Spin Squeezing in a Quadrupolar Nuclei NMR System

We have produced and characterized spin-squeezed states at a temperature of 26 degrees C in a nuclear magnetic resonance quadrupolar system. The experiment was carried out on Cs-133 nuclei of spin I = 7/2 in a sample of lyotropic liquid crystal. The source of spin squeezing was identified as the interaction between the quadrupole moment of the nuclei and the electric field gradients present within the molecules. We use the spin angular momentum representation to describe formally the nonlinear operators that produce the spin squeezing on a Hilbert space of dimension 2I + 1 = 8. The quantitative and qualitative characterization of this spin-squeezing phenomenon is expressed by a squeezing parameter and squeezing angle developed for the two-mode Bose-Einstein condensate system, as well as by the Wigner quasiprobability distribution function. The generality of the present experimental scheme points to potential applications in solid-state physics.