Exact Solution to Spin Squeezing of the Arbitrary-Range Spin Interaction and Transverse Field Model

We investigate spin squeezing effects of trapped ions in an off-resonance optical potential system using the arbitrary range spin-spin interaction and transverse field model. The collective spin noises at any time are analyzed exactly. The general expression of spin squeezing factor is presented for arbitrary-range spin interaction. For the nearest-neighbor and next-nearest neighbor spin interaction model, the analytic solutions are reduced from the general expressions. It is shown that the maximum spin squeezing is enhanced for the general arbitrary-range spin interaction compared with the nearest-neighbor interaction model as the long-range interaction with arbitrary sites enforces stronger correlation.