlike particles(ALPs), which are promising candidates of dark matter. When the domain wall crosses over the Earth, the pseudoscalar field of ALPs could couple to the atomic spins. Such exotic spin-dependent couplings can be searched for by monitoring the transient-in-time change of the atomic spin precession frequency in the presence of a magnetic field. We propose here a single-species cesium atomic comagnetometer, which measures the spin precession frequencies of atoms in different ground-state hyperfine levels, to eliminate the common-mode magnetic-field variations and search for the exotic nonmagnetic couplings solely between protons and ALPs. With the single-species atomic comagnetometer, we experimentally rule out the possibility that the decay constant of the linear pseudoscalar couplings of ALPs to protons is fp■ 3.71 ×107 Ge V. The advanced system has the potential to constrain the constant to be fp■ 10.7 × 109 Ge V, promising to improve astrophysical constraint level by at least one order of magnitude. Our system could provide a sensitive detection method for the global network of optical magnetometers to search for exotic physics.

Spin dynamics of the potassium magnetometer in spin-exchange relaxation free regime

The laser-pumped potassium spin-exchange relaxation free （SERF） magnetometer is the most sensitive detector of magnetic field and has many important applications. We present the experimental results of our potassium SERF magne- tometer. A pump-probe approach is used to identify the unique spin dynamics of the atomic ensemble in the SERF regime. A single channel sensitivity of 8 f.THz-1/2 is achieved with our SERF magnetometer.

Coherent population trapping magnetometer by differential detecting magneto–optic rotation effect

A pocket coherent population trapping（CPT） atomic magnetometer scheme that uses a vertical cavity surface emitting laser as a light source is proposed and experimentally investigated.Using the differential detecting magneto–optic rotation effect,a CPT spectrum with the background canceled and a high signal-to-noise ratio is obtained.The experimental results reveal that the sensitivity of the proposed scheme can be improved by half an order,and the ability to detect weak magnetic fields is extended one-fold.Therefore,the proposed scheme is suited to realize a pocket-size CPT magnetometer.

In-situ measurement of magnetic field gradient in a magnetic shield by a spin-exchange relaxation-free magnetometer

A method of measuring in-situ magnetic field gradient is proposed in this paper. The magnetic shield is widely used in the atomic magnetometer. However, there is magnetic field gradient in the magnetic shield, which would lead to additional gradient broadening. It is impossible to use an ex-situ magnetometer to measure magnetic field gradient in the region of a cell, whose length of side is several centimeters. The method demonstrated in this paper can realize the in-situ measurement of the magnetic field gradient inside the cell, which is significant for the spin relaxation study. The magnetic field gradients along the longitudinal axis of the magnetic shield are measured by a spin-exchange relaxation-free （SERF） magnetometer by adding a magnetic field modulation in the probe beam＇s direction. The transmissivity of the cell for the probe beam is always inhomogeneous along the pump beam direction, and the method proposed in this paper is independent of the intensity of the probe beam, which means that the method is independent of the cell＇s transmissivity. This feature makes the method more practical experimentally. Moreover, the AC-Stark shift can seriously degrade and affect the precision of the magnetic field gradient measurement. The AC-Stark shift is suppressed by locking the pump beam to the resonance of potassium＇s D1 line. Furthermore, the residual magnetic fields are measured with σ＋- and σ--polarized pump beams, which can further suppress the effect of the AC-Stark shift. The method of measuring in-situ magnetic field gradient has achieved a magnetic field gradient precision of better than 30 pT/mm.

Combined effect of light intensity and temperature on the magnetic resonance linewidth in alkali vapor cell with buffer gas

One of the peculiar phenomenons in non-zero magnetic resonance magnetometer is that, with the increase of the temperature, the magnetic resonance linewidth is narrowed at first instead of broadened due to the increasing collision rate. The magnetometer usually operates at the narrowest linewidth temperature to obtain the best sensitivity. Here, we explain this phenomenon quantitatively considering the nonlinear of the optical pumping in the cell and did experiments to verify this explanation. The magnetic resonance linewidth is measured using one amplitude-modulated pump laser and one continuous probe laser. The field is along the direction orthogonal to the plane of pump and probe beams. We change the temperature from 53℃ to 93℃ and the pumping light from 0.1 mW to 2 mW. The experimental results agree well with the theoretical calculations.

Spin dynamics of magnetic resonance with parametric modulation in a potassium vapor cell

A typical magnetic-resonance scheme employs a static bias magnetic field and an orthogonal driving magnetic field oscillating at the Larmor frequency, at which the atomic polarization precesses around the static magnetic field. Here we demonstrate both theoretically and experimentally the variations of the resonance condition and the spin precession dynamics resulting from the parametric modulation of the bias field. We show that the driving magnetic field with the frequency detuned by different harmonics of the parametric modulation frequency can lead to resonance as well. Also, a series of frequency sidebands centered at the driving frequency and spaced by the parametric modulation frequency can be observed in the precession of the atomic polarization. We further show that the resonant amplitudes of the sidebands can be controlled by varying the ratio between the amplitude and the frequency of the parametric modulation. These effects could be used in different atomic magnetometry applications.

Magnetic shielding property for cylinder with circular, square, and equilateral triangle holes

The shielding property of cylinder with circular, square, and equilateral triangle holes was investigated by finite element analysis(FEA). The hole area(S_(hole)) plays an important role in magnetic circuit on the surface of cylinder. When Sholeis less than the critical area(S_(H)), cylinder with three shapes of holes obtained the same remanent magnetization inside,indicating that the shielding property is unaffected by the shape of the hole. Hence, high-permeability material is the major path of the magnetic field. On the condition of S_(hole)> S_(H), the sequence of the shielding property is equilateral triangle >square > circular, resulting from magnetoresistance of leakage flux in air dielectric. Besides, the anisotropy of shielding property caused by hole structural differences of the cylinder is evaluated. We find that a good shielding effectiveness is gained in the radial direction, compared with the axis direction. This research focuses on providing a theoretical support for the design of magnetic shield and improvement on the magnetic shielding ability.

Measurement of ^(129)Xe frequency shift due to Cs–^(129)Xe collisions

Enhancement factor K0, which characterizes NMR and EPR frequency shifts for Cs-129Xe, is measured for the first time. The enhancement factor r-o was measured to be （702±41） at 80 ℃ and （653±20） at 90 ℃, using the NMR frequency shift, detected by atomic magnetometer at a low magnetic field of 100 nT. This result is useful for predicting the EPR frequency shifts for Cs and the NMR frequency shifts for 129Xe in spin-exchange cells.

Zero-to ultralow-field nuclear magnetic resonance and its applications

As a complementary analysis tool to conventional high-field nuclear magnetic resonance(NMR),zero-to ultralow-field(ZULF)NMR detects nuclear magnetization signals in the sub-microtesla regime.Spin-exchange relaxation-free(SERF)atomic magnetometers provide a new generation of sensitive detectors for ZULF NMR.Owing to features such as low cost,high resolution,and portability,ZULF NMR has recently attracted considerable attention in chemistry,biology,medicine,and tests of fundamental physics.This review describes the basic principles,methodology,and recent experimental and theoretical development of ZULF NMR as well as its applications in spectroscopy,quantum control,imaging,NMR-based quantum devices,and tests of fundamental physics.The future prospects of ZULF NMR are also discussed.