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IEEE Transactions on Instrumentation and Measurement

Circular Dichroism Analysis and Ellipticity Measurement in SERF Atom Ensemble

Haoran Lv, Bozheng Xing, Xiujie Fang, Danyue Ma, Hongtao Lu

Published Jan 1, 2025• 6 citations
Publisher

Abstract

In the research of the interaction between light and atoms, ellipticity is an important characterization of the pump and absorption rates. In previous researches, it was generally believed that ellipticity only originated from the interaction between magnetic fields and polarized alkali metal atomic ensembles. In this article, we derive and analyze the circular dichroism based on density matrix and Maxwell equations during the interaction between magnetic fields, probe light, and alkali metal atomic ensembles in spin-exchange relaxation-free (SERF) regime. We construct an optical path for measuring ellipticity based on photo elastic modulator (PEM) to measure ellipticity. Under different experimental conditions, we compare the measurement results of ellipticity from circular dichroism effect and rotation angle from circular birefringence effect. The results indicates that the interaction between magnetic field and alkali metal atomic ensemble which is polarized by probe light is a new source of ellipticity. Then, we research the ratio of rotation angle to ellipticity, and the results indicates that ellipticity generated by the interaction between the magnetic field and the alkali metal atomic ensemble is an intrinsic characteristic, which is independent of external conditions. The confidence level of the fitting between the experimental results and the theoretical equation is 99.7%. This research can be applied to SERF magnetometers and co-magnetometers.

DOI
10.1109/tim.2025.3545202

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In the research of the interaction between light and atoms, ellipticity is an important characterization of the pump and absorption rates. In previous researches, it was generally believed that ellipticity only originated from the interaction between magnetic fields and polarized alkali metal atomic ensembles. In this article, we derive and analyze the circular dichroism based on density matrix and Maxwell equations during the interaction between magnetic fields, probe light, and alkali metal atomic ensembles in spin-exchange relaxation-free (SERF) regime. We construct an optical path for measuring ellipticity based on photo elastic modulator (PEM) to measure ellipticity. Under different experimental conditions, we compare the measurement results of ellipticity from circular dichroism effect and rotation angle from circular birefringence effect. The results indicates that the interaction between magnetic field and alkali metal atomic ensemble which is polarized by probe light is a new source of ellipticity. Then, we research the ratio of rotation angle to ellipticity, and the results indicates that ellipticity generated by the interaction between the magnetic field and the alkali metal atomic ensemble is an intrinsic characteristic, which is independent of external conditions. The confidence level of the fitting between the experimental results and the theoretical equation is 99.7%. This research can be applied to SERF magnetometers and co-magnetometers.
The spin-exchange relaxation-free (SERF) comagnetometers, owing to their ultra-high sensitivity, are widely applied in fields such as inertial and magnetic field measurements, frontier physics research, etc. This technology relies on pump light to achieve the spin polarization of alkali metal atoms. During this process, the pump light is absorbed and thus attenuated by the alkali metal atoms. In this study, an absorption decay model for elliptically polarized light was solved by the fourth-order Runge-Kutta method, breaking through the applicability limitations of conventional analytical solutions for arbitrary polarized light. The effects of pump light polarization states and power on optical pumping rate, electron polarization, and measurement sensitivity were further investigated. It was found that there is a contradiction in achieving low polarization gradient and high scale coefficient by adjusting light intensity, increasing the pump light intensity can reduce the polarization gradient but will decrease the scale coefficient. Elliptically polarized light can realize low polarization gradient while enhancing the magnetic field response. This research establishes a theoretical foundation for optimizing the selection of pump light parameters in quantum sensors.
High sensitivity measurements of inertia and magnetic field could be achieved by utilizing a category of devices, which manipulate the atomic spins in the spin-exchange-relaxation-free regime. The alkali cell which contains the alkali metal vapor is used to sense magnetic field and inertia. The atomic number density of alkali vapor and the polarization of alkali metal vapor are two of the most important parameters of the cell. They play an important role in the research on atomic spins in the spin-exchange-relaxation-free regime. Besides, optical polarization plays an important role in quantum computing and atomic physics. We propose a measurement of alkali vapor polarization and alkali number density by detecting the optical rotation in one system. This method simplifies existing experimental equipment and processes. A constant bias magnetic field is applied and the Faraday rotation angle is detected by a bunch of the probe beam to deduce alkali-metal density. Then the magnetic field is closed and a bunch of the pump laser is utilized to polarize alkali-metal. Again, the probe beam is utilized to obtain the polarization of alkali metal. The alkali density obtained at first is used to deduce the polarization. This paper applies a numerical method to analyze the Faraday rotation and the polarization rotation. According to the numerical method, the optimal wavelength for the experiment is given. Finally, the fluctuation of magnetic field and wavelength on signal analysis are analyzed.
Optical rotation detection systems are widely used in various kinds of atomic sensors, such as atomic magnetometers, co-magnetometers, and nuclear magnetic resonance (NMR) gyroscopes; and appear in many applications such as fundamental physics, biomagnetism, magnetism test, etc. The study analyses the frequency responses to three-axis dynamic magnetic fields in optical rotation detection systems (ORDS) of Spin-Exchange Relaxation-Free (SERF) magnetometers. Because of the imperfections of the optical elements, the probe light is actually elliptically polarised in ORDS, which can polarise the atom ensemble and cause the responses to the three-axis magnetic field. Theoretically it analyse the frequency responses to the sinusoidal magnetic field, and prove that the responses are closely associated with the DC magnetic field. The values of the DC magnetic fields are calculated with special frequency points, called ‘break points’, in the transverse responses. The relationships between the DC magnetic field and the sensitivities of ORDS, and effectively suppress the magnetic noise responses with the residual magnetic field compensation. The paper demonstrated the influence of elliptically polarised light on the sensitivity of ORDS in SERF magnetometers. The elliptically polarised probe light polarises the alkali atom ensemble, which leads to the responses of the magnetic noise in the shield. Finally, the sensitivity of ORDS is improved by approximately two times at 10-20 Hz. This method is beneficial for improving probe sensitivity in SERF magnetometers, co-magnetometers, and NMR gyroscopes.
Bias instability is one of the most critical factors in the performance of spin-exchange relaxation-free (SERF) co-magnetometers. Previous studies on SERF co-magnetometers have shown that changes in the atomic ensemble temperature can lead to variations in the alkali metal atom density, which in turn affect the optical rotation angle and light shift, ultimately influencing the system’s stability. Building on this understanding, this paper introduces the thermoelectric analogy method for the first time in the transient heat transfer analysis of SERF co-magnetometer atomic ensembles. Using this method, the primary factors affecting the atomic ensemble temperature in a SERF co-magnetometer were analyzed, and transient heat transfer models were established for the following processes: the interaction between the non-magnetic electric heating system and the atomic ensemble temperature, laser heating of the atomic ensemble by the optical system, and the effect of environmental temperature changes on the non-magnetic electric heating system. These models were experimentally validated through active temperature variation experiments. The experimental results show that the proposed transient heat transfer models accurately describe the related heat transfer processes of the atomic ensemble, with model fitting accuracy exceeding 98%. This lays a solid foundation for the high-precision closed-loop control of the atomic ensemble temperature in SERF co-magnetometers and provides valuable insights for the structural design and engineering applications of SERF co-magnetometers.
Recently, atomic magnetometers have been reported as the most sensitive magnetometers by completely eliminating the spin exchange relaxation. In this paper, we described a design of highly sensitive cesium atomic magnetometer based on circular dichroism, which had the advantage of easily locking the probing laser to the necessary frequency compared with those based on circular birefringence. In order to polarize the cesium atoms uniformly, the pumping laser light was separated into two counter-propagating and counter-circular polarization beams through the atomic vapor cell. We employed a circular analyzer optical configuration to measure the ellipticity of the probing light, which indicated the amplitude of the magnetic field. The external magnetic field was tracked by a digital auto frequency tracking system.
Spin-exchange relaxation free alkali-metal magnetometers typically operate in the regime of high optical density, presenting challenges for simple and efficient optical pumping and detection. We describe a high-sensitivity Rb magnetometer using a single elliptically polarized off-resonant laser beam. Circular component of the light creates relatively uniform spin polarization while the linear component is used to measure optical rotation generated by the atoms. Modulation of the atomic spin direction with an oscillating magnetic field shifts the detected signal to high frequencies. Using a fiber-coupled distributed feedback laser, we achieve magnetic field sensitivity of 7 fT/Hz7\text{ }\text{fT}/\sqrt{\text{Hz}}7 fT/Hz​ with a miniature $5\ifmmode\times\else\texttimes\fi{}5\ifmmode\times\else\texttimes\fi{}5\text{ }\text{mm}\text{ }\text{Rb}$ vapor cell.