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Physica Scripta

Sudden death of entanglement and its rebirth in a system of two nonlinear oscillators

A. Kowalewska-Kudłaszyk, W. Leoński

Published Sep 1, 2010• 7 citations
Publisher

Abstract

The problem of generating a sudden death and sudden birth of entanglement in a system of two nonlinear oscillators interacting with an external reservoir is presented. The physical mechanism needed for observing these phenomena is indicated. It is found that an external driving field (coupling to one of the nonlinear oscillator modes) can be responsible for entanglement return to the system considered.

DOI
10.1088/0031-8949/2010/t140/014051

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The problem of generating a sudden death and sudden birth of entanglement in a system of two nonlinear oscillators interacting with an external reservoir is presented. The physical mechanism needed for observing these phenomena is indicated. It is found that an external driving field (coupling to one of the nonlinear oscillator modes) can be responsible for entanglement return to the system considered.
We analyze the entanglement dynamics in a nonlinear Kerr-like coupler interacting with external environment. Whenever the reservoir is in a thermal vacuum state, the entanglement (measured by concurrence for a two-qubit system) exhibits regular oscillations of decreasing amplitude. In contrast, for thermal reservoirs we can observe dark periods in concurrence oscillations (which can be called a sudden death of the entanglement) and the entanglement rebuild (which can be named the sudden birth of entanglement). We show that these features can be observed when we deal with two-qubit system as well as qubit-qutrit system.
The quantum dynamics of two weakly coupled nonlinear oscillators is analytically and numerically investigated in the context of nonlinear dissipation. The latter facilitates the creation and preservation of nonclassical steady states. Starting from a microscopic description of two oscillators individually interacting with their dissipative environments, it is found that in addition to energy relaxation, dephasing arises due to the mutual coupling. Using the negativity as an entanglement measure, it is shown that the coupling entangles the oscillators in the long-time limit. For finite temperatures, entanglement sudden death and rebirth are observed.
In this paper, we consider the entanglement dynamics of two cavities interacting with independent reservoirs. When the cavity entanglement suddenly disappeared, the reservoir entanglement suddenly and necessarily appears. We study the effect of purity of initial entangled state of two cavities on the entanglement evolution, and acquire that the purity of initial entangled state of two cavities can control the apparition time of the entanglement sudden death and the entanglement sudden birth. Also, we find that the conditions on the apparition of the entanglement sudden death and the entanglement sudden birth can be generalized when the initial entangled state of cavities is not pure, which is a complement to the result in the paper [Phys. Rev. Lett.101 (2008) 080503] for the pure case.
We discuss the evolution of entanglement for a system of two two-level atoms interacting with a common reservoir at finite temperature. The Markovian master equation is used to describe the evolution of entanglement measured by concurrence. The phenomena of sudden birth and sudden death of entanglement are discussed. It is shown that entanglement sudden death is a standard feature when the reservoir has finite temperature. Entanglement sudden birth, which is the result of the collective behaviour of atoms, appears only for a sufficiently small mean number of photons of the reservoir (sufficiently low temperatures), and it gradually diminishes as the temperature increases. The results are illustrated for the system prepared in the Werner state.