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arXiv:quant-ph/0702137 · Journal of the Optical Society of America B

Nonclassicality of quantum excitation of classical coherent fields in thermal environments

Shangbin Li, Justin Liu, Xu‐Bo Zou, Guang‐Can Guo

Published Dec 20, 2007• 13 citations
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Abstract

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.

DOI
10.1364/josab.25.000054

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Journal of the Optical Society of America B•Jun 29, 2012•40 citations
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.
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.
Theoretical analysis is given of nonclassicality and decoherence of the field states generated by adding any number of photons to the squeezed thermal state (STS). Based on the fact that the squeezed number state can be considered as a single-variable Hermite polynomial excited state, the compact expression of the normalization factor is derived, a Legendre polynomial. The nonclassicality is investigated by exploring the sub-Poissonian and negative Wigner function (WF). The results show that the WF of single-photon–added STS (PASTS) always has negative values at the phase space center. The decoherence effect on PASTS is examined by the analytical expression of WF. It is found that a longer threshold value of decay time than in single-photon–subtraction STS is included in single PASTS.
We studied the nonclassicality of photon-added squeezed vacuum (PASV) and its decoherence in thermal environment in terms of the sub-Poissonian statistics and the negativity of the Wigner function (WF). By converting the PASV to a squeezed Hermite polynomial excitation state, we derive a compact expression for the normalization factor of m-PASV, which is an m-order Legendre polynomial of squeezing parameter r. We also derive the explicit expression of WF of m-PASV and find the negative region of WF in phase space. We show that there is an upper bound value of r for this state to exhibit sub-Poissonian statistics increasing as m increases. Then we derive the explicit analytical expression of time evolution of WF of m-PASV in the thermal channel and discuss the loss of nonclassicality using the negativity of WF. The threshold value of decay time is presented for the single PASV.
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 and decoherence of a photon-subtraction-addition coherent state (a++a)m|a in a thermal environment. Its nonclassicality is discussed by deriving analytically Mandel's Q parameter, photon number distribution, and Wigner function. It is shown that if the condition |2z*+ -*|2 1 is satisfied, the Wigner function always presents the negativity for the one-order photon-subtraction-addition coherent state (m=1). Based on the evolution formula of Wigner function, we derive a compact expression for Wigner function in the thermal environment. It is found that when t(1/2)ln[(2N+2)/(2N+1)] there is no negativity for the case of m=1. In addition, the evolution of nonclassicality is discussed in terms of the negative volume of Wigner function.
We investigate nonclassicality and decoherence of field states generated with the non-Gaussian operation of photon addition to a two-mode squeezed thermal state (TSTS) using the normally ordered density operator of the photon-added TSTS (PTSTS). The normalization factor of the PTSTS is just a Jacobi polynomial of the squeezing parameter γ and the average photon number n¯ of the thermal field. We show that the fields in such states exhibit remarkable quantum features, such as sub-Poissonian photon statistics, the anti-bunching effect, and photon-number distribution. The nonclassicality is discussed in phase space based on the partial negativity of the Wigner function (WF) with two-variable Hermite polynomials. The results show that the non-Gaussian WF always exhibits the quantum interference structure caused by the two-mode squeezing operation and has some negative regions for any value of n¯, γ, and the photon-addition numbers m, n. In addition, the effect of decoherence on the PTSTS in the thermal channel is studied by analytically deriving the time-evolution WF. We find that the WF becomes Gaussian (corresponding to a classical thermal state) at long times, losing its nonclassicality as a result of decoherence, and a larger m (or n) leads to a longer decoherence time κt.