Spin squeezing by tensor twisting and Lipkin-Meshkov-Glick dynamics in a toroidal Bose-Einstein condensate with spatially modulated nonlinearity

We propose a scheme for spin squeezing in the orbital motion of a Bose-Einstein condensate in a toroidal trap. A circular lattice couples two counterrotating modes and squeezing is generated by the nonlinear interaction spatially modulated at half the lattice period. By varying the amplitude and phase of the modulation, various cases of the twisting tensor can be directly realized, leading to different squeezing regimes. These include the one-axis twisting and two-axis countertwisting that are often discussed as the most important paradigms for spin squeezing. Our scheme naturally realizes the Lipkin-Meshkov-Glick model with the freedom to vary all its parameters simultaneously.