Quantum Spin Squeezing in a Squeezed Environment

We apply the stochastic Schrödinger equation approach to study the non-Markovian dynamics of open quantum systems when coupled to the environment that is initially prepared in a squeezed state. After deriving the non-Markovian quantum diffusion equation and the associated master equation, we study the nonequilibrium dynamics of general models in a pure quantum context. Particularly, we compare the quantum spin squeezing resulting from the environment, which is prepared as the squeezed states, and the coherent states, respectively. In addition, we numerically show how the squeezing of the environment is transferred into the system. Besides the spin squeezing model discussed, our method can be extended to generic open quantum systems coupled with a finite temperature environment.