Deformed squeezed states in noncommutative phase space

A deformed boson algebra is naturally introduced from studying quantum mechanics on noncommutative phase space in which both positions and momenta are noncommuting each other. Based on this algebra, corresponding intrinsic noncommutative coherent and squeezed state representations are constructed, and variances of single- and two-mode quadrature operators on these states are evaluated. The result indicates that in order to maintain Heisenberg's uncertainty relations, a restriction between the noncommutative parameters is required.     

Quasiprobabilities based on squeezed states

We introduce quasiprobabilities based on the so-called squeezed states to represent the density operator of an oscillator. Such representations become especially useful for oscillators designed to display, strong excitation notwithstanding, pronounced quantum features such as squeezing of the quantum fluctuations of certain observables below the limit characteristic of coherent states.     

On the stable evolution of squeezed and correlated states

It is shown that the stable evolution equations for the squeezed and correlated states (SS and CorS) in the form of H_w × SU (l.l)-coherent states with maximal symmetry are classical Hamiltonian equations with a Kaehler symplectic 2-form of Onofri type. The evolution of the second momenta of the Hermitian quadratures of the boson operator is described by canonical equations. The general form of the Hamiltonian which correlates without squeezing is found and the connection of the stable evolution of SS and CorS with the existence of linear integrals of motion is pointed out.Presented at the International Workshop on Squeezed and Correlated States in Quantum Optics, Moscow, December 3–7, 1990.     

Dual squeezed states

Collective operators corresponding to two different algebras have been introduced for a simple system consisting of a single two-level atom and a high-quality cavity mode. The generators of the first algebra satisfy boson commutation relations, whereas the generators of the second algebra have been obtained by polynomial deformation of su(2) algebra. It has been shown that dual squeezed states identified using the considered commutation relations can be observed in the system placed in an entangled bath with quantum correlations.     

Generalized squeezed states

Squeezed states are one of the most useful quantum optical models having various applications in different areas, especially in quantum information processing. Generalized squeezed states are even more interesting since, sometimes, they provide additional degrees of freedom in the system. However, they are very difficult to construct and, therefore, people explore such states for individual setting and, thus, a generic analytical expression for generalized squeezed states is yet inadequate in the literature. In this article, we propose a method for the generalization of such states, which can be utilized to construct the squeezed states for any kind of quantum models. Our protocol works accurately for the case of the trigonometric Rosen–Morse potential, which we have considered as an example. Presumably, the scheme should also work for any other quantum mechanical model. In order to verify our results, we have studied the nonclassicality of the given system using several standard mechanisms. Among them, the Wigner function turns out to be the most challenging from the computational point of view. We, thus, also explore a generalization of the Wigner function and indicate how to compute it for a general system like the trigonometric Rosen–Morse potential with a reduced computation time.     

On collective two-phonon states in deformed nuclei

The centroid energies of the two-phonon states in doubly even deformed nuclei are calculated within the quasiparticle-phonon nuclear model taking into account the Pauli principle in the two-phonon components of the wave functions. It is shown that the collective two-phonon energies are shifted by 1–2 MeV to higher energies due to the Pauli principle. A strong fragmentation of the two-phonon collective states over many nuclear levels occurs at the excitation energies of 3–4 MeV. It is concluded that the two-phonon states cannot exist in deformed nuclei. The analysis of the available experimental data on the two-phonon states shows that the experimental data do not contradict the results of these calculations.     

Extended two-parameter squeezed states

In a recent paper, a new λ-dependent squeezed states was proposed [J. Beckers, N. Debergh and F.H. Szafraniec, Phys. Lett. A 243 (1998) 256–260] in which the usual Fock-space creation operator has been modified by introducing a simple translational term. In this paper, we generalize this approach by adding a new term proportional to the creation operator using exponential quadratic operators.     

General two-mode squeezed states

The states |A ₁ A ₂ are considered, where the operators are associated with a unitary representation of the groupSp(4,), and the two-mode Glauber coherent states |A ₁ A ₂> are joint eigenstates of the destruction operatorsa ₁ anda ₂ for the two independent oscillator modes. We show that they are ordinary coherent states with respect to new operatorsb ₁ andb ₂, which are themselves general linear (Bogolibov) transformations of the original operatorsa ₁,a ₂ and their hermitian conjugatesa ¹ ,a ² . We further show how they may be regarded as the most general two-mode squeezed states. Most previous work on two-mode squeezed states appears to be based on more restrictive definitions than our own, and thereby reduces to special cases which are unified within our treatment.     

On the generation of a generalized superposition of displaced squeezed states

A feasible scheme is presented to generate a generalized superposition of displaced squeezed states, cosθ|α,z〉±sinθ|-α,z〉, in a single mode of the electromagnetic field inside a microwave cavity. The scheme employs a two-level (Rydberg) atom driven by an external classical field. The success probability and the interaction time of such generation are also considered.     

On the theory of limiting states of deformed nanostructured solids

Mechanisms are analyzed that determine the kinetics of approach to the limiting states of deformed nanostructured solids. These states are characterized by the smallest possible average grain size. It is shown that the limiting states correspond to dynamic equilibria between competing processes of fragmentation and deformation-induced growth of nanograins.     

Displaced and squeezed number states

From a background of displaced (coherent) and squeezed states, previous (often forgotten) work on displaced and squeezed number states is reviewed. We derive the most general of such states. The time-dependent expectation values, uncertainties, wave-functions, and probability densities are obtained. We comment on the possibility of experimentally observing these states.     

低频压缩态光场的制备

低频压缩态光场可用于提高引力波探测器灵敏度, 近年来受到人们的广泛关注. 相对于高频段而言, 低频压缩态的产生更容易受到外界环境噪声的干扰而不易被观察到. 本文采用全固化单频倍频Nd: YVO4/KTP激光器作为光源, 利用双波长共振的光学参量振荡器实现参量过程, 以1064 nm波长的红外作为基频光, 激光器腔内倍频产生的532 nm绿光作为抽运光, 通过调节周期性极化磷酸氧钛钾晶体温度使光学参量振荡器达到双波长同时共振, 采用真空注入的方式, 利用Pound-Drever-Hall锁腔技术锁定抽运场. 输出压缩光通过平衡零拍探测, 最终在实验上获得了频率低至3 kHz的真空压缩, 所直接观察到的压缩度为2 dB.     

Linear dependence of deformed two-photon quadrature operators on spatial noncommutative parameter

By deriving useful formulas on the variances of the deformed two-photon quadrature operators in noncommutative space, we show that the variances in general have a linear dependence on the spatial noncommutative parameter θ  , significantly different from the previous θ²${\theta }^2$-dependence results. The θ  -dependence instead of θ²${\theta }^2$-dependence results make the scheme of testing the space noncommutativity via measuring such variances much easier to realize experimentally, well within the reach of nowadays technology.     

Coherent and squeezed states on physical basis

A definition of coherent states is proposed as the minimum uncertainty states with equal variance in two hermitian non-commuting generators of the Lie algebra of the hamiltonian. That approach classifies the coherent states into distinct classes. The coherent states of a harmonic oscillator, according to the proposed approach, are shown to fall in two classes. One is the familiar class of Glauber states whereas the other is a new class. The coherent states of spin constitute only one class. The squeezed states are similarly defined on the physical basis as the states that give better precision than the coherent states in a process of measurement of a force coupled to the given system. The condition of squeezing based on that criterion is derived for a system of spins.