Spin Squeezing via One-Axis Twisting in a Quadrupolar NMR system under relaxation effects

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.