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Dynamics of the entanglement between two oscillators in the same environment
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.Comment: 4 pages, 5 figure
Entanglement dynamics during decoherence
The evolution of the entanglement between oscillators that interact with the
same environment displays highly non-trivial behavior in the long time regime.
When the oscillators only interact through the environment, three dynamical
phases were identified and a simple phase diagram characterizing them was
presented. Here we generalize those results to the cases where the oscillators
are directly coupled and we show how a degree of mixidness can affect the final
entanglement. In both cases, entanglement dynamics is fully characterized by
three phases (SD: sudden death, NSD: no-sudden death and SDR: sudden death and
revivals) which cover a phase diagram that is a simple variant of the
previously introduced one. We present results when the oscillators are coupled
to the environment through their position and also for the case where the
coupling is symmetric in position and momentum (as obtained in the RWA). As a
bonus, in the last case we present a very simple derivation of an exact master
equation valid for arbitrary temperatures of the environment.Comment: to appear in QIP special issue on Quantum Decoherence and
Entanglemen
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