相量的q形变相干态及其压缩性质

研究位相正交算符在相量的q形变相干态中的压缩性质和二能级系统中粒子数-位相压缩及其不确定关系，进而得到了一些新的粒子数-位相不确定态. 关键词：     

Number-phase uncertainty relationship for the nonlinear number-phasesqueezed state

For an harmonic oscillator with a field intensity related external source we establish the nonlinear number-phase squeezed state, in this state we find that while the number fluctuation increases, the phase fluctuation decreases correspondingly. The number-phase uncertainty relationship is exactly derived. In contrast to the usual coherent state which makes up the minimum number-phase uncertainty relationship, the nonlinear number-phase squeezed state does not reach its minimum uncertainty.     

Phase Properties of Photon-Added Coherent States for Nonharmonic Oscillators in a Nonlinear Kerr Medium

The potential of nonharmonic systems has several applications in the field of quantum physics. The photonadded coherent states for annharmonic oscillators in a nonlinear Kerr medium can be used to describe some quantum systems. In this paper, the phase properties of these states including number-phase Wigner distribution function,Pegg-Barnett phase distribution function, number-phase squeezing and number-phase entropic uncertainty relations are investigated. It is found that these states can be considered as the nonclassical states.     

Entropic uncertainty relations for nonextensive quantum scattering

In this paper the angle-angular momentum entropic uncertainty relations are obtained for Tsallis-like entropies for nonextensive quantum scattering of spinless particles. The number-phase entropic uncertainty relations are also proved for nonextensive quantum scattering. Numerical results on the experimental tests of these entropic uncertainty relations, for the nonextensive (q≠1) statistics case are obtained by calculations of Tsallis-like scattering entropies from the 48 experimental sets of the pion-nucleus phase shifts.     

Number-phase entropic uncertainty relations and Wigner functions for solvable quantum systems with discrete spectra

In this Letter, the “number-phase entropic uncertainty relation” and the “number-phase Wigner function” of generalized coherent states associated to a few solvable quantum systems with non-degenerate spectra are studied. We also investigate time evolution of “number-phase entropic uncertainty” and “Wigner function” of the considered physical systems with the help of temporally stable Gazeau-Klauder coherent states.     

Complementarity in atomic (finite-level quantum) systems: an information-theoretic approach

We develop an information theoretic interpretation of the number-phase complementarity in atomic systems, where phase is treated as a continuous positive operator valued measure (POVM). The relevant uncertainty principle is obtained as an upper bound on a sum of knowledge of these two observables for the case of two-level systems. A tighter bound characterizing the uncertainty relation is obtained numerically in terms of a weighted knowledge sum involving these variables. We point out that complementarity in these systems departs from mutual unbiasededness in two significant ways: first, the maximum knowledge of a POVM variable is less than log (dimension) bits; second, surprisingly, for higher dimensional systems, the unbiasedness may not be mutual but unidirectional in that phase remains unbiased with respect to number states, but not vice versa. Finally, we study the effect of non-dissipative and dissipative noise on these complementary variables for a single-qubit system.     

一种新的非线性叠加相干态的相位特性

根据Pegg-Barnett 相位定义,计算了一种新的非线性叠加相干态的相位概率分布函数和光子数-相位压缩效应,并进行了数值模拟.     

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.     

Number-phase quantization of a mesoscopic RLC circuit

With the help of the time-dependent Lagrangian for a damped harmonic oscillator, the quantization of mesoscopic RLC circuit in the context of a number-phase quantization scheme is realized and the corresponding Hamiltonian operator is obtained. Then the evolution of the charge number and phase difference across the capacity are obtained. It is shown that the number-phase analysis is useful to tackle the quantization of some mesoscopic circuits and dynamical equations of the corresponding operators.     

Soliton squeezing in a highly transmissive nonlinear optical loop mirror

A perturbation approach is used to study the quantum noise of optical solitons in an asymmetric fiber Sagnac interferometer (a highly transmissive nonlinear optical loop mirror). Analytical expressions for the three second-order quadrature correlators are derived and used to predict the amount of detectable amplitude squeezing along with the optimum power-splitting ratio of the Sagnac interferometer. We find that it is the number-phase correlation owing to the Kerr nonlinearity that is primarily responsible for the observable noise reduction. The group-velocity dispersion affecting the field in the nonsoliton arm of the fiber interferometer is shown to limit the minimum achievable Fano factor.     

Generalized coherent states for solvable quantum systems with degenerate discrete spectra and their nonclassical properties

In this paper, the generalized coherent state for quantum systems with degenerate spectra is introduced. Then, the nonclassicality features and number-phase entropic uncertainty relation of two particular degenerate quantum systems are studied. Finally, using the Gazeau-Klauder coherent states approach, the time evolution of some of the nonclassical properties of the coherent states corresponding to the considered physical systems are discussed.     

Amplitude squeezed and number-phase intelligent states via coherent state superposition

It is shown that Gaussian superpositions of coherent states along an arc are approximate number-phase intelligent states associated with the Pegg-Barnett phase operator and describe amplitude squeezing.     

Number-Phase Quantization Scheme for L-C Circuit

For a mesoscopic L-C circuit, besides the Louisell's quantization scheme in which electric charge q and electric current I are respectively quantized as the coordinate operator Q and momentum operator P, in this paper we propose a new quantization scheme in the context of number-phase quantization through the standard Lagrangian formalism. The comparison between this number-phase quantization with the Josephson junction's Cooper pair number-phase-difference quantization scheme is made.     

Phase and number

Contrary to the widespread belief that no phase observable exists which is canonically conjugate to the number operator, a selfadjoint operator is given with the right properties to be a firm candidate for the quantum phase. Its spectrum, commutation relations, uncertainty inequalities and classical limit are discussed.     

Entangled State in Quantization of Magnetic Flux Qubits with Mutual Inductance Coupling

Via the Hamilton dynamical approach we have constructed Hamiltonian for the mutual inductance coupling magnetic flux qubits. The entangled state representation is used to propose Cooper-pair number-phase quantization and the Hamiltonian operator for the whole system. The dynamical evolution of the phase difference operator and the Cooper-pairs number operator is investigated by virtue of Heisenberg equations. Project 10574060 supported by the National Natural Science Foundation of China and project X071045 supported by the Science Foundation of Liaocheng University.     

Uncertainty relations for general phase spaces

We describe a setup for obtaining uncertainty relations for arbitrary pairs of observables related by a Fourier transform. The physical examples discussed here are the standard position and momentum, number and angle, finite qudit systems, and strings of qubits for quantum information applications. The uncertainty relations allow for an arbitrary choice of metric for the outcome distance, and the choice of an exponent distinguishing, e.g., absolute and root mean square deviations. The emphasis of this article is on developing a unified treatment, in which one observable takes on values in an arbitrary locally compact Abelian group and the other in the dual group. In all cases, the phase space symmetry implies the equality of measurement and preparation uncertainty bounds. There is also a straightforward method for determining the optimal bounds.     

A rigorous uncertainty relation (Cauchy Inequality) for an electromagnetic field in quantum superpositions of coherent states and in a two-photon coherent state

It is shown that the Heisenberg uncertainty relation (or soft uncertainty relation) determined by the commutation properties of operators of electromagnetic field quadratures differs significantly from the Robertson–Schrödinger uncertainty relation (or rigorous uncertainty relation) determined by the quantum correlation properties of field quadratures. In the case of field quantum states, for which mutually noncommuting field operators are quantum-statistically independent or their quantum central correlation moment is zero, the rigorous uncertainty relation makes it possible to measure simultaneously and exactly the observables corresponding to both operators or measure exactly the observable of one of the operators at a finite measurement uncertainty for the other observable. The significant difference between the rigorous and soft uncertainty relations for quantum superpositions of coherent states and the two-photon coherent state of electromagnetic field (which is a state with minimum uncertainty, according to the rigorous uncertainty relation) is analyzed.     

Estimation of shift parameters of a quantum state

Estimation of shift parameters such as arrival time, phase, angle of rotation, position of a non-relativistic or relativistic particle is considered. An approach from the point of view of quantum estimation theory enables to give a proper definition of the time observable and the position observables of a massless relativistic particle, i.e. observables to which there do not correspond self-adjoint operators. Some new inequalities for estimates of shift parameters are obtained; in particular a rigorous uncertainty relation for coordinates of the photon is established.     

Entangled States in the Capacitance Coupling Double Josephson Junction Mesoscopic Circuit

The number-phase quantization scheme of the capacitance coupling double Josephson junction mesoscopic circuit is given. The eigenvalues and the eigenstates of the system are investigated. It is found that using this system the entangled states can be prepared.