Nonclassicality and decoherence of coherent superposition operation of photon subtraction and photon addition on squeezed state

The statistical properties of m-coherent superposition operation (μa+νa⁺)^m on the single-mode squeezed vacuum state (M-SSVS) and its decoherence in a thermal environment have been studied. Converting the M-SSVS to a squeezed Hermite polynomial excitation state, we obtain a compact expression for the normalization factor of M-SSVS, which is the Legendre polynomial of the squeezing parameter. We also derive the explicit expression of Wigner function (WF) of M-SSVS, and find the negative region of WF in phase space. The decoherence effect on this state is then discussed by deriving the time evolution of the WF. Using the negativity of WF, the loss of nonclassicality has been discussed.     

Measurement-induced decoherence and Gaussian smoothing of the Wigner distribution function

We study the problem of measurement-induced decoherence using the phase-space approach employing the Gaussian-smoothed Wigner distribution function. Our investigation is based on the notion that measurement-induced decoherence is represented by the transition from the Wigner distribution to the Gaussian-smoothed Wigner distribution with the widths of the smoothing function identified as measurement errors. We also compare the smoothed Wigner distribution with the corresponding distribution resulting from the classical analysis. The distributions we computed are the phase-space distributions for simple one-dimensional dynamical systems such as a particle in a square-well potential and a particle moving under the influence of a step potential, and the time-frequency distributions for high-harmonic radiation emitted from an atom irradiated by short, intense laser pulses.     

Wigner distribution,nonclassicality and decoherence of generalized and reciprocal binomial states

There are quantum states of light that can be expressed as finite superpositions of Fock states (FSFS). We demonstrate the nonclassicality of an arbitrary FSFS by means of its phase space distributions such as the Wigner function and the Q-function. The decoherence of the FSFS is studied by considering the time evolution of its Wigner function in amplitude decay and phase damping channels. As examples, we determine the nonclassicality and decoherence of generalized and reciprocal binomial states.     

Nonclassicality and decoherence of two-mode photon-added squeezed vacuum

We investigate the nonclassicality of two-mode photon-added squeezed vacuum state (TPASV) and its decoherence in a thermal environment according to the sub-Poissonian statistics and the negative region of Wigner function (WF). Based on the fact that the TPASV can be seen as a squeezed Hermite polynomial excitation state, we further obtain a compact expression for the normalization factor of TPASV, i.e., a Jacobi polynomial of the squeezing parameter. We also derive the explicit expression of WF of TPASV and then the decoherence effect on this state is also discussed by deriving the time evolution of the WF and its negative region.     

The Nonclassicality and Decoherence of a Superposition State Generated in a Resonant Cavity

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 behaviour of the nonclassicality indicator.     

光子增减叠加相干态在热环境中的退相干

研究了由光子增减叠加操作作用于相干态而得量子态的非经典性及其在热环境中的退相干问题.通过解析导出了Mandel's Q参数、光子数分布、Wigner函数等,讨论其非经典性.研究表明一阶光子增减相干叠加相干态在相空间总是取负值,只要满足条件∣2z* +α-α*∣2＜1.基于Wigner函数的演化积分公式,解析地推导出了在热环境中Wigner函数的简洁表达式.研究首次表明:如果κt＜1/2ln[(2(η)+2)/(2(η)+1)]得以满足,一阶光子增减相干叠加相干态在相空间最小值点处Wigner函数分布总存在负部.此外,根据Wigner函数负部体积讨论了其非经典特性.     

Nonclassicality and Decoherence of Generalized Photon-Modulated Squeezed Thermal State

In this paper, we introduce the generalized photon-modulated squeezed thermal states (GPMSTS) obtained by repeatedly acting the combination of Bosonic creation and annihilation operation on the squeezed thermal state. We investigate the nonclassical properties of GPMSTS and its decoherence in a thermal environment according to the negative region of Wigner function. It is found that the normalization factor of GPMSTS is a Legendre polynomial. Especially, the decoherence effect is discussed by deriving the time evolution of the Wigner function.     

A Generalized Bell Inequality and Decoherence for the K0KO

First, a generalized Bell inequality for different times and for different quasi-spin states is developed. We focus on special quasi-spin eigenstates and times. The inequality based on a local realistic theory is violated by the CP-violating parameter [1] if the quantum theory is used to recalculate the probabilities. Next, the quantum mechanical probabilities are modified by the decoherence approach, which enables the initial state to factorize spontaneously. In this way we get a lower limit for the decoherence parameter , which measures the degree of decoherence. This result is compared with the experimental value [2, 3] of the decoherence parameter deduced from the data of the CPLEAR experiment [4].     

Decoherence of Photon-Added Schrödinger Cat States in Thermal Environment

We analyze the statistical properties and decoherence of the field states produced by adding any number of photons to the Schrodinger Cat states (SCSs) in a thermal environment. It is found that the normalization factor of PA-SCS is the Hermite polynomial of the coherent factor α. The statistical properties and decoherence is discussed by deriving analytically the time evolution of the Q-function, Wigner function and the photon-number distribution. It is shown that the single photon-added even SCSs, the Wigner function is always positive in the whole phase space when κt exceeds the threshold value $\frac{1}{2}\ln [ ( 2\bar{n}+2 ) / ( 2\bar{n}+1 ) ] $ . This implies that the single photon-added even SCSs possesses a robustness due to the presence of photon-addition, which can also be seen from the point of view of the volume of negative region of Wigner function.     

Decoherence of quantum excitation of even/odd coherent states in thermal environment

In this paper, we study the decoherence of quantum excitation (photon-added) even /odd coherent states, \(((\hat a{^{\dagger }})^{m} \left | {\alpha _ \pm } \right \rangle )\), in a thermal environment by investigating the variation of negative part of the Wigner quasidistribution function vs. the rescaled time. For this purpose, at first we obtain the time-dependent Wigner function corresponding to the mentioned states in the framework of standard master equation. Then, the time evolution of the Wigner function associated with photon-added even /odd coherent states, as well as the number of added photons m are analysed. It is shown that, in both states, the negative part of the Wigner function decreases with time. By deriving the threshold value of the rescaled time for single photon-added even /odd coherent states, it is also found that, if the rescaled time exceeds the threshold value, the associated Wigner function becomes positive, i.e., the decoherence occurs completely.     

Wave Decoherence for the Random Schrödinger Equation with Long-Range Correlations

In this paper, we study the loss of coherence of a wave propagating according to the Schrödinger equation with a time-dependent random potential. The random potential is assumed to have slowly decaying correlations. The main tool to analyze the decoherence phenomena is a properly rescaled Wigner transform of the solution of the random Schrödinger equation. We exhibit anomalous wave decoherence effects at different propagation scales.     

Realistic clocks, universal decoherence, and the black hole information paradox

Ordinary quantum mechanics is formulated on the basis of the existence of an ideal classical clock external to the system under study. This is clearly an idealization. As emphasized originally by Salecker and Wigner and more recently by others, there exist limits in nature to how "classical" even the best possible clock can be. With realistic clocks, quantum mechanics ceases to be unitary and a fundamental mechanism of decoherence of quantum states arises. We estimate the rate of the universal loss of unitarity using optimal realistic clocks. In particular, we observe that the rate is rapid enough to eliminate the black hole information puzzle: all information is lost through the fundamental decoherence before the black hole can evaporate. This improves on a previous calculation we presented with a suboptimal clock in which only part of the information was lost by the time of evaporation.     

Nonclassicality and Decoherence of Photon-Subtraction Squeezing-Enhanced Thermal State

We introduce a kind of non-Gaussian state—photon-subtracted squeezing-enhanced thermal state (PSSETS) characteristics by two-squeezing parameters (λ,r). Its normalization factor is a Legendre polynomial of two-squeezing parameters and average photon number of the thermal state. The nonclassicality is investigated by using the negativity of Wigner function (WF). It is shown that the single PSSETS always has negative values when . The decoherence effect on PSSETS is then included by analytically deriving the time evolution of WF. For the single PSSETS, the characteristic time is longer than that of photon-subtracted squeezing thermal state.     

Weyl Ordering Symbol Method for Studying Wigner Function of the Damping Field

The symbolic method (including normal ordering. antinormal ordering and Weyl ordering symbol) is usually utilized to tackle miscellaneous operators which have different commutative relations. Considering the Weyl ordering symbol’s remarkable properties, we have efficiently and conveniently derived the Wigner distribution function for field damping in a squeezed bath and a vacuum bath respectively, and then examined the decoherence processes from the plots of Wigner function and its contour in quantum phase space. Alternatively, we can employ a general Wigner operator under phase space transform to calculate distribution function and discuss the damping process.     

广义压缩粒子数态的非经典性质及其退相干

研究了三参数的压缩算符产生的广义压缩粒子数态的非经典性质及其在光子损失通道中的退相干问题.利用有序算符内的积分技术和Weyl编序算符在相似变换下的不变性,简洁地导出了广义压缩粒子数态的Wigner函数(Laguerre-Gaussian函数).基于Wigner函数的演化积分公式,解析地推导出了在耗散通道中的Wigner函数表达式.特别地,根据Wigner函数负部体积讨论了其非经典性.     

Exact master equation for a noncommutative Brownian particle

We derive the Hu-Paz-Zhang master equation for a Brownian particle linearly coupled to a bath of harmonic oscillators on the plane with spatial noncommutativity. The results obtained are exact to all orders in the noncommutative parameter. As a by-product we derive some miscellaneous results such as the equilibrium Wigner distribution for the reservoir of noncommutative oscillators, the weak coupling limit of the master equation and a set of sufficient conditions for strict purity decrease of the Brownian particle. Finally, we consider a high-temperature Ohmic model and obtain an estimate for the time scale of the transition from noncommutative to ordinary quantum mechanics. This scale is considerably smaller than the decoherence scale.     

增光子奇偶相干态的Wigner函数

利用相干态表象下的Wigner算符, 重构了增光子奇偶相干态的Wigner函数.根据此Wigner函数在相空间中随复变量α的变化关系, 讨论了增光子奇偶相干态的非经典性质. 结果表明, 增光子奇偶相干态总可呈现非经典性质, 且在m取奇(或偶)数时, 增光子偶(或奇)相干态更容易出现非经典性质. 根据增光子奇偶相干态的Wigner函数的边缘分布, 阐明了此Wigner函数的物理意义. 同时, 利用中介表象理论获得了增光子奇偶相干态的量子tomogram函数. 关键词： 增光子奇偶相干态 Wigner函数 中介表象 tomogram函数     

Wigner Functions for Two-Variable Hermite Polynomial States and Their Time-Evolutions Under Thermal Environment

We analytically study the Wigner function (WF) for the two-variable Hermite polynomial state (TVHPS) and the effect of decoherence on the TVHPS in thermal environment. The nonclassicality of the TVHPS is investigated in terms of the partial negativity of the WF which depends on the polynomial orders m,n and the squeezing parameter r. We also investigate how the WF for the TVHPS evolves in the thermal environment. At long times, the TVHPS decays to thermal, a mixed Gaussian state, within the thermal environment.