Entanglement evolution in the open quantum systems consisting of asymmetric oscillators

Using the theory of open quantum systems, we study the entanglement evolution in two and three-mode systems consisting of uncoupled harmonic oscillators which interact with a thermal bath as the environment. The evolution of the system is obtained with the use of the master equation in the Lindblad form with the Markovian approximation. The coherent states of a spinless charged particle in an anisotropic harmonic potential and a uniform magnetic field are considered as the initial states of two and three-mode systems. Then by the use of the positive partial transpose criterion for three-mode system and the logarithmic negativity for two-mode system, the entanglement evolution is obtained as a function of the temperature, dissipation coefficient, magnetic field and asymmetric parameter. In both two and three-mode systems, by increasing the dissipation coefficient and temperature, the entanglement sudden death occurs sooner. Also, for certain values of the magnetic field and asymmetric parameter which depend on the other parameters, the entanglement survives the most