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arXiv:quant-ph/0701021 · Physical Review A

Nonclassicality of quantum excitation of classical coherent field in photon-loss channel

Shangbin Li, Xu‐Bo Zou, Guang‐Can Guo

Published Apr 9, 2007• 27 citations
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Abstract

We investigate the nonclassicality of photon-added coherent states in the photon-loss channel by exploring the entanglement potential and negative Wigner distribution. The total negative probability defined by the volume of the negative part of the Wigner function reduces with the decay time. The total negative probability and the entanglement potential of pure photon-added coherent states exhibit the similar dependence on the beam intensity. The reduce of the total negative probability is consistent with the behavior of entanglement potential for the dissipative single-photon-added coherent state at short decay times.

DOI
10.1103/physreva.75.045801

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We investigate the nonclassicality of photon-added coherent states in the photon-loss channel by exploring the entanglement potential and negative Wigner distribution. The total negative probability defined by the volume of the negative part of the Wigner function reduces with the decay time. The total negative probability and the entanglement potential of pure photon-added coherent states exhibit the similar dependence on the beam intensity. The reduce of the total negative probability is consistent with the behavior of entanglement potential for the dissipative single-photon-added coherent state at short decay times.
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.
In this paper, the decoherence of the quantum excitation (the photon-added case) of even/odd coherent states, in a photon-loss channel is studied via the evaluation of the negative part of the Wigner quasi-distribution function in terms of the rescaled time ( ). We first obtain the explicit form of the time-dependent Wigner functions of the states considered, for arbitrary values of the photon excitations. To achieve this purpose, an equivalent Fokker–Planck-like equation which describes the time evolution of the Wigner function in the framework of the standard master equation of the density matrix is used. Then, by analyzing the time variation of the corresponding Wigner functions, the loss of the nonclassicality behavior and, hence, the decay of the negative part of the Wigner functions as a result of decoherence are clearly shown. In particular, we derive the threshold value of the rescaled time for single-photon-added even and odd coherent states; through this it is observed that the associated Wigner functions become positive whenever the rescaled time exceeds that value, i.e., the decoherence has become complete. By virtue of numerical calculations, it is also illustrated that the negative volume of the corresponding Wigner functions decreases with increasing time. In addition, the states with larger values of the excitation number m generally (but not absolutely always) possess smaller values of the rescaled threshold time.
We investigate the nonclassicality of several kinds of nonclassical optical fields such as the pure or mixed single photon-added coherent states and the cat states in the photon-loss or the dephasing channels by exploring the entanglement potential as the measure. It is shown that the long-time decay of entanglement potentials of these states in photon loss channel is dependent of their initial quadrature squeezing properties. In the case of photon-loss, transition of long-time decay rate emerges at the boundary between the squeezing and non-squeezing initial non-gaussian states if log-negativity is adopted as the measure of entanglement potential. However, the transition behavior disappears if the concurrence is adopted as the measure of entanglement potential. For the case of the dephasing, distinct decay behaviors of the nonclassicality are also revealed.
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In this paper the photon addition-then-subtraction coherent state (PASCS) is put forward by first adding multiphotons to and then subtracting multiphotons from the coherent state. By taking advantage of the technique of integration within an ordered product of operators, the analytical expressions of the normalization constant, photon-number distribution, Mandel’s Q parameter, the P function, the Q function, and the Wigner function (WF) of the PASCS are derived. The fidelity between the PASCS and the initial coherent state is also deduced and its nonclassicality discussed. In addition, the time evolution of the WF is derived analytically and the decoherence of the PASCS in the photon-loss channel is studied.