Darboux transformation of coherent states for a Lobachevski plane

A Darboux transformation of coherent states is considered for a singular oscillator. A coordinate representation and a holomorphic representation are obtained for the Darboux transformation operator and the coherent states. The Hermitian metric and the Kaler potential of the transformed system are calculated. It is established that a Darboux transformation corresponds to curvature of the phase space of the classical system. Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 29–36, September, 1997.     

Pseudoharmonic oscillator and their associated Gazeau–Klauder coherent states

In the paper we have constructed and examined the properties of the Gazeau–Klauder coherent states (GK-CSs) for the pseudoharmonic oscillator (PHO), one of three possible kinds in order to define the coherent states for this oscillator potential. In the second part, we have examined some nonclassical properties of these states. Our attention has been concentrated on the mixed states (thermal states). The diagonal P-representation of the corresponding density operator and some thermal expectations for the quantum canonical ideal gas of pseudoharmonic oscillators have also been examined. Like the CSs for the harmonic oscillator (HO), the GK-CSs for the PHO can be useful in the quantum information theory (QIT).     

Darboux transformation of the coherent states of a nonrelativistic free particle

Various systems of soliton-potential coherent states have been derived. Measures are found that realize the expansion of a unit operator in terms of projectors on these states. Two different realizations of Hilbert state space are constructed as functions holomorphic throughout the complex plane and with a certain constraint on their increase. Tomsk State University and Tomsk State Pedagogic University, Tomsk. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, Vol. 42, No. 2, pp. 19–25, February, 1999.     

Information cloning of harmonic oscillator coherent states

We show that in the case of unknown harmonic oscillator coherent states it is possible to achieve what we call perfect information cloning. By this we mean that it is still possible to make arbitrary number of copies of a state which has exactly the same information content as the original unknown coherent state. By making use of this perfect information cloning it would be possible to estimate the original state through measurements and make arbitrary number of copies of the estimator. We define the notion of a measurement fidelity and calculate it for our case as well as for the Gaussian cloners.     

Invariants and coherent states for a nonstationary fermionic forced oscillator

Invariant creation and annihilation operators and related Fock states and coherent states are built up for the system of nonstationary fermionic forced oscillator.     

Photon-added coherent states for the Morse oscillator

In the paper we have constructed and investigated some properties of the Perelomov's “generalized coherent states” and photon-added coherent states for the Morse one-dimensional Hamiltonian (MO-PACSs), using the SU(2) group generators. We have found the integration measure in the resolution of unity and we have calculated some expectation values in the MO-PACSs representation. Using these states, the diagonal P-representation of the density operator is constructed as a new result for Morse potential. In addition, we have calculated some thermal expectation values for the quantum canonical diatomic gas of the Morse oscillators.     

Generalized deformed para-Bose oscillator and its coherent states

Generalized deformed commutation relations for a single-mode para-Bose oscillator are constructed. The connection of generalized deformed para-Bose oscillators with para-Bose oscillators is determined. From these, the energy spectrum of generalized deformed para-Bose oscillators and the coherent states of the annihilation operators are discussed. On leave from Department of Physics, Hanoi National University, 90 Nguyen Trai, Hanoi, Vietnam.     

A comment on coherent states of the isotonic oscillator

Landau's theory of density and pair fluctuations in a Fermi liquid is extended to include also fluctuations in the vertex functions, i.e. in the Landau parameters themselves. This is a natural consequence of the higher effective action Г[G, α] which depends explicitly on the full propagator G and the vertex α and whose extreme in G and α determine physical configurations of these quantities.     

Charged particle coherent states in tomographic probability representation

The symplectic tomograms of coherent states of a charged particle moving in a constant uniform magnetic field are obtained in explicit form. The tomograms are shown to coincide with normal probability distributions of two random variables. The means and dispersions of the variables are found and expressed in terms of means and dispersions of the charged particle coordinates and momenta. The characteristic function of the tomographic probability distribution is found. The center of mass tomogram of the coherent state of charge in magnetic field is also found and the relation of the symplectic tomogram and the center of mass tomogram is established.     

纠缠相干态及其非经典特性

通过引入正交基矢，连续变量形式的纠缠相干态转化成分立形式，然后用concurrence方法计算了纠缠度，同时研究了其非经典效应(压缩效应，反聚束效应).发现纠缠总是伴随着压缩效应和反聚束效应两者之一，并随相应非经典效应的增大而增大. 关键词： 纠缠 非经典效应 concurrence     

Generalized path-integral solution and coherent states of the harmonic oscillator in D-dimensions

We construct a general form of propagator in arbitrary dimensions and give an exact wavefunction of a time- dependent forced harmonic oscillator in D（D ≥ 1） dimensions. The coherent states, defined as the eigenstates of annihilation operator, of the D-dimensional harmonic oscillator are derived. These coherent states correspond to the minimum uncertainty states and the relation between them is investigated.     

q-形变的非简谐振子广义相干叠加态的高阶压缩效应

研究了q-形变的非简谐振子的广义相干态的高阶压缩效应,给出了出现高阶压缩现象的条件.     

The general anharmonicx 2q+2 damped oscillator and the coherent state representation

We obtain here a perturbative solution of the generalx ^2q+2 anharmonic damped oscillator in the coherent state representation. The solution does not contain any secular term and shows, explicitly, the damping and the anharmonic effects.     

Two-mode excited entangled coherent states and their entanglement properties

This paper introduces two types of two-mode excited entangled coherent states (TMEECSs) |Ψ_±(α,m,n)>, studies their entanglement characteristics, and investigates the influence of photon excitations on quantum entanglement. It shows that for the state |Ψ₊(α,m,m)> the two-mode photon excitations affect seriously entanglement character while the state |Ψ_-(α,m,m)> is always a maximally entangled state, and shows how such states can be produced by using cavity quantum electrodynamics and quantum measurements. It finds that the entanglement amount of the TMEECSs is larger than that of the single-mode excited entangled coherent states with the same photon excitation number.     

Diffusion and correlation in a coherent representation

Using a Fock-space formalism for the Master equation and introducing the density operator we present an unified method to derive kinetic equations for hopping processes with and without exclusion on a lattice. The corresponding Liouvillians are written in terms of Fermi or Bose operators, respectively. Although the Liouvillians are different the averaged particle numbers obey the same diffusion equation. Differences appear in the correlation functions only. The Master equation can be transformed into a differential equation in a coherent state representation. Using the algebraic properties of Grassmann numbers we are able to find the exact statonary solution for diffusion with exclusion. The conductivity can be derived in the bosonic and the fermionic case. The results are in accordance with those obtained with different other methods.     

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.     

Amplitude-squared squeezing of the generalized odd-even coherent states of the anharmonic oscillator in a finite-dimensional Hilbert space

This paper discusses the properties of amplitude-squared squeezing of the generalized odd-even coherent states of anharmonic oscillator in finite-dimensional Hilbert space. It demonstrates that the generalized odd coherent states do exhibit strong amplitude-squared squeezing effects in comparison with the generalized even coherent states.