This study investigates spin squeezed states in nuclear magnetic resonance (NMR) quadrupolar systems with spins I=3/2 and I=7/2 at room temperature, taking into account the effects of relaxation on the dynamics. The origin of spin squeezing is attributed to the interaction between the nuclear quadrupole moment and the electric field gradients in the molecular environment. The formal description of the nonlinear operators responsible for spin squeezing is achieved using the spin angular momentum representation via the one-axis twisting mechanism. This approach provides a framework for quantum control and metrology over the spin squeezing process while accounting for the influence of relaxation phenomena. Non-Cartesian angular momentum operators are proposed, with their variances products catching the quantum effects during the dynamics. An upper bound for the squeezing parameter and the Heisenberg uncertainty at thermal equilibrium are also predicted for any spin quantum number.
High Resolution Image Download MS PowerPoint Slide Research on the electric quadrupole frequency shift mechanism and nuclear spin relaxation of 129 Xe– 131 Xe in alkali metal atomic vapor cells fabricated using microelectromechanical systems (MEMS) technology remains in its early stages. Therefore, an in-depth investigation in this field is crucial for enhancing the performance of miniaturized atomic gyroscopes and other quantum devices. This study provides a comprehensive analysis of the electric quadrupole frequency shift and relaxation of 129 Xe– 131 Xe nuclear spins in a stemless cubic MEMS vapor cell. To elucidate the microscopic characteristics of wall interactions, nuclear spin quadrupole interactions with mixed silicon and glass surfaces in MEMS vapor cells were examined. The influence of the angle between the vapor cell’s geometric axis and the applied magnetic field on the electric quadrupole frequency shift was investigated, leading to the determination of the vapor cell’s asymmetry parameter η and the average twist angle ⟨ θ ⟩ of nuclear spin-wall collisions. Furthermore, the temperature dependence of the electric quadrupole frequency shift in 131 Xe atoms was characterized, enabling the extraction of the desorption activation energy ( E A ) of 131 Xe on the MEMS vapor cell surface. By analyzing the free induction decay (FID) signals of 129 Xe and 131 Xe at varying temperatures, the relationship between their relaxation rates and temperature was established. These findings offer valuable insights for optimizing nuclear spin relaxation times in microatomic gyroscopes.