Many-body entanglement in disentangling process

Abstract

Decoherence has been studied in the context of quantum-classical correspondence, providing a quantum-to-classical transition of a system [1]. A pure single-mode field becomes a mixed state and loses its quantum nature by decoherence in an environment. Most of the studies on decoherence have focused on a single-body system [2] because the decoherence process of a many-body system is expected to be a straightforward extension of a single-body system in a Markov environment, if it is separable. However, if it is entangled, the decoherence mechanism may impose a different nature. In this paper, we propose a new formalism, so-called, effective environmental approach. The approach is based on the proof that the system interacting with the infinite environmental variables is equivalent to a system interacting with a small number of effective environmental variables: Their interactions result in the same Fokker-Planck equation of the system. For instance, a single-mode field in a thermal environment is equivalent to one interacting with a single mode "environment" in a thermal state. The sufficiency of the small environmental variables in describing the decoherence enables one to manipulate an experiment so as to investigate the decoherence by introducing such effective environmental variables and even controlling their couplings to the system. Further we apply the present scheme to the disentangling process by "directly" investigating the quantum correlation of a two-mode entangled continuous-variable system and an environment in thermal equilibrium.