Magnetic field gradients reduce the transverse relaxation time of nuclear spins, which usually degrades the sensitivity of atomic sensors based on nuclear spins. We demonstrate improved magnetic field gradient compensation by applying first-order and second-order magnetic gradients simultaneously in a cubic vapor cell containing ⁸⁷Rb vapor and ¹²⁹Xe gas. Compared with applying only first-order magnetic gradient compensation, the transverse relaxation time of ¹²⁹Xe is up to 4.3 times longer when applying both first-order and second-order compensating magnetic gradients, which indicates that the total magnetic gradient is greatly suppressed by the joint compensation in our experiment. The magnetic gradients induced by the polarized ⁸⁷Rb spins, the static magnetic field, and the residual magnetic field are also explored. As the main sources of internal magnetic inhomogeneities, these gradients are experimentally validated to have a sizable value. Furthermore, the total internal magnetic gradient in the system could be self-compensated when the directions of these internal gradient components are appropriately set. The experimental results in this paper are important for suppressing the magnetic gradients and optimizing the gradient compensation in nuclear magnetic resonance systems.

The transverse relaxation time τ₂ of the built-in alkali metal magnetometer is an important parameter to characterize its performance and the working state of the nuclear magnetic resonance (NMR) oscillator system. The method we propose to measure τ₂ is to apply the frequency-scanning magnetic fields along the x-axis and obtain τ₂ from the 3 dB bandwidth of the measured x-axis amplitude–frequency response curve of the magnetometer. We give a detailed and rigorous theoretical derivation by using the perturbation-iteration method to demonstrate the rationality of this measuring method. Then, both the actual experiment and the simulation experiment results are presented to verify the validity and good accuracy of the method. All the sampled frequencies in the scanning range should be far away from both the ¹²⁹Xe and ¹³¹Xe NMR frequencies, to avoid introducing any influence on the nuclear spins; therefore, this method can provide a non-interference way for measurement of τ₂, helping us monitor the NMR oscillator system’s state under normal operating conditions.