Multiphoton Squeezed States

We present analytical results for the multiphoton squeezed states defined through nonlinear quadraturedependent Bogoliubov transformations. These analytical results turn a nonlinear problem into an essentially linear one and they can be utilized to express explicitly the mean values and deviations of the quadrature operators and the photon variables under the multiphoton states in terms of those quantities averaged over the standard squeezed states which only involves the quadrature-independent Bogoliubov transformation.     

Three-Mode Nonlinear Bogoliubov Transformations

We introduce the three-mode nonlinear Bogoliubov transformations based on the work of Siena et al. (Phys. Rev. A 64:063803, 2001) and Ying Wu (Phys. Rev. A 66:025801, 2002) about nonlinear Bogoliubov transformations. We show that three-mode nonlinear Bogoliubov transformations can be constructed by the combination of two unitary transformations, a coordinate-dependent displacement followed by the standard squeezed transformation. Such decomposition turns all the nonlinear canonic coordinate-dependent Bogoliubov transformations into essentially linear problems as we shall prove and hence greatly facilitate calculations of the properties and the quantities related to the nonlinear transformations.     

Coherence Properties of Squeezed Photon States

Within the algebraic frame of smeared photon fields, the coherence properties of squeezed multi-photon states are elaborated. The squeezing Bogoliubov automorphisms are constructed by means of suitable one-mode symplectic transformations in the infinite-dimensional test-function space. Transposed into the state space, these transformations are shown to preserve first-order coherence when applied to coherent, classical, Fock-normal states in spite of rendering them nonclassical. The cases, where first-order coherence is destroyed, are also classified. Very special conditions on the initial state modes and on the operation parameters are worked out, under which even second-order coherence is still valid for the transformed classical coherent states, in spite of exhibiting squeezed fluctuations.     

Nonlinear squeezed states for SU(1,1) Lie algebra

The nonlinear extensions of the single-mode squeezed vacuum and squeezed coherent states are studied. We have constructed the nonlinear squeezed states (NLSS's) realization of SU(1,1) Lie algebra. Two cases of this realization are considered for unitary and non-unitary deformation operator function. The nonlinear squeezed coherent states (NLSCS's) are defined and special cases of these states are obtained. Some nonclassical properties of these states are discussed. The s-parameterized characteristic function and various moments are calculated. The Glauber second-order coherence function is calculated. The squeezing properties of the NLSCS's are studied. Analytical and numerical results for the quadrature component distributions for the NLSCS's are presented. A generation scheme for NLSCS's using the trapped ions centre-of-mass motion approach is proposed.     

Holstein-Primakoff/Bogoliubov Transformations and the Multiboson System

As an aid to understanding the displacement operator definition of squeezed states for arbitrary systems, we investigate the properties of systems where there is a Holstein-Primakoff or Bogoliubov transformation. In these cases the ladder-operator or minimum-uncertainty definitions of squeezed states are equivalent to an extent displacement-operator definition. We exemplify this in a setting where there are operators satisfying [A, A^å] = 1, but the A's are not necessarily the Fock space a's; the multiboson system. It has been previously observed that the ground state of a system often can be shown to to be a coherent state. We demonstrate why this must be so. We close with a discussion of an alternative, effective definition of displacement-operator squeezed states.     

量子玻色流体中的压缩玻色子对数态

导出参量相关的Bogoliubov幺正变换的封闭性表达式，在原粒子数表象中对角化量子玻色流体的约化Hamiltonian．将两模辐射场的非经典特性的表述推广到与流体的相互作用机制相应的量子玻色场，从波动和粒子统计的角度确认Hamiltonian本征态是非经典的压缩玻色子对数态． 关键词：     

f-Deformed Squeezed Vacuum and First Excited States,Their Superposition and Corresponding Nonclassical Properties

In this paper, we introduce two new classes of nonlinear squeezed states that we name as f-deformed squeezed vacuum state|ξ, f even and f-deformed squeezed first excited state |ξ, f odd, which according to their production processes, essentially include only even and odd bases of Fock space, respectively. In the continuation, we introduce the superposition of these two distinct nonlinear squeezed states with a respective phase ?. Then, some of the criteria which imply the nonclassicality of the states, such as Mandel parameter, second-order correlation function, quadrature squeezing, amplitude-squared squeezing, Husimi and Wigner–Weyl quasi-distribution functions, are numerically examined. At last, by considering a well-known nonlinearity function associated with a nonlinear physical system, we present our results which outcome from the numerical calculations. It is shown that, the introduced f-deformed states can reveal high nonclassical features.     

Even and odd nonlinear coherent states

New types of even and odd nonlinear coherent states are defined. The squeezed vacuum and the squeezed first excited state are shown to be even and odd nonlinear coherent states, respectively. The nonclassical properties of some related states are studied.     

Quantum phase distribution and the number—phase Wigner function of the generalized squeezed vacuum states associated with solvable quantum systems

The quantum phase properties of the generalized squeezed vacuum states associated with solvable quantum systems are studied by using the Pegg-Barnett formalism.Then,two nonclassical features,i.e.,squeezing in the number and phase operators,as well as the number-phase Wigner function of the generalized squeezed states are investigated.Due to some actual physical situations,the present approach is applied to two classes of generalized squeezed states:solvable quantum systems with discrete spectra and nonlinear squeezed states with particular nonlinear functions.Finally,the time evolution of the nonclassical properties of the considered systems has been numerically investigated.     

A new class of quantum states generated by m-fold application of Bogoliubov＇s transformation

By applying higher powers of the Bogoliubov transformation operator b^{\dagger }=ν^*a+μ^*a^{\dagger } to the two-photon coherent states (or minimum uncertainty squeezed states) we construct a new type of quantum state which we call the generalized excited two-photon coherent states. Analytic expressions for the quantum statistical properties are derived, and through numerical computation the phase space quasi-probability distributions are found. These states can exhibit highly nonclassical behaviour depending on the degree of excitation m and other parameters. For particular values of two parameters λ and ρ, these generalized states reduce to other classes of coherent states formerly reported. Our theory thus presents a much broader approach to these types of quantum states.     

Coordinate-Dependent One- and Two-Mode Squeezing Transformation and the Corresponding Squeezed States

We introduce the coordinate-dependent one- and two-mode squeezing transformations and discuss the properties of the corresponding one-and two-mode squeezed states. We show that the coordinate-dependent one-and two-mode squeezing transformations can be constructed by the combination of two transformations, a coordinate-dependent displacement followed by the standard squeezed transformation. Such a decomposition turns a nonlinear problem into a linear one because all the calculations involving the nonlinear one- and two-mode squeezed transformation have been shown to be able to reduce to those only concerning the standard one- and two-mode squeezed states.     

A theoretical scheme for generation of nonlinear coherent states in a micromaser under intensity-dependent Jaynes-Cummings model

In this paper we propose a theoretical scheme to show the possibility of generating various families of nonlinear (f-deformed) coherent states of the radiation field in a micromaser. We show that these states can be provided in a lossless micromaser cavity under the weak Jaynes-Cummings interaction with intensity–dependent coupling of large number of individually injected two-level atoms in a coherent superposition of the upper and lower states. In particular, we show that the so-called nonlinear squeezed vacuum and nonlinear squeezed first excited states, as well as the even and odd nonlinear coherent states can be generated in a two-photon micromaser.     

基于双模压缩态的量子密钥分发方案

提出了一种基于双模压缩态的量子密钥分发方案，采用Shannon信息论分析了该协议抵抗光束分离攻击的能力，得到秘密信息速率与压缩因子、信道参数之间的解析表达式，双模压缩态的模间关联性保证了该方案的安全性.     

High-Lying Vibrational Spectrum of Ammonia via Nonlinear Quantum Theory

We introduce a simple three-parameter model in nonlinear quantum theory-the discrete self-trapping equation to describe the stretching spectrum of ammonia at highlying vibrational states. The model calculations appear to describe the data well. These results obtained are conducive to researching the quantum chaotic manner and the multiphoton processes and isotope separation by multiphoton dissociation of ammonia molecular system.     

Security of quantum key distribution using two-mode squeezed states against optimal beam splitter attack

For the beam splitter attack strategy against quantum key distribution using two-mode squeezed states, the analytical expression of the optimal beam splitter parameter is provided in this paper by applying the Shannon information theory. The theoretical secret information rate after error correction and privacy amplification is given in terms of the squeezed parameter and channel parameters. The results show that the two-mode squeezed state quantum key distribution is secure against an optimal beam splitter attack.     

Degree of fourth-order coherence by double Hanbury Brownben Twiss detections

Photon quantum statistics of light can be shown by the high-order coherence. The fourth-order coherences of various quantum states including Fock states, coherent states, thermal states and squeezed vacuum states are investigated based on a double Hanbury Brown–Twiss (HBT) scheme. The analytical results are obtained by taking the overall efficiency and background into account.     

原子间相互作用对原子激光压缩性质的影响

研究了原子间相互作用对光场与原子玻色-爱因斯坦凝聚体相互作用系统中耦合输出的相干原子束压缩性质的影响．结果表明：原子激光的两正交分量的涨落均可压缩，玻色-爱因斯坦凝聚体中原子间的相互作用不利于原子激光的压缩． 关键词： 玻色-爱因斯坦凝聚 压缩相干态光场 压缩原子激光     

增光子奇偶相干态的相位特性

借助于Pegg-Barnett相位算符理论和数值计算方法,研究了增光子奇偶相干态的相位概率分布,在此基础之上,讨论了有关数算符和相位算符的压缩特性。结果表明,增光子奇偶相干态的相位概率分布与通常的奇偶相干态、非线性相干态不同,在这种新的奇偶相干态中,其Pegg-Barnett相位概率分布能明显地反映出不同的量子相位信息和干涉特性。同时发现,在参量α的某些不同的取值范围内,增光子奇偶相干态在数算符和相位算符分量上均存在压缩效应。     

A Quantum Dynamical Mode for the Control of Decoherence

We present a quantum measurement model where the meter is taken to be a squeezed reservoir. We realize decoherence in macroscopic limits using Bogoliubov transformation, and this kind of system-meter coupling has a dramatic influence on decoherence.     

Atomic Tunnelling Dynamics of Two Squeezed Bose-Einstein Condensates

In this paper, tunnelling dynamics of squeezed Bose-Einstein condensates (BEC's) in the presence of the nonlinear self-interaction of each species, the interspecies nonlinear interaction, and the Josephson-like tunnelling interaction is investigated by using the second quantization approach. The influence of BEC squeezing on macroscopic quantum self-trapping (MQST) and quantum coherent atomic tunnelling is analyzed in detail. It is shown that the MQST and coherent atomic tunnelling between two squeezed BEC's can be manipulated through changing squeezing amplitude and squeezing phase of BEC squeezed states.