Spin-exchange relaxation-free (SERF) comagnetometers have been widely applied in fundamental physics exploration, including the fifth force measurement, dark matter detection (axion and axion-like particles) and CPT (charge conjugation, parity inversion, time reversal) and Lorentz symmetry violations. Besides, it has an internationally recognized development potential in inertial navigation. SERF comagnetometers contains alkali metal electronic spin ensemble and noble gas nuclear spin ensemble. The study of the responses to external excitations inevitably involves the coupling of two ensembles. A general response model for K-³He comagnetometer has been introduced to characterize the dynamics of the hybrid pumping K-Rb-²¹Ne comagnetometer. However, there are significant differences between the two kinds of spin ensembles combinations. The unexplored comparison of dynamics between the two spin ensembles combinations would present fruitful discoveries. In this paper, we establish a complete model for K-Rb-²¹Ne comagnetometer and compare the responses of K-³He and K-Rb-²¹Ne comagnetometers. The influencing factors of the response rate and the amplitude are quantified. This research sheds light on the study of the difference between different spin ensembles combinations for the improvement of the dynamic performance and sensitivity of comagnetometers, and is expected to promote the development of inertial navigation and fundamental physics exploration.

In this paper, transient and steady-state response models are established from the Bloch equations that describe the coupling of electronic and nuclear spins. In the K-Rb-²¹Ne comagnetometer, the electronic effective magnetic field cannot be ignored, so the spin exchange relaxation rate is considered in the model. Based on the established model, the influence of various influencing factors on the dynamic response is analyzed. For the transient response, the main influencing factor is the bias magnetic field. The dynamic responses to the magnetic field, angular velocity and anomalous field at the compensation point and the strong coupling point are compared through experiments and simulations. For the steady-state response, the relationship between response coefficients and bias magnetic field for different input signals is simulated. In order to further study the influencing factors of the angular velocity response strength, we analyze the variation of the angular velocity response coefficient with electronic spin polarization and relaxation rate at the self-compensation point.

The dynamic response model of coupled ensembles in the SERF comagnetometer is established, and the influencing factors of the dynamic response are quantitatively analyzed with simulation and experiments. The effects of bias magnetic field, coupled spin ensemble polarization, electronic spin relaxation rate and other factors on the steady response signal are clarified. We find that there is a significant difference of 75 times in the dynamic response rate between the strong coupling point and the self-compensation point (Fig. 3). Besides, the response strengths to different input signals are simulated under various bias magnetic fields. At the self-compensation point, the responses of comagnetometer to the anomalous field and inertial rotation are maximized, while the sensitivity to the magnetic field is minimized (Fig. 4). It is further analyzed that there is an optimal polarization at the self-compensation point, which makes the angular velocity response coefficient the highest (Fig. 5). This optimal point is related to the atomic species and the electronic spin relaxation rate, at which the angular velocity response coefficient can be doubled by reducing the electronic spin relaxation rate. This paper clarifies that the sensitivity and dynamic performance of SERF comagnetometers can be further improved by optimizing the electronic spin polarization and the relaxation rate, which is expected to expand its application in inertial navigation and fundamental physics exploration.

In the present study, a complete coupled ensemble dynamic response model of the SERF comagnetometer is established. The dynamics of K-Rb-³He system is studied via simulation, and the dynamics of K-Rb-²¹Ne system is experimentally studied to verify the correctness of the established model. The dynamic response rate is found to be significantly affected by the bias magnetic field. Based on the experimental conditions such as the experimental temperature and optical power in this paper, the response rate at the strong coupling point is 75 times faster than that at the self-compensation point. The influencing factors of the steady-state response strength are quantitatively analyzed by simulation. The steady-state response is mainly affected by the electronic spin polarization and the electronic spin relaxation rate. There is an optimal polarization which maximizes the angular velocity response coefficient. At the same time, the decrease of the electronic spin relaxation rate can increase the angular velocity response coefficient of the K-Rb-³He system from 0.26 to 0.51, and that of the K-Rb-²¹Ne system from 1.48 to 2.31. Therefore, by reducing the electronic spin relaxation rate and optimizing the electronic spin polarization, the response coefficient can be improved, thereby improving the sensitivity of inertial measurement, providing a good foundation for the development of fundamental physics exploration and inertial navigation.