Exact solution and short-time dynamics of multimode Gaussian states embedded in a common non-Markovian environment
Department of Physics and Information Engineering, Huaihua
University, Huaihua, Hunan
Received: 4 January 2013
Published online: 24 July 2013
We investigate a system of N mutually coupled harmonic oscillators interacting with the same environment and derive the corresponding exact non-Markovian master equation using our introduced approach. We obtain an explicit formula for the covariance matrix of the evolved state by taking a Gaussian state as initial one. With this, we analyze the short-time non-Markovian dynamics of three-mode Gaussian state in high-temperature limit. Our results show that the short-time evolution behavior of bipartite entanglement for 1 × 2 bipartition is similar to that of genuine tripartite entanglement, while the 1 × 1 bipartition entanglement does not. It is also shown that there exists a threshold that makes the initial tri- and bipartite entanglement increase or decrease. For the squeezing degree of the initial state than this critical value, the entanglement is increased with the evolution time; otherwise it is decreased. Finally, we present a physical positivity criterion for the covariance matrix of the evolved state.
Key words: Quantum Information
© EDP Sciences, Società Italiana di Fisica and Springer-Verlag 2013