Spin Squeezing in Mixed Model of the One-Axis Twisting and Two-Axis Counter-Twisting with Decay

We investigate spin squeezing of a collective spin system governed by mixed Hamiltonian of the one-axis twisting and two-axis counter-twisting with decay. The analytic solutions of the optimally squeezed angle and the spin squeezing parameter are derived. It is shown that the two-axis counter-twisting Hamiltonian induces stronger spin squeezing than the one-axis twisting one. It is also shown that the decay rate has no effect on the size of the squeezing parameter, it only affects the period of squeezing parameter.