Entanglement in a Bipartite Gaussian State
Ghesquière, Anne (2009) Entanglement in a Bipartite Gaussian State. PhD thesis, National University of Ireland Maynooth.
To examine the loss of entanglement in a two-particle Gaussian system, we couple it to an environment and use the Non-Rotating Wave master equation to study the system's dynamics. We also present a derivation of this equation. We consider two dierent types of evolution. Under free evolution we nd that entanglement is lost quickly between the particles. When a harmonic potential is added between the particles, two very dierent behaviours can be observed, namely in the over and under-damped cases respectively, where the strength of the damping is determined by how large the coupling to the bath is with respect to the frequency of the potential. In the over-damped case, we nd that the entanglement vanishes at even shorter times than it does in the free evolution. In the (very) under-damped case, we observe that the entanglement does not vanish. Instead it oscillates towards a stable value
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