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Continuous Variables Approach to Entanglement Creation and Processing |
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PP: 315-339 |
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Author(s) |
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Li-Hui Sun,
Gao-Xiang Li,
Zbigniew Ficek,
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Abstract |
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| We apply the continuous variable approach to study entangled dynamics of coupled
harmonic oscillators interacting with a thermal reservoir and to a deterministic creation
of entanglement in an atomic ensemble located inside a high-Q ring cavity. In the case
of harmonic oscillators, we show that a suitable unitary transformation of the position
and momentum operators transforms the system to a set of independent harmonic oscillators
with only one of them coupled to the reservoir. Working in the Wigner representation
of the density operator, we find that the covariance matrix has a block diagonal
form of smaller size matrices. This simple property allows to treat the problem to some
extend analytically. We analyze the time evolution of an initial entanglement and find
that the entanglement can persists for long times due to presence of constants of motion
for the covariance matrix elements. In the case of an atomic ensemble located inside
the cavity, the attention is focused on creation of one and two-mode continuous variable
entangled states from the vacuum by applying laser pulses of a suitably adjusted amplitudes
and phases. The pulses together with the cavity dissipation prepare the collective
modes of the atomic ensemble in a desired entangled state. |
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