PHYSICAL REVIEW A 101, 053427 (2020) Combined effect of pump-light intensity and modulation field on the performance of optically pumped magnetometers under zero-field parametric modulation Jing Wang , Wenfeng Fan , Kaifeng Yin , and Yeguang Yan School of Instrumentation Science and Optoelectronics Engineering, Beihang University, Beijing 100191, China and Hangzhou Innovation Institute of Beihang University, Hangzhou 310051, China Binquan Zhou * and Xinda Song † Research Institute of Frontier Science, Beihang University, Beijing 100191, China and Beijing Advanced Innovation Center for Big Data-Based Precision Medicine, Beihang University, Beijing, 100191, China (Received 30 December 2019; accepted 17 April 2020; published 19 May 2020) This paper investigates the performance optimization of optically pumped magnetometers under zero-field parametric modulation. Based on the analytical solutions of the Bloch equation, both longitudinal and transverse modulations are studied experimentally. To estimate the nonuniform polarization distribution of alkali-metal atoms in the vapor cell, an average pumping rate model is proposed. Furthermore, the accuracy of this model and the measurement of the transverse relaxation rate are verified via the agreement between experimental and theoretical values. The results indicate that optimal performance can be achieved by employing a suitable modulation field, the selection of which is related to the modulation index u in the Bessel series and the pump-light intensity. Although both operating modes show similar responses to weak magnetic fields, their effects on pump-light intensity are different due to the means of detecting atomic polarization. An optimal value of the pump-light intensity on the response strength exists in longitudinal modulation. However, with regard to transverse modulation, the sensitivity under weak pump-light intensity is better. This research has far-reaching significance for cases when the parametric modulation is manipulated. DOI: 10.1103/PhysRevA.101.053427 I. INTRODUCTION Optically pumped magnetometers (OPMs) hold the promise of excellent sensitivity for the detection of weak magnetic fields [1]. Since their development [2–4], they have been investigated intensively, and a variety of types have been reported [5–7]. Traditional OPMs are typically operated in the geomagnetic field, such as Mx and Mz magnetometers that utilize the technique of magnetic resonance to observe the Larmor frequency [8–10]. Their fundamental sensitivity is limited by the spin-exchange relaxation [11]; therefore, it is difficult to meet the demands of biomagnetism measurement. To obtain subfemtotesla sensitivity, Kominis et al. proposed a spin-exchange-relaxation-free (SERF) magnetometer [12], which surpassed the superconducting quantum interference devices (SQUIDs). Another core branch is zero-field parametric modulation, which emerged in the 1970s [13,14] and was recently oper- ated in the SERF regime [15]. Parametric modulation forces optically pumped atoms to precess at a frequency consistent with the modulation field of several kilohertz. Because of the inherent technical suppression of low-frequency noises, this has become a research hot spot [16,17]. Especially in magne- toencephalography, OPMs offer the advantages of noncryo- * bqzhou@buaa.edu.cn † songxinda@buaa.edu.cn genic operation and wearable system construction compared with SQUIDs [18] and have been developed rapidly [19,20]. Two structures of zero-field parametric modulation have been developed depending on the modulation direction. The parametric modulation scheme with a longitudinal modulation field along the direction of the pump light (z axis) is named the Z mode. The transverse modulation field in the plane perpendicular to the pump beam is named the X mode. The X mode is superior in compact miniaturization where one laser beam is sufficient to detect weak magnetic fields [21]. Several micromachined OPMs have been proposed with the X mode [22–25]. The Z mode was first introduced in the SERF regime in 2006 by the Walker group, who demonstrated that parametric modulation resulted in only a slight loss of sensitivity compared with a nonmodulated SERF magnetome- ter [26]. This can enable simultaneous detection of the two magnetic components B x and B y with one probe beam. Later, Zhang et al. developed a multichannel magnetometer and realized simultaneous multilocation magnetic-field measure- ments [27]. In either case, due to the presence of the mod- ulation field, final analytical solutions of atomic responses can be expanded into the superposition of multiple harmonics with Bessel series by employing the Jacobi-Anger expansion. However, few studies have provided comparative analyses of these two modes, and the optimization of their sensitivity requires theoretical support. The pursuit of sensitivity in OPMs follows a process of optimizing the polarization of an alkali metal to maximize 2469-9926/2020/101(5)/053427(8) 053427-1 ©2020 American Physical Society