Evolution of a quantum harmonic oscillator coupled to a minimal thermal environment

• Physical system: quantum oscillator (A) coupled to a second oscillator (minimal environment).
• Oscillator A initially in a coherent state and environment in a thermal state.
• Study of the short-time dynamics of the linear entropy of oscillator A.
• Comparison among simple analytical models and the master equation approach.
• Analysis of entropy production and dependence on the effective temperature of the environment.

In this paper it is studied the influence of a minimal thermal environment on the dynamics of a quantum harmonic oscillator (labelled AA), prepared in a coherent state. The environment itself consists of a second oscillator (labelled BB), initially in a thermal state. Two types of interaction Hamiltonians are considered, and the time-evolution of the reduced density operator of oscillator AA is compared to the one obtained from the usual master equation approach, i.e., assuming that oscillator AA is coupled to a large reservoir. An analysis of the linear entropy evolution of oscillator AA shows that simplified models may be able to describe important features related to the phenomenon of decoherence, such as the rapid growth of the linear entropy, as well as its dependence on the effective temperature of the environment.