A Fast Measurement for Relaxation Rates and Fermi-Contact Fields in Spin-Exchange Relaxation-Free Comagnetometers

We propose a novel method for measuring relaxation rates and Fermi-contact fields of the electron and nuclear spin ensembles rapidly and synchronously in spin-exchange relaxation-free (SERF) atomic comagnetometers based on the transient response. The transient response model of the comagnetometer is established by solving a set of Bloch equations. The decay rates and oscillation frequencies of the transient response as functions of the longitudinal magnetic field are investigated theoretically and experimentally. The total relaxation rate of the nuclear spin ensemble is obtained from its decay rate. A linear model is presented with a detailed mathematical derivation based on the decay rates and oscillation frequencies of the spin ensembles. The Fermi-contact fields of the spin ensembles and the slowing-down factor are extracted from the slope and intercept of the linear model. The total relaxation rate of the electron spins is obtained from the decay rates of the spin ensembles and the measured slowing-down factor. The validity of this method is further checked by the magnetic resonance (MR) method from a perspective of the electron resonance linewidth. Identification of these systematic parameters paves the way for operating the comagnetometers efficiently as well as the practical applications of the comagnetometers.