Correlated coherent states and emission by quantum systems

Translated from Transactions of the Lebedev Physics Institute, Moscow, Vol. 192, pp. 204–220 (1988).     

有限维希尔伯特空间中的非线性相干态

在有限维希尔伯特空间中构造了非线性相干态,并研究了该量子态的压缩效应和反聚束效应,给出了压缩效应和反聚束效应与有限维希尔伯特空间维数关系的数值计算结果.     

Classical breathers and quantum coherent states in discrete NLS systems

We present a comparison of quantum and “semiclassical” trajectories of coherent states that correspond to classical breather solutions of finite discrete nonlinear Schrödinger (DNLS) lattices. The main goal is to explain earlier numerical observations of recurrent return to the vicinity of initial coherent states corresponding to stable breathers that are also spatially localized. This effect can be considered as a quantum manifestation of classical spatial localization. We show that these phenomena are encoded in a simple expression for the distance between the quantum and semiclassical states that involves the basic frequencies of the classical and quantum systems, as well as the breather amplitude and quantum spectral decomposition of the system. A corollary is that recurrence phenomena are robust under perturbation of the initial conditions for stable breathers.     

Entangled coherent states for quantum information processing

Entangled coherent states (ECSs) with relative phase equal to the phase shift between two coherent states are constructed. We study the degree of entanglement and the nonclassical features exhibited by the so-constructed states keeping in view their role in quantum information processing (QIP).     

On coherent states for the simplest quantum groups

The coherent states for the simplest quantum groups (q-Heisenberg-Weyl, SU _q (2) and the discrete series of representations of SU _q (1, 1)) are introduced and their properties investigated. The corresponding analytic representations, path integrals, and q-deformation of Berezin's quantization on , a sphere, and the Lobatchevsky plane are discussed.     

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.     

Formation of entangled states in nonequilibrium quantum systems with partial coherent pumping

The problem of generating the entangled states of two parametrically coupled quantum oscillators at finite temperatures is considered. For coherent pumping, an analytical expression describing the behavior of logarithmic negativity is obtained using the Heisenberg–Langevin formalism. The expression also describes the attaining of a long nonzero steady-state value of logarithmic negativity. It is shown numerically that pumping noise limits the lifetime of entanglement in the system.     

Bounded coherent states and excitonic systems

New bounded coherent state construction, based in a Keldysh conjecture, is presented. The particular group structure arising from the model leads a new symmetry transformations for the coherent state system. The emergent new symmetry transformations are reminiscent of the Bogoliubov ones. This construction is applied to describe an excitonic system. We discuss how the symmetry of these transformations is intrinsically related with the stability and the behavior of the physical systems as in the excitonic case.     

Passive states and KMS states for general quantum systems

We characterize equilibrium states of quantum systems by a condition of passivity suggested by the second principle of thermodynamics. Ground states and -KMS states for all inverse temperatures 0 are completely passive. We prove that these states are the only completely passive ones. For the special case of states describing pure phases, assuming the passivity we reproduce the results of Haag et al.     

Continuous variable quantum cryptography using coherent states

We propose several methods for quantum key distribution (QKD) based on the generation and transmission of random distributions of coherent or squeezed states, and we show that they are secure against individual eavesdropping attacks. These protocols require that the transmission of the optical line between Alice and Bob is larger than 50%, but they do not rely on "sub-shot-noise" features such as squeezing. Their security is a direct consequence of the no-cloning theorem, which limits the signal-to-noise ratio of possible quantum measurements on the transmission line. Our approach can also be used for evaluating various QKD protocols using light with Gaussian statistics.     

On symbolic-numerical representation of the evolution operator for finite-dimensional quantum systems

A symbolic algorithm to generate the multilayer operator-difference schemes for solving the evolution problem of the time-dependent Schrödinger equation is elaborated. An additional gauge transformation of operator-difference schemes to make good use of the finite-element discretization is applied. The efficiency of the generated numerical schemes until the sixth order with respect to the time step and until the seventh order with respect to the spatial step is demonstrated by calculations of some finite-dimensional quantum systems in external fields.     

Multi-layer evolution schemes for the finite-dimensional quantum systems in external fields

The operator-difference multi-layer (ODML) schemes for solving the time-dependent Schrödinger equation (TDSE) till six order accuracy by a time step are presented. The reduced schemes for solving a set of the coupled TDSE’s are devised by using a set of appropriate basis angular functions and a finite element method with respect to a hyper-radial variable. Convergence by a number of the basis functions and efficiency of the numerical schemes are demonstrated in the case of an exactly solvable model of the two-dimensional oscillator in time-depended electric fields.     

Entanglement diversion and quantum teleportation of entangled coherent states

The proposals on entanglement diversion and quantum teleportation of entangled coherent states are presented.In these proposals, the entanglement between two coherent states, $|\alpha\rangle$ and $|-\alpha\rangle$, with the same amplitude but a phase difference of $\pi$ is utilized as a quantum channel. The processes of the entanglement diversion and the teleportation are achieved by using the 50/50 symmetric beam splitters, the phase shifters and the photodetectors with the help of classical information.     

Quantum phase properties associated to solvable quantum systems using the nonlinear coherent states approach

In this paper we study the quantum phase properties of “nonlinear coherent states” and “solvable quantum systems with discrete spectra” using the Pegg-Barnett formalism in a unified approach. The presented procedure will then be applied to few special solvable quantum systems with known discrete spectrum as well as to some new classes of nonlinear oscillators with particular nonlinearity functions. Finally the associated phase distributions and their nonclasscial properties such as the squeezing in number and phase operators have been investigated, numerically.     

Macroscopic quantum control of exact many-body coherent states

We demonstrate that the idea of quantum control can be generalized to construct the exact many-body coherent state (MBCS) in a trapped Bose-Einstein condensate (BEC) of N atoms. Such a MBCS possesses the form of the single-particle coherent state, which does not deform in propagation and is stable for a repulsive BEC. The results suggest an experimental scheme for resonantly generating and coherently controlling the MBCSs.     

Demonstration of quantum telecloning of optical coherent states

We demonstrate unconditional telecloning for the first time. In particular, we symmetrically and unconditionally teleclone coherent states of light from one sender to two receivers, achieving a fidelity for each clone of F = 0.58 +/- 0.01, which surpasses the classical limit. This is a manipulation of a new type of multipartite entanglement whose nature is neither purely bipartite nor purely tripartite.     

Non-Gaussian cloning of quantum coherent states is optimal

We consider the optimal cloning of quantum coherent states with single-clone and joint fidelity as figures of merit. While the latter is maximized by a Gaussian cloner, the former is not: the optimal single-clone fidelity for a symmetric 1-to-2 cloner is 0.6826, compared to 2/3 in a Gaussian setting. This cloner can be realized with an optical parametric amplifier and certain non-Gaussian bimodal states. Finally, we show that the single-clone fidelity of the optimal 1-to-infinity cloner is 1/2. It is achieved by a Gaussian scheme and cannot be surpassed even with supplemental bound entangled states.     

Scale-renormalized matrix-product states for correlated quantum systems

A generalization of matrix product states (MPS) for interacting quantum systems in two and three dimensions is introduced. These scale-renormalized matrix-product states (SR-MPS) are based on a coarse graining of the lattice in which the blocks at each level are associated with matrix products that are further transformed (scale renormalized) with other matrices before they are assembled to form blocks at the next level. Using the two-dimensional transverse-field Ising model as a test, it is shown that the SR-MPS converge much more rapidly with the matrix size than a standard MPS. It is also shown that the use of lattice symmetries speeds up the convergence very significantly.     

有限维Hilbert空间Roy型奇偶非线性相干态的振幅平方压缩

构造出了有限维Hilbert空间Roy型奇偶非线性相干态, 讨论了它们的正交归一完备性和振幅平方压缩效应. 研究表明, 在此空间中Roy型奇偶非线性相干态是归一完备的, 但不具有正交性; 当复参数相位角θ满足一定条件时它们存在振幅平方压缩效应, 同时导出了压缩条件与参数s,r以及函数f(n)之间的关系. 最后借助于数值计算, 发现对于5维(或7维)Hilbert空间中Roy型偶(或奇)非线性相干态, 当参数θ和Lamb-Dike参数η取某一给定值时, 在参数r变化的不同取值范围内, 它们均可以呈现振幅平方 关键词： 有限维Hilbert空间 Roy型非线性相干态 奇偶非线性相干态 振幅平方压缩