Decoherence of odd compass states in the phase-sensitive amplifying/dissipating environment

We study the evolution of odd compass states (specific superpositions of four coherent states), governed by the standard master equation with phase-sensitive amplifying/attenuating terms, in the presence of a Hamiltonian describing a parametric degenerate linear amplifier. Explicit expressions for t...

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Bibliographic Details
Published in:Annals of physics 2016-08, Vol.371 (Complete), p.296-312
Main Authors: Dodonov, V.V., Valverde, C., Souza, L.S., Baseia, B.
Format: Article
Language:English
Subjects:
ANNIHILATION OPERATORS
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Coherent states superpositions
COMPARATIVE EVALUATIONS
COUPLING
EIGENSTATES
EVOLUTION
FOKKER-PLANCK EQUATION
HAMILTONIANS
INTERFERENCE
PARAMETRIC AMPLIFIERS
PHASE SPACE
Phase-sensitive reservoirs
Physics
QUANTUM DECOHERENCE
Quantum degenerate parametric amplifier
QUANTUM STATES
Quantum–classical transition
Studies
TIME DEPENDENCE
Wigner function negativity
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Summary:We study the evolution of odd compass states (specific superpositions of four coherent states), governed by the standard master equation with phase-sensitive amplifying/attenuating terms, in the presence of a Hamiltonian describing a parametric degenerate linear amplifier. Explicit expressions for the time-dependent Wigner function are obtained. The time of disappearance of the so called “sub-Planck structures” is calculated using the negative value of the Wigner function at the origin of phase space. It is shown that this value rapidly decreases during a short “conventional interference degradation time” (CIDT), which is inversely proportional to the size of quantum superposition, provided the anti-Hermitian terms in the master equation are of the same order (or stronger) as the Hermitian ones (governing the parametric amplification). The CIDT is compared with the final positivization time (FPT), when the Wigner function becomes positive. It appears that the FPT does not depend on the size of superpositions, moreover, it can be much bigger in the amplifying media than in the attenuating ones. Paradoxically, strengthening the Hamiltonian part results in decreasing the CIDT, so that the CIDT almost does not depend on the size of superpositions in the asymptotical case of very weak reservoir coupling. We also analyze the evolution of the Mandel factor, showing that for some sets of parameters this factor remains significantly negative, even when the Wigner function becomes positive.
ISSN:0003-4916
1096-035X
DOI:10.1016/j.aop.2016.04.019