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International Journal of Modern Physics B

WIGNER FUNCTION EVOLUTION OF EXCITED EVEN AND ODD COHERENT STATE IN THERMAL ENVIRONMENT VIA THERMO ENTANGLED APPROACH

Hong‐Chun Yuan, Ye‐Jun Xu, Lei Chen, Xuefen Xu

Published Aug 2, 2013• 1 citation
Publisher

Abstract

We adopt a new approach, thermo entangled representation, to study time evolution of density operator in thermal environment. We then investigate the analytical expressions of Wigner function (WF) evolution of arbitrary number excited coherent states (ECSs) and excited even (odd) coherent states (EECSs, EOCSs) in thermal environment, respectively. In addition, their nonclassicality is numerically discussed by exploring the negativity of WF with decay time in thermal channel, respectively. It is found that WF loses its non-Gaussian nature and becomes Gaussian after long times.

DOI
10.1142/s0217979213501208

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We adopt a new approach, thermo entangled representation, to study time evolution of density operator in thermal environment. We then investigate the analytical expressions of Wigner function (WF) evolution of arbitrary number excited coherent states (ECSs) and excited even (odd) coherent states (EECSs, EOCSs) in thermal environment, respectively. In addition, their nonclassicality is numerically discussed by exploring the negativity of WF with decay time in thermal channel, respectively. It is found that WF loses its non-Gaussian nature and becomes Gaussian after long times.
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The nonclassicality of photon-added coherent fields in the thermal channel is investigated by exploring the volume of the negative part of the Wigner function that reduces with the dissipative time. The Wigner functions become positive when the decay time exceeds a threshold value. For the case of the single photon-added coherent state, we derive the exact threshold values of decay time in the thermal channel. For arbitrary partial negative Wigner distribution function, a generic analytical relation between the mean photon number of heat bath and the threshold value of decay time is presented. Finally, the possible application of single photon-added coherent states in quantum computation has been briefly discussed.
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By introducing the thermo entangled state representation, we convert the calculation of Wigner function (WF) of density operator to an overlap between "two pure" states in a two-mode enlarged Fock space. Furthermore, we derive a new WF evolution formula of any initial state in self-Kerr Medium with photon loss and find that the photon number distribution for any initial state is independent of the coupling factor with Kerr Medium, where the number state is not affected by the Kerr nonlinearity and evolves into a density operator of binomial distribution.