Multipartite entanglement in harmonic oscillators subjected to dissipative quantum dynamics

Résumé

A meaningful description of the low-energy dynamics of multipartite entanglement is provided for harmonic oscillator systems in general dissipative scenarios. Without doing any central approximation, this mainly relies on a set of reasonable physical statements on the environment and system-environment interaction consistent with a linear analysis of the open-system dynamics. Using a Gaussian-like assumption analogous to that used in the derivation of Gaussian entanglement of formation, we derive a hierarchy of separability criteria that permit in a unified way to characterize k-partite entanglement of broad classes of Gaussian and non- Gaussian states. The separability criteria allow to monitor the evolution of multipartite entanglement under the environmental influence. We devote special attention to the stationary properties of tripartite entanglement when the system oscillators are in contact with either a common environment or independent environments at initial different temperatures. Finally, the stationary entanglement and energy current across a finite harmonic chain are studied in detail by doing an extensive numerical analysis of both phenomena for a broad range of the parameters (i.e., temperatures, oscillator frequencies, and oscillator coupling strengths).