Dynamics of the entanglement between two oscillators in the same environment

TL;DR

This paper characterizes the long-term entanglement dynamics of two oscillators in a shared environment, identifying phases with sudden death, revival, or persistent entanglement, supported by analytic and numerical analysis.

Contribution

It provides a comprehensive phase diagram and analytic expressions for entanglement behavior in non-Markovian environments, including non-resonant cases.

Findings

Identifies three distinct entanglement phases: sudden death, revival, and persistent entanglement.

Derives analytic expressions for phase boundaries and validates them with numerical simulations.

Applicable to a wide range of non-Markovian environments and oscillator configurations.

Abstract

We provide a complete characterization of the evolution of entanglement between two oscillators coupled to a common environment. For initial Gaussian states we identify three phases with different qualitative long time behavior: There is a phase where entanglement undergoes a sudden death (SD). Another phase (SDR) is characterized by an infinite sequence of events of sudden death and revival of entanglement. In the third phase (NSD) there is no sudden death of entanglement, which persist for long time. The phase diagram is described and analytic expressions for the boundary between phases are obtained. Numerical simulations show the accuracy of the analytic expressions. These results are applicable to a large variety of non--Markovian environments. The case of non--resonant oscillators is also numerically investigated.