Coherent quantum states of a relativistic particle in an electromagnetic plane wave and a parallel magnetic field

We analyze the solutions of the Klein–Gordon and Dirac equations describing a charged particle in an electromagnetic plane wave combined with a magnetic field parallel to the direction of propagation of the wave. It is shown that the Klein–Gordon equation admits coherent states as solutions, while the corresponding solutions of the Dirac equation are superpositions of coherent and displaced-number states. Particular attention is paid to the resonant case in which the motion of the particle is unbounded.     

Superradiance from three-level systems in atomic coherent state representation

A Fokker-Planck equation describing the coherent spontaneous emission from a system of 3-level atoms is derived using the atomic coherent states representation. The variables in this equation correspond directly to the number of atoms in the two excited states. The corresponding Langevin equations are discussed and their solutions for some special cases are presented.     

Gauge covariant construction of the coherent states for a time-dependent harmonic oscillator by algebraic dynamical method

Time-dependent coherent states for a time-dependent harmonic oscillator are constructed in the framework of algebraic dynamics. These coherent states are gauge-covariant, and its time evolution is governed only by the solutions of a linear differential equation which describes the motion of the corresponding classical timedependent harmonic oscillator. Its non-classical and quantum statistical properties can thus be controlled by a proper choice of the frequency of the harmonic oscillator. Our coherent states reduce to Glauber coherent states in the case as the frequency is independent of time.     

Qudit-type entanglement of continuous variables via weak cross-Kerr non linearity

We propose a protocol for creating arbitrary qudit state (including entangled states) with arbitrary dimensionality in continuous variable system using weak cross-Kerr nonlinearity, linear beamsplitters, detectors not resolving photon numbers, and sources of coherent states. The equation for unique determination of the used coherent states amplitudes is found. The protocol is applicable for creating entangled states at distances of 100 km using cross-Kerr nonlinearity χ ≥ χ _min ≃ 0.01 and optical fiber quantum channel.     

Painlevé IV coherent states

A simple way to find solutions of the Painlevé IV equation is by identifying Hamiltonian systems with third-order differential ladder operators. Some of these systems can be obtained by applying supersymmetric quantum mechanics (SUSY QM) to the harmonic oscillator. In this work, we will construct families of coherent states for such subset of SUSY partner Hamiltonians which are connected with the Painlevé IV equation. First, these coherent states are built up as eigenstates of the annihilation operator, then as displaced versions of the extremal states, both involving the related third-order ladder operators, and finally as extremal states which are also displaced but now using the so called linearized ladder operators. To each SUSY partner Hamiltonian corresponds two families of coherent states: one inside the infinite subspace associated with the isospectral part of the spectrum and another one in the finite subspace generated by the states created through the SUSY technique.     

Coherence and squeezing in Z3‐graded spin coherent states

A new kind of spin coherent state called a Z₃‐graded spin coherent state is constructed by using the complex solution of the equation q³ = 1. We explicitly find three kinds of Z₃‐graded spin coherent states. The associated coherent property and spin squeezing are also examined.     

Comments on “Barut-Girardello Coherent States for the Parabolic Cylinder Functions”

In Chenaghlou and Faizy (Int. J. Theor. Phys. 2008), the authors claim that they have constructed the Barut-Girardello coherent states for the parabolic cylinder functions. However, we point out here that by introducing these coherent states, Schrödinger was able to put forth the idea of “coherent states of the quantum harmonic oscillator” over eighty years ago. These coherent states are derived not only from the Barut-Girardello eigenvalue equation, but also from the Schrödinger and the Klauder-Perelomov approaches. Thus, contrary to their claim, the authors have not introduced new coherent states. In particular, a wide range of the parabolic cylinder functions do not form an orthonormal basis.     

双模纠缠相干光场与V型三能级原子相互作用系统的原子偶极压缩效应

采用求解Schroedinger方程和数值计算方法，研究了双模纠缠相干光场与V型三能级原子相互作用过程中原子偶极算符的压缩效应，结果表明：此压缩效应与双模纠缠光场的纠缠程度、失谐量相关联。     

双模纠缠相干光场与Ⅴ型三能级原子相互作用系统的原子偶极压缩效应

采用求解Schrodinger方程和数值计算方法,研究了双模纠缠相干光场与Ⅴ型三能级原子相互作用过程中原子偶极算符的压缩效应,结果表明:此压缩效应与双模纠缠光场的纠缠程度、失谐量相关联.     

Coherent states of nonstationary soliton potentials

With the help of a nonstationary Darboux transformation, we have obtained a system of coherent states for the potential which is a solution of the Kadomtsev-Petviashvili equation. We have determined the measure realizing expansion of unity with respect to these states. We have constructed a holomorphic representation of the state vectors and the ladder operators for the discrete basis of the Hilbert space of solutions of the Schrödinger equation.     

The driven-oscillator evolution in the tomographic-probability representation

We consider the problem of the driven harmonic oscillator in the probability representation of quantum mechanics, where the oscillator states are described by fair nonnegative probability distributions of position measured in rotated and squeezed reference frames in the system??s phase space. For some specific oscillator states like coherent states and nth excited states, the tomographic-probability distributions (called the state tomograms) are found in an explicit form. The evolution equation for the tomograms is discussed for the classical and quantum driven oscillators, and the tomographic propagator for this equation is studied.     

三能级原子与奇偶纠缠相干光作用的光场压缩

采用求解薛定谔方程和数值计算方法,研究了V型三能级原子与双模奇偶纠缠相干光场相互作用过程中的光场压缩效应,讨论了压缩效应与双模奇偶纠缠相干光场的纠缠程度、系统失谐量、双模光场的平均光子数和原子基态概率幅的依赖关系。结果表明：光场压缩效应与双模奇偶纠缠相干光场的纠缠程度、失谐量、平均光子数和原子初态相关联：双模纠缠相干光场处于非纠缠状态时的光场压缩量比光场处于纠缠状态时要大;原子处在单纯的基态或激发态时光场都有明显的压缩现象出现;而原子初态中基态和激发态的概率幅较接近时无光场压缩现象;无论光场是否处于纠缠态,只有两模平均光子数接近时,光场才会出现压缩效应。     

Statistical Properties and Algebraic Characteristics of Quantum Superpositions of Negative Binomial States

We introduce new kinds of states of quantized radiation fields,which are the superpositions of megative binomial states.They exhibit remarkable nonclassical properties and reduce to Schrodinger cat states in a certain limit.The algebras involved in the even and odd negative binomial states turn out to be generally deformed oscillator algebras.It is found that the even and odd negative binomial states satisfy the same eigenvalue equation with the same eigenvalue and they can be viewed as two-photon nonlinear coherent states.Two methods of generating such the states are proposed.     

双模纠缠相干光场与V型三能级原子相互作用系统的光子统计性质

本文采用求解Schrodinger方程和数值计算方法,研究了双模纠缠相干光场与三能级原子相互作用系统的光子统计性质,结果表明:此性质与双模纠缠相干光场的纠缠程度、失谐量、双模光的平均光子数和原子的初态相关联.     

Nonlinear evolution of coarse-grained quantum systems with generalized purity constraints

Constrained quantum dynamics is used to propose a nonlinear dynamical equation for pure states of a generalized coarse-grained system. The relevant constraint is given either by the generalized purity or by the generalized invariant fluctuation, and the coarse-grained pure states correspond to the generalized coherent, i.e. generalized nonentangled states. Open system model of the coarse-graining is discussed. It is shown that in this model and in the weak coupling limit the constrained dynamical equations coincide with an equation for pointer states, based on Hilbert-Schmidt distance, that was previously suggested in the context of the decoherence theory.     

QUANTUM FIELD THEORY IN EXTERNAL SOURCE:COHERENT STATE AND EIGENSTATES OF FIELDS

The real scalar field and the spinor field with external sources present are studied. The relationship between external sources and coherent states is given. In the case of real scalar field the eigenstates of field and its canonically conjugate field are derived in terms of coherent state and functional integration techniques. For a fermion field, it is demonstrated that Schwinger's external sources technique can lead to the spinor coherent states, with which we can also derive the eigenstates of fie3d operators and their conjugate field operators.The Yang-Feldman equation with the Grassmann sources is also obtained.     

Generalized coherent state for soft gluon emission

By using a recursive soft insertion technique, many gluon emission amplitudes are computed to all orders in α_s and leading infrared accuracy. The resulting correlation structure is systematically exponentiated to yield a generalized coherent state operator which satisfies an integral equation where virtual corrections occur as a Sudakov matrix for many parton states. Infrared cancellations for physical quantities, including Drell-Yan processes, are derived on the basis of the unitarity relation for the coherent state. By further assuming strong ordering in emission angles, all known results on coherent effects and multiplicity distributions are easily recovered.