His Function and Its Environmental Decoherence
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Wigner distribution function
We discuss nonclassicality of a superposition of coherent states in terms of sub-Poissonian photon statistics as well as the negativity of the Wigner function. We derive an analytic expression for the Wigner function from which we find that the function has some negative region in phase space. We obtain a compact form of the Wigner function when decoherence occurs and study the effect of decoherence on the state. We demonstrate the behavior of the nonclassicality indicator.PACS Nos.: 42.50.Dv, 03.65.Yz
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In 1983, Wigner outlined a modified Schrödinger--von-Neumann equation of motion for macroobjects, to describe their typical coupling to the environment. This equation has become a principal model of environmental decoherence which is beleived responsible for the emergence ofclassicality in macroscopic quantum systems. Typically, this happens gradually and asymptotically after a certain characteristic decoherence time. For the Wigner-function, however, one can prove that it evolves perfectly into a classical (non-negative) phase space distribution after a finite time of decoherence.
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Much of the discussion of decoherence has been in terms of a particle moving in one dimension that is placed in an initial superposition state (a Schr\{o}dinger cat state) corresponding to two widely separated wave packets. Decoherence refers to the destruction of the interference term in the quantum probability function. Here, we stress that a quantitative measure of decoherence depends not only on the specific system being studied but also on whether one is considering coordinate, momentum or phase space. We show that this is best illustrated by considering Wigner phase space where the measure is again different. Analytic results for the time development of the Wigner distribution function for a two-Gaussian Schrodinger cat state have been obtained in the high-temperature limit (where decoherence can occur even for negligible dissipation) which facilitates a simple demonstration of our remarks.
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Wave Function Collapse
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In this paper we study the effect of decoherence on the photon-added even/odd coherent states. For this purpose, the time-dependent Wigner function of the considered states during their interaction with the environment in zero temperature (that is called photon-loss channel) is obtained in the framework of standard master equation. Then, by analyzing the evolution of Wigner distribution of the mentioned states, the loss of nonclassicality behavior as a result of decoherence is clearly shown.
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Abstract A direct classical analogue of quantum decoherence is introduced. Similarities and differences between decoherence dynamics examined quantum-mechanically and classically are exposed via a second-order pertur-bative treatment and via a strong decoherence theory, providing new insights both into the dynamics of decoherence described quantum mechanically and into the conditions for quantum-classical correspondence in decoherence dynamics.
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