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

Ultrasensitive SERF atomic magnetometer with a miniaturized hybrid vapor cell

The chip-scale hybrid optical pumping spin-exchange relaxation-free (SERF) atomic magnetometer with a single-beam arrangement has prominent applications in biomagnetic measurements because of its outstanding features, including ultrahigh sensitivity, an enhanced signal-to-noise ratio, homogeneous spin polarization and a much simpler optical configuration than other devices. In this work, a miniaturized single-beam hybrid optical pumping SERF atomic magnetometer based on a microfabricated atomic vapor cell is demonstrated. Although the optically thin Cs atoms are spin-polarized, the dense Rb atoms determine the experimental results. The enhanced signal strength and narrowed resonance linewidth are experimentally proven, which shows the superiority of the proposed magnetometer scheme. By using a differential detection scheme, we effectively suppress optical noise with an approximate five-fold improvement. Moreover, the cell temperature markedly affects the performance of the magnetometer. We systematically investigate the effects of temperature on the magnetometer parameters. The theoretical basis for these effects is explained in detail. The developed miniaturized magnetometer has an optimal magnetic sensitivity of 20 fT/Hz1/2. The presented work provides a foundation for the chip-scale integration of ultrahighly sensitive quantum magnetometers that can be used for forward-looking magnetocardiography (MCG) and magnetoencephalography (MEG) applications.

Quantum-Enhanced Magnetometry at Optimal Number Density

We study the use of squeezed probe light and evasion of measurement backaction to enhance the sensitivity and measurement bandwidth of an optically pumped magnetometer (OPM) at sensitivity-optimal atom number density. By experimental observation, and in agreement with quantum noise modeling, a spin-exchange-limited OPM probed with off-resonance laser light is shown to have an optimal sensitivity determined by density-dependent quantum noise contributions. Application of squeezed probe light boosts the OPM sensitivity beyond this laser-light optimum, allowing the OPM to achieve sensitivities that it cannot reach with coherent-state probing at any density. The observed quantum sensitivity enhancement at optimal number density is enabled by measurement backaction evasion.

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.

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.

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.

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.

In-situ measurement of the density ratio of K-Rb hybrid vapor cell using spin-exchange collision mixing of the K and Rb light shifts

We investigate a new method that enables the direct measurement of the density ratio of a K-Rb hybrid vapor cell, using the spin-exchange collision mixing of the K and Rb light shifts. The densities for each alkali metals can be further determined using Raoult's law. The mixture of the light shifts in both magnetometers and comagnetometers is formulated using Bloch equations and explained by considering the fast spin-exchange interaction. The relationship between the density ratio and the mixed light shifts is both formulated and simulated. The method was performed on several K-Rb magnetometer- and K-Rb-²¹Ne comagnetometer-cells at different temperatures, pump light powers, and mole fractions of K. The method was further verified by the conventional laser-absorption-spectroscopy method. The new approach has the advantage to measure the density ratio of the optically-thick hybrid alkali atoms, while requiring no additional magnetic field necessary for conventional magnetic-field induced Faraday-rotation techniques. It also has the advantage of in-situ measuring the density ratio under exactly the normal operation of the devices, which means that the errors caused by the heating-effect of the strong pump light and the temperature drift during long-term operation can be real-time monitored.

Temperature characteristics of K-Rb hybrid optically pumped magnetometers with different density ratios

Optically pumped magnetometers (OPMs) that are equipped with hybrid cells of K and Rb have been studied for improving their sensitivity and biomagnetic field measurements. The densities of the two alkali metal atoms and their density ratio are especially important for hybrid OPMs. In this study, we fabricated five hybrid cells using different K and Rb atom densities and measured the output signal intensities by controlling their cell temperatures. The output signal intensity of OPMs has different temperature characteristics depending on the density ratios of K and Rb atoms. The densities of the two atoms at any temperature were estimated based on the Raoult's law, and we compared the experimental results with the calculated results based on the Bloch equations. Furthermore, the numerical calculations that were obtained based on the Bloch equation by incorporating a relaxation term due to the absorption of the probe beam exhibited good agreement with the experimental results. Finally, in case of n_K/n_Rb = 4.85, it is estimated that a sensitivity of 1.6 fT/Hz^1/2 can be achieved by increasing the temperature to 270 °C.

High-sensitivity multi-channel probe beam detector towards MEG measurements of small animals with an optically pumped K-Rb hybrid magnetometer

Multi-channel measurements with fine spatial resolution will make magnetoencephalograms (MEGs) possible with small animals using optically pumped magnetometers (OPMs). Therefore, we fabricated a 20-channel probe-beam detector that uses a K-Rb hybrid OPM to increase the spatial resolution. First, we investigated the sensitivity of the detector using the multi-channel measurements and demonstrated that the detector had a fine sensitivity (10-20 fT/Hz^1/2 at 10 Hz). Subsequently, we measured magnetic field distribution generated from a loop coil and compared those measurements with analytically calculated distributions. The measurements were in good agreement with the theoretical predictions. The experimental results indicate that our newly developed multi-channel OPM detector has sufficient performance specifications for MEG 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.