Statistical properties of the nonlinear negative binomial state

In this context, we introduce and investigate the properties of the nonlinear negative binomial state (the state which interpolates between the nonlinear coherent and the number states). Mainly we concentrate on the statistical properties for such state where we have discussed two different cases of squeezing phenomenon. The first case is the normal squeezing while the second is the amplitude squared squeezing, further the second order correlation function is also considered. Our discussion have been extended to include the quasi-probability distribution functions (W-Wigner and Q-functions). The quadrature distribution and the phase properties in Pegg-Barnett formalism besides the phase variances are considered. Examination of the resonance fluorescence against the present state is given (single atom and thermodynamic limit). It has been shown that the atomic inversion is sensitive to any variation in the nonlinear negative binomial number m.     

Generalized Photon Added and Subtracted f-Deformed Displaced Fock States

In this paper, by making use of the nonlinear coherent states approach, the generalized photon added and subtracted f-deformed displaced Fock states are introduced. In other words, a natural link between photon added and subtracted displaced Fock states and nonlinear coherent states associated with nonlinear oscillator algebra is obtained. It is found that various kinds of nonclassical states can be generated by adopting appropriately controlling parameters in both linear and nonlinear regimes. Moreover, examining some of the most nonclassical properties such as Mandel's Q parameter, different types of squeezing, namely, quadrature, amplitude–squared and phase entropic squeezing, and Vogel's characteristic function, the nonclassicality features of the considered quantum states of interest are studied. Furthermore, to obtain the degree of quantum coherence, the relative entropy of coherence is investigated. Indeed, the nonclassicality aspects of the states obtained have been numerically studied to understand the roles of deformation functions, photons added and subtracted, and photon number occupied in the Fock state on physical properties. It is demonstrated that the depth and the domain of the nonclassicality features of the system can properly be controlled by selecting the suitable parameters.     

Photon-Added SU(1, 1) Coherent States and their Non-Classical Properties

The photon-added coherent states of Barut-Girardello and Perelomov types are constructed using Holstein-Primakoff realization of the su(1, 1) Lie algebra. Basic properties of the constructed states have been discussed. In addition, their non-classical features have been analyzed by computing photon detection probability distribution, Mandel Q-parameter and quadrature squeezing. It is shown that SU(1, 1) photon-added coherent states may exhibit sub-Poissonian statistics and quadrature squeezing for a chosen set of parameters. Moreover, it has been observed that their non-classical behavior increases as the number of added-photons increases.

     

Nonclassicality of two-mode nonorthogonal states

Nonclassical features of Schrödinger cat state with two-mode superposition state based on two coherent states π out of phase by fixing the relative phase equal to average photon number are discussed. Study of two-mode quadrature squeezing, oscillatory and sub-Poissonian photon statistics show that nonclassicality exists for these states. However, it is observed that the considered states do not violates the Cauchy–Schwarz inequality. Furthermore, simultaneously existence of quadrature squeezing and sub-Poissonian photon statistics shows that these states have more nonclassical features than that of famous even and odd coherent states.     

与Λ型三能级原子非共振相互作用的SU(1,1)场的性质

导出了介质中双模SU(1,1)相干态场与Λ型三能级原子非共振相互作用系统的态函数,研究了场模失谐量、克尔介质以及原子初态对场的互关联函数和Mandel Q参量的影响.结果表明:失谐量将削弱光场两模的关联性,并影响场模光子数的统计分布;当SU(1,1)场两模间的光子数之差增大时,失谐量对它们产生的影响变得更弱,此时克尔效应的影响变得明显,它使两模的关联性和光子数的统计分布趋于稳定.     

Generation and Properties of a Superposition of Four Displaced Fock States

A detailed discussion of a type of four-component superposition of displaced Fock states (DFSs) is presented. A generation scheme is proposed for these states. The s-parameterized characteristic function (CF) and the quasiprobability distribution functions (QDFs) of these states are calculated. The nonclassical properties of these states such as photon number distribution and squeezing are discussed. The quadrature distributions are illustrated. The Pegg–Barnett phase distribution is discussed.     

虚光场对玻色-爱因斯坦凝聚体与二项式光场相互作用系统中光场压缩性质的影响

在二项式光场和二能级原子玻色-爱因斯坦凝聚体相互作用系统中, 应用全量子理论, 分别在旋波近似和非旋波近似下, 研究了光场的压缩特性以及原子本征频率、原子-光场的耦合系数、光场参数以及虚光场对系统光场压缩特性的影响. 研究表明, 光场的两个正交分量均被周期性压缩, 光场压缩持续时间与原子的本征频率有关, 压缩深度与二项式光场概率分布参数和虚光场有关, 光场与原子的耦合系数决定了光场涨落的崩塌-回复频率. 关键词： 量子光学 玻色-爱因斯坦凝聚 虚光场 光场压缩     

Quasiprobability distribution in a Kerr-nonlinear blackbody

In a Kerr-nonlinear blackbody, bare photons with opposite wave vectors and helicities are bound into pairs and unpaired photons are transformed into a new kind of quasiparticle, the nonpolariton. The nonpolariton system constitutes free thermal radiation in the blackbody. In this paper, the quasiprobability (Q function) distribution of thermal radiation is investigated. Non-classical effects of quadrature squeezing have been observed. The structure of nonpolaritons is unsteady and governed by the temperature. The phase space of the photon system is considered and found that in the transition from the normal to the squeezed thermal radiation state, the phase symmetry of the photon system is spontaneously broken.     

纠缠微波信号的特性及表示方法

纠缠微波信号是电磁场微波频段量子特性的体现.在总结了现有纠缠微波信号产生及验证实验的基础上,针对目前没有统一的表达式来描述纠缠微波信号格式的问题,通过深入分析纠缠微波信号的特性,提出了两种纠缠微波信号的表示方法.一种是在量子框架下,利用双模压缩真空态表示,并分别在光子数表象下和Wigner分布下分析了其信号特征,刻画了正交分量之间的正反关联特性;另一种是在经典框架下,利用关联随机信号表示,刻画了测量后纠缠微波信号场幅度正交分量随时间变化的波形图.两种表示恰当合理地反映了纠缠微波信号连续变量纠缠的特性.     

Quantum Phase Properties of Photon Added and Subtracted Displaced Fock States

Quantum phase properties of photon added and subtracted displaced Fock states (and their limiting cases) are investigated from a number of perspectives, and it is shown that the quantum phase properties are dependent on the quantum state engineering operations performed. Specifically, the analytic expressions for quantum phase distributions and angular Q distribution as well as measures of quantum phase fluctuation and phase dispersion are obtained. The uniform phase distribution of the initial Fock states is observed to be transformed by the unitary operation (i.e., displacement operator) into non‐Gaussian shape, except for the initial vacuum state. It is observed that the phase distribution is symmetric with respect to the phase of the displacement parameter and becomes progressively narrower as its amplitude increases. The non‐unitary (photon addition/subtraction) operations make it even narrower in contrast to the Fock parameter, which leads to broadness. The photon subtraction is observed to be a more powerful quantum state engineering tool in comparison to the photon addition. Further, one of the quantum phase fluctuation parameters is found to reveal the existence of antibunching in both the engineered quantum states under consideration. Finally, the relevance of the engineered quantum states in the quantum phase estimation is also discussed.     

类Kerr介质中双模SU(1,1)相干态场与Λ型三能级原子相互作用的量子统计性质

导出了类Kerr介质中双模SU(1,1)相干态场与Λ型三能级原子相互作用系统的态函数,研究了Kerr效应对Λ型三能级原子布居概率、双模SU(1,1)相干态场的互关联函数、Cauchy-Schwartz不等式及二阶相干度的影响.结果表明:Kerr效应使原子与光场的耦合减弱,原子布居的崩塌与复苏的周期缩短;在初始光场较弱和较强两种情况下,类Kerr介质对双模SU(1,1)相干态场两模间的相关性、相关程度以及光子的聚束与反聚束效应产生的作用有明显的区别.     

Photon-Subtracted Two-Mode Squeezed Thermal State and Its Photon-Number Distribution

We construct the photon-subtracted two-mode squeezed thermal state (PSTMSTS) by subtracting any number of photons from two-mode squeezed thermal state (TMSTS). It is found that the normalization factor of the density operator of PSTMSTS is a Jacobi polynomial of squeezing parameter λ and average photon number [`(n)]\bar{n} of the thermal state. We investigate the photon-number distribution (PND) of PSTMSTS and find a remarkable result that it is a quotient of two Jacobi polynomials, as well as derive a corresponding character of Jacobi polynomial.     

Even and Odd Nonlinear Negative Binomial States

In this paper the even and odd nonlinear negative binomial states of the radiation field are introduced. These states interpolates between even (odd) number states and the even (odd) nonlinear coherent states. The Glauber second-order correlation function is calculated for these states. The squeezing phenomenon (normal and amplitude-squared squeezing), the quasi-probability distribution function Q-function, Wigner-function and the phase properties, are also discussed. Examination of the resonance fluorescence against the present state is given. It has been shown that the atomic inversion is sensitive to any variation in the even and odd nonlinear negative binomial number M and the nonlinearity parameter η.     

Manipulating nonclassical quantum statistical properties of light field by an f-deformed Bose–Einstein condensate

We consider the interaction between an f-deformed Bose–Einstein condensate and a single-mode quantized light field. By using the Gardiner’s phonon operators, we find that there exists a natural deformation in the model which modifies the Bogoliubov approximation under the condition of large but finite number of particles in condensate. This approach introduces an intrinsically deformed Bose–Einstein condensate, where the deformation parameter, well-defined by the particle number N in condensate, controls the strength of the associated nonlinearity. By introducing the deformed Gardiner’s phonon operators we modify the very dilute-gas approximation through including atomic collisions in condensate. The rate of atomic collisions κ, as a new deformation parameter in the deformed Bose–Einstein condensate, controls the nonlinearity related to the atomic collisions. We show that by controlling the nonlinearities in the f-deformed atomic condensate through the two atomic parameters N and κ, it is possible to generate and manipulate the nonclassical quantum statistical properties of radiation field, such as, the sub-Poissonian photon statistics and quadrature squeezing. Also, it is possible to control the collapses and revivals phenomena in the average number of photons by atomic parameters N and κ.     

双模SU(2)相干态场与一个Λ型三能级原子共振相互作用的光场非经典性质

采用全量子理论和数值计算方法, 研究了初始处于SU(2)相干态的双模腔场与一个Λ型三能级原子共振相互作用的光场非经典性质,讨论了在没有对原子进行态选择测量、 直接对原子进行态选择测量和应用经典微波场并对原子进行态选择测量的三种情况下,两个腔模总光子数、配分参量和耦合系数对光场非经典性质的影响.结果表明,增加两个腔模的总光子数M或对原子进行态选择测量,双模差压缩明显增强;减小配分参量和应用经典场并对原子进行态选择测量,a模光子的亚Poisson统计分布的平均程度变浅,而b模变深;两模间的反相关特征保持不变,增加M或直接对原子进行态选择测量,反相关平均程度变浅;直接对原子进行态选择测量,违背Cauchy-Schwartz不等式. 关键词： SU(2)相干态场')" href="#">SU(2)相干态场 Λ型三能级原子 态选择测量     

Statistical properties of a two-photon cavity mode in the presence of degenerate parametric amplifier

A Hamiltonian model that includes two-photon interaction with a two-level atom and a degenerate parametric amplifier is considered. By invoking a canonical transformation an exact solution of the wave function in the Schrödinger picture is obtained. The result presented in this context is employed to discuss the purity, the entropy squeezing, and the variance squeezing, in addition to the normal squeezing. It has been shown that the existence of the second harmonic generation leads to reduction in the squeezing amount for all quadrature variances and we found that as the value of the coupling parameter λ₂ increases the squeezing phenomenon gets more apparent. Further we have also considered the Q-function as an example of the quasi-probability distribution.     

Statistical properties of the output of linear amplifier with superpositions of squeezed displaced Fock states as an input state

The s-parameterized characteristic function for the output field with the superposition of squeezed displaced Fock states (SDFS's) as input field is given. The s-ordered distribution functions for the output field with superposition of SDFS's as input state are investigated. Various moments are calculated by using the s-ordered characteristic function for that field. The Glauber second-order coherence function is calculated. The quadrature squeezing for the output field are discussed. Some Quasiprobability distribution functions of the output fields are plotted as functions of the interaction time. The quadrature squeezing for the output field are discussed. Received 30 September 1998     

Wigner functions for two arbitrary operators and spectrum perturbation

We have concentrated on the Wigner function for the photon number and a quadrature operator, which we find to differ from zero outside the spectrum of the photon number operator. We have provided an illustration with a coherent state.     

激发双模压缩真空态的非经典特性

通过数值计算研究了激发双模压缩真空态a^+mb^+m|ξ>的非经典特性.结果表明:对于a^+mb^+m|ξ>,Cauchy-Schwartz不等式受到破坏;当取适当的压缩参量r(例如0.4～0.7)时,a^+mb^+m|ξ>呈现出正交分量的压缩和光子的亚泊松分布,而且压缩程度和亚泊松特性都随m的增大而有所增强.     

Number-Phase Quantization Scheme and the Quantum Effects of a Mesoscopic Electric Circuit at Finite Temperature

For L-C circuit, a new quantized scheme has been proposed in the context of number-phase quantization. In this quantization scheme, the number n of the electric charge q(q=en) is quantized as the charge number operator and the phase difference θ across the capacity is quantized as phase operator. Based on the scheme of number-phase quantization and the thermo field dynamics (TFD), the quantum fluctuations of the charge number and phase difference of a mesoscopic L-C circuit in the thermal vacuum state, the thermal coherent state and the thermal squeezed state have been studied. It is shown that these quantum fluctuations of the charge number and phase difference are related to not only the parameters of circuit, the squeezing parameter, but also the temperature in these quantum states. It is proven that the number-phase quantization scheme is very useful to tackle with quantization of some mesoscopic electric circuits and the quantum effects.