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.     

Decoherence and Fidelity in Teleportation of Coherent Photon-Added Two-Mode Squeezed Thermal States

We theoretically introduce a kind of non-Gaussian entangled resources, i.e., coherent photon-added two-mode squeezed thermal states (CPA-TMSTS), by successively performing coherent photon addition operation to the two-mode squeezed thermal states. The normalization factor related to bivariate Hermite polynomials is obtained. Based upon it, the nonclassicality and decoherence process are analyzed by virtue of the Wigner function. It is shown that the coherent photon addition operation is an effective way in generating partial negative values of Wigner function, which clearly manifests the nonclassicality and non-Gaussianity of the target states. Additionally, the fidelity in teleporting coherent states using CPA-TMSTS as entangled resource is quantified both analytically and numerically. It is found that the CPA-TMSTS is an entangled resource of high-efficiency and high-fidelity in quantum teleportation.     

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.     

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 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.     

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.     

Long-time death of nonclassicality of a cavity field interacting with a charge qubit and its own reservoir

A measure of nonclassicality of quantum states based on the negative values of the Wigner function (WF) of a charge qubit-field system is proposed. It is found that, the negative values of the field WF are very sensitive to any change in dissipation parameter. The dissipation leads to a long-time death for both entanglement and nonclassicality, and also the coherence of the cavity state is lost completely.     

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.     

Non-Gaussianity and decoherence of generalized photon-added coherent state as a Hermite-excited coherent state

Generalized photon-added coherent state (GPACS) is obtained by repeatedly acting the combination of Bose creation and annihilation operations on the coherent state. It is found that GPACS can be regarded as a Hermite-excited coherent state due to its normalization factor related to a Hermite polynomial. In addition, we adopt the Hilbert-Schmidt distance to quantify the non-Gaussian character of GPACS and discuss the decoherence of GPACS in dissipative channel by studying the loss of nonclassicality in reference of the negativity of Wigner function.     

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.     

Nonclassicality and Decoherence of Photon-added Thermo-invariant Coherent State

By introducing a kind of new quantum state—Photon-added thermo invariant coherent state (PATCS), we discuss its nonclassicality in terms of the negativity of Wigner function (WF) after deriving its analytical expression. It is found that the Wigner function is related to Lagurre-Gaussian function. We then study the effect of decoherence (a thermal environment) on the PATCS according to its WF (also related to Lagurre-Gaussian function). It is shown that it is not possible for WF to present the negative region when the decay time $\kappa t>\frac{1}{2}\ln \frac{2\bar{n}+2}{2\bar{n}+1}$\kappa t>\frac{1}{2}\ln \frac{2\bar{n}+2}{2\bar{n}+1} .     

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.     

Nonclassical state via superposition of two coherent states (π/2 out of phase) and related entangled states

Nonclassical features of the superposition of two coherent states which are π/2 out of phase are discussed, such as sub-Poissonian photon statistics and quadrature squeezing, as well as negativity of the Wigner function. Special nonclassicality is found in the special state where the relative phase of superposition has relationship with the average photon number. The analysis of the amount of entanglement is also presented for the related two-mode entangled coherent states.     

Nonclassical and non-Gaussian properties of states generated by the superposed photon added-and-subtracted operation on squeezed vacuum

A new kind of non-Gaussian quantum state is constructed by operating the superposed operator (SO) (cos θaa^† + sin θa^†a) on a squeezed vacuum state (SVS) S(r)|0〉. It is found that the SOSVS is just a superposition state between S(r)|0〉 and S(r)|2〉 with only even numbers of photons. The nonclassicality is investigated by exploring the negativity of Wigner function (WF) and the sub-Poissonian distribution of Mandel's Q-parameter. The non-Guassianity is exhibited via the fidelity between the SOSVS and the SVS and the marginal distribution of its Wigner function. It is found that such SO on the SVS can enhance the nonclassicality and change the non-Gaussianity of the SOSVS. This provides the possibility of generating quantum states with specific nonclassical and non-Gaussian properties.     

Nonclassicality of photon-modulated spin coherent states in the Holstein—Primakoff realization

Two new photon-modulated spin coherent states (SCSs) are introduced by operating the spin ladder operators J_± on the ordinary SCS in the Holstein-Primakoff realization and the nonclassicality is exhibited via their photon number distribution, second-order correlation function, photocount distribution and negativity of Wigner distribution. Analytical results show that the photocount distribution is a Bernoulli distribution and the Wigner functions are only associated with two-variable Hermite polynomials. Compared with the ordinary SCS, the photon-modulated SCSs exhibit more stronger nonclassicality in certain regions of the photon modulated number k and spin number j, which means that the nonclassicality can be enhanced by selecting suitable parameters.     

Nonclassicality of a single quantum excitation of a thermal field in thermal environments

The nonclassicality of single photon-added thermal states in the thermal channel is investigated by exploring the volume of the negative part of the Wigner function. The Wigner functions become positive when the decay time exceeds a threshold value γtc, which only depends on the effective temperature of the thermal channel. Furthermore, we firstly demonstrate γtc is the same for arbitrary pure or mixed nonclassical optical fields with zero population in vacuum state.     

The effect of atomic spontaneous decay on the dynamics of the negativity of the Wigner function of radiation

The exact solution of the master equation for the case of a high-Q cavity with atomic decay is found. We use the negativity of the Wigner function (WF) as an indicator of nonclassicality. It is found that the negative values of the field WF are very sensitive to any change in the damping parameter. The atomic spontaneous decay leads to the simultaneous disappearance of both entanglement and nonclassicality of quantum states. Moreover, the purity of the field states is completely lost.     

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.     

Entangled Finite Dimensional Pair Coherent States and Their Applications

Intermediate states of electromagnetic field are reviewed. It is a type of the correlated two-mode states (converter state). Based on the resonant ion-cavity interaction, we propose a scheme to generate these states revealing their connection with the converter state. The practical feasibility of this method is also discussed. We discuss nonclassicality of a finite dimensional pair coherent states in terms of sub-Poissonian photon statistics as well as the negativity of the Wigner function after deriving the analytic expression for the Wigner function. We explore a superposition of two finite dimensional pair coherent states. We show that such states possess inherent nonclassical properties such as sub-Poissonian distribution, anti-correlation between the two modes and violation of Cauchy-Schwarz inequalities. The s-parameterized characteristic function (CF) is considered. The phase distribution in the framework of Pegg and Barnett formalism, W-function and Q-function are discussed. Furthermore, a two-level atom in interaction with a two-mode quantized electromagnetic fields besides a frequency converter interaction initially prepared in an entangled two-mode coherent state is presented. Exact solution of the wave function in the Schrödinger picture is obtained. Some statistical aspects of this model are presented. The results are employed to perform a careful investigation of the temporal evolution of the atomic inversion, entropy squeezing and variance squeezing. General conclusions reached are illustrated by numerical results.     

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.