International Research Journal of Applied and Basic Sciences © 2014 Available online at www.irjabs.com ISSN 2251-838X / Vol, 8 (12): 2280-2285 Science Explorer Publications Dynamics of Entanglement In Two-Mode Gaussian Open Quantum Systems Mohsen Balvasi 1 , Farshad Baharvand 2 1. Department of physics, Sama technical and vocational training college, Omidiyeh branch, Islamic Azad University Omidiyeh, Iran. 2. Department of physics, Birjand University, Birjand, Iran. Corresponding Author: Mohsen Balvasi ABSTRACT: In the framework of the theory of open systems, we give a description of quantum entanglement for two non-interacting modes embedded in a common thermal environment. We describe the evolution of entanglement in terms of the covariance matrix for the initial Gaussian state. We study the dependence of time evolution of entangled initial squeezed thermal states on the squeezing parameter, the average numbers of thermal photons associated with the two modes, the dissipation parameter and the frequencies in resonant and non-resonant cases. We found that with decreasing the dissipation parameter; the entanglement suppression happens later. By selecting equal frequency for two mode, we can preserve more entanglement of system. Keywords: dissipation parameter, entanglement, logarithmic negativity, sudden death, time evolution INTRODUCTION In the recent years, the development of the theory of quantum information has aroused the interest in open quantum systems. These systems dealing with the decoherence phenomenon and generating entanglement in multipartite systems interacting with the environments. The generation, detection and use of the entanglement continue to be currently a problem of probe. When two systems are interacting with an environment, at the same time with the quantum decoherence, the environment can also produce quantum entanglement of the two systems. In certain circumstances, the environment enriches quantum entanglement and in others it conceals the entanglement and the state becomes separable. The time evolution of entanglement was obtained previously (Isar, 2009b; Isar, 2011) for an initial two –mode squeezed vacuum state and thermal state(Isar, 2013). In this work we study, in the framework of the theory of open quantum systems based on completely positive dynamical semigroups, the dependence of dynamics of the continuous variable entanglement on some parameters for a subsystem composed of two identical harmonic oscillators interacting with a thermal bath. The initial state of the subsystem is taken of Gaussian form and the progression under the quantum dynamical semi group guarantees the preservation in time of the Gaussian form of the state. The paper is organized as follows. In Sec. 2 we give the solution of the evolution equation for the covariance matrix corresponding to a two-mode Gaussian state of the two uncoupled modes interacting with the environment. We investigate in Sec. 3 the dynamics of entanglement, by studying the time evolution of the logarithmic negativity. A summary and conclusions are given in Sect. 4. Equations Of Motion We study the dynamics of a subsystem composed of two independent modes in weak interaction with a common thermal environment. In the self-evident formalism based on completely positive quantum dynamical semigroups, the Markovian irreversible time evolution of an open system is characterized by the Lindblad- Kossakowski equation (Kossakowski, 1972; Lindblad, 1976). We are curious about the set of Gaussian states, so we present such quantum dynamical semigroups that preserve this set over time evolution of the system. The two-mode Gaussian state is completely specified by its covariance matrix (Sandulescu et al., 1987):