Entanglement dynamics in two-mode Gaussian systems

Abstract

The current study investigated the time evolution of entanglement in an open quantum system. This system includes two independent harmonic oscillators interacting with a general environment. This study reports the solution of the time evolution of the covariance matrix by using the Markovian master equation. It was found that the entanglement for a preferred Gaussian state, is a continuous variable system. This study examined the time evolution of the entanglement by using Simon’s separability criterion for continuous variable systems and computing covariance matrix with considering environmental factors such as temperature for two initial state of system (separable and entangled) with drawing Simon’s criterion and logarithmic negativity. The results demonstrated that for a certain value of dispersion and dissipation coefficient, the initial state of the system is saved over the time. But for other amounts of the above factors, entanglement birth, entanglement death and repeated entanglement birth and entanglement death happen in the system. Furthermore, the present study investigated the behavior of system’s purity under the effects of environmental factors, such as temperature and environment parameter with regard to the relation between purity and covariance matrix for two-mode Gaussian state.