Nonclassical properties and algebraic characteristics of negative binomial states in quantized radiation fields

We study the nonclassical properties and algebraic characteristics of the negative binomial states introduced by Barnett recently. The ladder operator formalism and displacement operator formalism of the negative binomial states are found and the algebra involved turns out to be the SU(1,1) Lie algebra via the generalized Holstein-Primarkoff realization. These states are essentially Perelomov's SU(1,1) coherent states. We reveal their connection with the geometric states and find that they are excited geometric states. As intermediate states, they interpolate between the number states and geometric states. We also point out that they can be recognized as the nonlinear coherent states. Their nonclassical properties, such as sub-Poissonian distribution and squeezing effect are discussed. The quasiprobability distributions in phase space, namely the Q and Wigner functions, are studied in detail. We also propose two methods of generation of the negative binomial states. d 32.80.Pj Optical cooling of atoms; trapping Received 8 May 1999 and Received in final form 8 November 1999     

Quantum state engineering using conditional measurement on a beam splitter

State preparation via conditional output measurement on a beam splitter is studied, assuming the signal mode is mixed with a mode prepared in a Fock state and photon numbers are measured in one of the output channels. It is shown that the mode in the other output channel is prepared in either a photon-subtracted or a photon-added Jacobi polynomial state, depending upon the difference between the number of photons in the input Fock state and the number of photons in the output Fock state onto which it is projected. The properties of the conditional output states are studied for coherent and squeezed input states, and the probabilities of generating the states are calculated. Relations to other states, such as near-photon-number states and squeezed-state-excitations, are given and proposals are made for generating them by combining the scheme with others. Finally, effects of realistic photocounting and Fock-state preparation are discussed. Received: 17 March 1998 / Revised and Accepted: 8 May 1998     

压缩奇偶相干态的量子统计性质

用压缩算子作用在奇偶相干态上即可得到压缩奇偶相干态.本文研究了这类量子态的统计特性.结果表明,压缩奇相干态和压缩偶相干态都能处于压缩状态,它们的光子亦都可能出现反聚束的现象.     

Phase properties of superposed squeezed states

The phase properties of the superposed squeezed states are studied. The superposed squeezed states are obtained by inserting two squeezers in a Mach-Zehnder interferometer one for each arm. The visibility of the states as a measure of the coherence of the generated photons in the nonlinear interferometer is analyzed. And the mean-square phase fluctuations are also considered to analyze the phase properties of the superposed squeezed states. The quantities are obtained as a function of gain and the input phase, when the amplified input is a coherent state, a number state, a thermal state, a displaced number state, or a coherent thermal state.     

Squeezing properties of light field in the process preparing Raman atom laser

In this paper, the squeezing properties of the probe light field in the process preparing Raman-type atom laser via stimulated Raman transition of the sodium atom Bose-Einstein condensate (BEC) interacting with two light beam of a weaker squeezed coherent probe light and a stronger classical pump light are studied. The results show that the probe light can be periodically squeezed. The squeezing period is related to the mean number of atoms in trap, the strength of interaction between squeezed light and BEC atoms, and the detuning of the light, and the squeezing depth is determined by the initial squeezing factor of the probe light.     

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.     

Polarization distributions and degree of polarization for quantum Gaussian light fields

We examine polarization properties of electromagnetic field states with Gaussian complex-amplitude distributions, such as quadrature coherent and squeezed states, thermal chaotic states, and two-mode squeezed vacuum states. We compute their polarization distribution and we apply to them diverse measures of degree of polarization and polarization fluctuations. This allows us to investigate the main properties of the degrees of polarization introduced so far.     

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.     

叠加多模薛定谔猫态纠缠光场的不等幂次高次差压缩

利用多模压缩态理论研究了由多模复共轭相干态、多模复共轭虚相干态和多模真空态的线性叠加所组成的三态叠加多模薛定谔猫态纠缠光场的广义非线性不等幂次高次差压缩特性.结果发现:①真空场对此猫态光场的不等幂次高次差压缩效应没有影响;②在一定条件下,此猫态光场的两个正交相位分量可分别呈现出不等幂次高次差压缩效应;③而在另外的条件下,此猫态光场的两个正交相位分量则可同时出现上述的不等幂次高次差压缩效应,这是一种与测不准关系相悖的现象,称此种现象为"双边差压缩"效应.     

New uncertainty relations for tomographic entropy: application to squeezed states and solitons

Using the tomographic probability distribution (symplectic tomogram) describing the quantum state (instead of the wave function or density matrix) and properties of recently introduced tomographic entropy associated with the probability distribution, the new uncertainty relation for the tomographic entropy is obtained. Examples of the entropic uncertainty relation for squeezed states and solitons of the Bose-Einstein condensate are considered.     

原子薛定谔猫态中角动量的压缩及其时间演化

在低Q值腔内，原子相干态在一些特定时刻可以演化为原子薛定谔猫态.讨论了在这种原子薛定谔猫态中原子角动量的涨落和高阶涨落.根据不确定性原理，进一步研究了原子角动量的压缩和高阶压缩性质及其演化.研究表明，原子薛定谔猫态可以被压缩到二阶和六阶，但不能被压缩到四阶.当原子薛定谔猫态中被叠加的原子相干态数为无限多项时，其压缩特性与原子相干态相同. 关键词： 原子相干态 薛定谔猫态 角动量压缩 Bloch态     

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。     

利用V型三能级原子与单模光场的非共振相互作用制备压缩相干态的叠加态

介绍了单模压缩相干态及其基本性质,根据简并V型三能级原子与单模光场的改进型有效哈密顿量,通过矩阵方法推导出原子-光场系统的态矢量.提出利用简并V型三能级原子与单模光场的非共振相互作用制备压缩相干态的叠加态的一种新方案,讨论了怎样进行控制单模压缩相干态光场中的压缩方向问题.     

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.     

Superpositions of excited–deexcited coherent states and some of their non-classical properties

Applying the operator a + a⁺ to the superposed coherent states several times, superpositions of the excited–deexcited coherent states are obtained. Compared with the original superposed coherent states, these new states can have stronger squeezing and anti-bunching effects. The operation a + a⁺ can also induce squeezing or antibunching effect if the original states do not possess these properties. Calculations about the phase properties, the Q function and the Wigner function reflect the non-classical character of the excited–deexcited states from different aspects.     

Variance squeezing and information entropy squeezing via Bloch coherent states in two-level nonlinear spin models

The nonclassical squeezing effect emerging from a nonlinear coupling model (generalized Jaynes–Cummings model) of a two-level atom interacting resonantly with a bimodal cavity field via two-photon transitions is investigated in the rotating wave approximation. Various Bloch coherent initial states (rotated states) for the atomic system are assumed, i.e., (i) ground state, (ii) excited state, and (iii) linear superposition of both states. Initially, the atomic system and the field are in a disentangled state, where the field modes are in Glauber coherent states via Poisson distribution. The model is numerically tested against simulations of time evolution of the based Heisenberg uncertainty relation variance and Shannon information entropy squeezing factors. The quantum state purity is computed for the three possible initial states and used as a criterion to get information about the entanglement of the components of the system. Analytical expression of the total density operator matrix elements at t > 0 shows, in fact, the present nonlinear model to be strongly entangled, where each of the definite initial Bloch coherent states is reduced to statistical mixtures. Thus, the present model does not preserve the modulus of the Bloch vector.     

Quantifying the decay of quantum properties in single-mode states

The dissipative dynamics of Gaussian squeezed states (GSS) and coherent superposition states (CSS) are analytically obtained and compared. Time scales for sustaining different quantum properties such as squeezing, negativity of the Wigner function or photon number distribution are calculated. Some of these characteristic times also depend on initial conditions. For example, in the particular case of squeezing, we find that while the squeezing of CSS is only visible for small enough values of the field intensity, in GSS it is independent of this quantity, which may be experimentally advantageous. The asymptotic dynamics however is quite similar as revealed by the time evolution of the fidelity between states of the two classes.     

真空场注入非对称五态叠加多模泛函叠加态的高次振幅压缩

构造了由多模真空态、多模泛函相干态、多模泛函相干态的相反态、多模复共轭泛函相干态和多模复共轭泛函相干态的相反态这五个宏观上完全可分辩的量子态线性叠加所构成的强度不等的非对称五态叠加多模泛函叠加态光场|Ψ(5)vas〉q.利用多模压缩态理论,首次研究了态|Ψ(5)vas〉q的广义非线性等幂奇数次高次振幅压缩特性.结果发现:在一定的条件下,态|Ψ(5)vas〉q可呈现任意次的广义非线性等幂次高次振幅压缩效应,其压缩程度、压缩深度和压缩幅度与压缩次数、腔模总数、态间叠加几率幅、各模光场的经典强度以及经典初始相位的空间分布函数等强烈地非线性相关联;特别是,在特定条件下,真空场的注入可以提高压缩程度.     

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.     

Fractals,coherent states and self-similarity induced noncommutative geometry

The self-similarity properties of fractals are studied in the framework of the theory of entire analytical functions and the q-deformed algebra of coherent states. Self-similar structures are related to dissipation and to noncommutative geometry in the plane. The examples of the Koch curve and logarithmic spiral are considered in detail. It is suggested that the dynamical formation of fractals originates from the coherent boson condensation induced by the generators of the squeezed coherent states, whose (fractal) geometrical properties thus become manifest. The macroscopic nature of fractals appears to emerge from microscopic coherent local deformation processes.