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Physics Letters A

Loss of nonclassical properties of quantum states in linear phase-insensitive processes with arbitrary time-dependent parameters

V. V. Dodonov

Published May 28, 2009• 5 citations
Publisher
DOI
10.1016/j.physleta.2009.05.054

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The existence of positive well-defined quasiprobabilities is known to be related to the measure of nonclassicality for a given field state. We test the coincidence of the loss of well-known nonclassical properties with the appearance of the positive well-defined quasiprobabilities for various fields influenced by phase-insensitive reservoirs. For Gaussian fields the appearance of a positive Glauber-Sudarshan P function coincides with the loss of nonclassical properties in quadrature fluctuations and in photon statistics. We find that when an initial Fock state dissipates or is amplified the initial field loses its nonclassicality in photon statistics before the P function becomes positive, which is different from the Gaussian field. The Wigner function may be positive even when the decaying Fock state is sub-Poissonian. For the amplification of the Fock state, however, the Wigner function is positive only when the field is super-Poissonian. For the dissipation and amplification of the Fock state the point when a certain quasiprobability function becomes positive definite depends only on the average number of photons N of the heat bath. \textcopyright{} 1996 The American Physical Society.
For nonclassical state generation, we demonstrate the possibility to compensate effects of strong linear loss by engineered nonlinear dissipation. We show that it is always possible to construct such a dissipative gadget that, for a certain class of initial states, the desired nonclassical state can be attained within a particular time interval with an arbitrary precision. Further we demonstrate that an arbitrarily large linear loss can still be compensated by a sufficiently strong coherent or even thermal driving, thus obtaining strongly nonclassical (in particular, sub-Poissonian) stationary mixed states.
We study the decoherence of superpositions of displaced quantum states of the form (where | g ⟩ is an arbitrary 'fiducial' state and is the usual displacement operator) within the framework of the standard master equation for a quantum damped or amplified harmonic oscillator interacting with a phase-insensitive (thermal) reservoir. We compare two simple measures of the degree of decoherence: the quantum purity and the height of the central interference peak of the Wigner function. We show that for N > 2 'mesoscopic' components of the superposition, the decoherence process cannot be characterized by a single decoherence time. Therefore, we distinguish the 'initial decoherence time' and 'final decoherence time' and study their dependence on the parameters α k and N . We obtain approximate formulae for an arbitrary state | g ⟩ and explicit exact expressions in the special case of | g ⟩ = | m ⟩, i.e., for (symmetrical) superpositions of displaced Fock states of occupation number m . We show that the superposition with a large number of components N and rich 'internal structure' ( m ∼ |α| 2 ) can be more robust against decoherence than simple superpositions of two coherent states (with m = 0), even if the initial decoherence times coincide. Also, we show how initial pure quantum superpositions are transformed into highly mixed and totally classical superpositions in the case of a phase-insensitive amplifier.