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arXiv:0905.4652 · Journal of the Optical Society of America B

Sudden death and birth of entanglement effects for Kerr-nonlinear coupler

A. Kowalewska-Kudłaszyk, W. Leoński

Published Jun 5, 2009• 30 citations
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Abstract

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.

DOI
10.1364/josab.26.001289

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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.
We consider time-evolution of the disentanglement process of once generated entangled qubit pair as a result of the phase variation of the pumping field. As a source of maximally entangled states we use the nonlinear coupler (two oscillators with Kerr-like nonlinearities) with nonlinear internal interactions. The coupler prepared in a maximally entangled state interacts afterwards with external reservoir of thermal character and pumping field as well. We show that the fact of the coupling with additional state (which can create additional entanglement with one of the 2-qubit system's previously entangled states) is an origin of interesting entanglement decay behaviour. We can observe shortening of both: entanglement death-time and entanglement birth caused by changing the phase of an external driving field.
By analytically solving the Lindblad form of the master equation, we investigate entanglement dynamics of two qubits coupled via the XY interaction, where each qubit is interacting with an independent reservoir with the squeezing parameters and squeezing angles. In the weak-squeezed reservoir, we show that the entanglement sudden death and entanglement sudden birth will happen for various entangled states. Some initial product states evolve into entangled ones, initially entangled states lose completely or partially their entanglement. The effects of varying the degree of entanglement of the initial states, the spin chain system parameters and different values of the degree of squeezing on the sudden death, revival and birth times are analyzed in detail. We also see that the steady state concurrence appears in the squeezed dissipative environments, which is affected by both the system parameters and the degree of squeezing.
We discuss the coupler system of two nonlinear oscillators excited by an external coherent field prepared in a maximally entangled state (Bell-like state). We show that as a result of the coupler interaction of the system with external broadband squeezed vacuum bath, entanglement decay dynamics can be considerably affected. Besides the phenomena of sudden entanglement death and its rebirth, a shortening (or lengthening) of the total disentanglement time τD can be observed, depending on the squeezing parameters. Moreover, on the example of one of the reborn entanglement cases it is shown that by changing the values of these parameters the maximal values of the negativity for the 3 \otimes 2 system discussed can be tailored.