Generalized definition of coherent states and dynamical groups

It is shown that coherent states may be defined for an arbitrary dynamical (Hamiltonian) quantum system and the definition is consistent with the requirement that the Hamiltonian commutes with a Lie algebra γ, and γ can be integrated to form a Lie groupG.     

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.     

Generalized coherent states of multimode light,and biphotons

Generalized coherent states of a multimode field are analyzed within the framework of the dynamic-symmetry approach and with allowance for polarization. A new class of unpolarized two-photon states is defined. The uncertainty relations and statistical and other properties of optical fields in these states are calculated and analyzed. The relations between the considered states and squeezed states of light are discussed.Optics Laboratory, Lebedev Physics Institute, Academy of Sciences of the USSR. Translated from Preprint No. 254 of the Lebedev Physics Institute, Academy of Sciences of the USSR, Moscow. 1988.     

Generalized Heisenberg algebra coherent states for power-law potentials

Coherent states for power-law potentials are constructed using generalized Heisenberg algebra. Klauder's minimal set of conditions required to obtain coherent states are satisfied. The statistical properties of these states are investigated through the evaluation of the Mandel's parameter. It is shown that these coherent states are useful for describing the states of real and ideal lasers.     

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.     

Generalized quantum spins,coherent states,and lieb inequalities

A mathematical generalization of the concept of quantum spin is constructed in which the role of the symmetry groupO ₃ is replaced byO _v (=2,3,4, ...). The notion of spin direction is replaced by a point on the manifold of oriented planes in ^v . The theory of coherent states is developed, and it is shown that the natural generalizations of Lieb's formulae connecting quantum spins and classical configuration space hold true. This leads to the Lieb inequalities [1] and with it to the limit theorems as the quantum spinl approaches infinity. The critical step in the proofs is the validity of the appropriate generalization of the Wigner-Eckart theorem.This paper is based largely on the Indiana University Ph. D. thesis of the first named author     

Generalized even and odd coherent states of a single bosonic mode

Some properties of the eigensolutions of two commuting non Hermitian operators are brought to the light and exploited to introduce a novel characterization of a set of non classical states of a single bosonic mode. In this context, the construction of possible generalizations of the even and odd coherent states is developed in detail.     

Generalized enveloping algebras and quantum kinematic coherent states of noncompact Lie groups

A new concept of generalized enveloping algebra is introduced by means of the generalized Heisenberg commutation relations of non-Abelian quantum kinematics. This concept is examined within the quantum-kinematic formalism of some noncompact Lie groups of a special kind. The well known Gel'fand theorem (which relates the center of the traditional enveloping algebra with the adjoint representation) is then extended to the generalized enveloping algebra of the group. In this way, the isomorphism of the generalized left-center and the traditional right-center of the corresponding enveloping algebras is proved within the left regular representation of noncompact Lie groups of the chosen kind. As an interesting application of generalized enveloping algebras, this paper contains a brief discussion of quantum-kinematic (boson) ladder operators for non-Abelian noncompact finite Lie groups and of their corresponding coherent states.     

Theory of coherent two-photon absorption

An exact solution for the propagation of two ultrashort pulses through a two-photon near resonant absorbing medium is obtained under the condition that the initial number of photons/s cm² in the two pulses are the same. High-power pulses develop sharp peaks as they propagate through the medium.     

Theory of two-photon lasers I

We start from the microscopic Hamiltonian formulated by means of creation and annihilation operators for the field modes, and creation and annihilation operators for the electrons. The virtual transitions via the intermediate atomic level are eliminated by second order perturbation theory so that an effective Hamiltonian results which describes two-photon creation or annihilation. In the next step Heisenberg equations of motion are derived for the field amplitudes, the atomic dipole moments, and the inversion. The effect of heatbaths is taken into account by means of damping terms and fluctuating forces. In the present paper these equations are averaged over the fluctuating forces and the resulting semiclassical equations are solved for the stationary state. We treat the degenerate and nondegenerate case including detuning and atomic levels with homogeneous and inhomogeneous broadening. The field modes may be either running or standing waves. A detailed discussion of the laser condition is given.     

Theory of two-photon lasers II

In order to treat two-photon laser action including noise close to threshold the Fokker-Planck equation is used and its steady state solution determined. It allows us to discuss the stable, unstable, and metastable states of the two-photon laser.     

Bistability in coherent two-photon processes

Using the coupled Maxwell-Bloch equations for coherent two photon processes, we show the existence of bistable behavior of systems undergoing coherent two photon resonant processes such as two photon absorption and Raman process. The system is taken to be contained in a ring cavity. The dependence of the bistable behavior on detuning parameter and the Stark shifts is also discussed.     

Lineshapes in coherent two-photon excitation

We compare lineshapes obtained in laser-induced fluorescence and resonantly enhanced multi-photon ionisation, resulting from coherent pulsed excitation of a two-photon transition in xenon atoms. We find that excitation profiles probed by ionisation show power broadening as expected. Here ionisation occurs simultaneously with the coherent excitation. The profiles observed by fluorescence show almost no broadening, because of coherent population return, since the fluorescence occurs predominantly after the excitation pulse is over. Thus the observed lineshape depends characteristically upon the nature of the probing process.     

Theory of two-photon lasers III

We treat the semiclassical equations and the Fokker-Planck equation of a two-photon laser with one or two injected signals and treat both the degenerate and nondegenerate case. The resulting behaviour in the two-photon laser is discussed by means of potential functions which allows one to determine the stable, unstable, and metastable states.     

Mode-locked two-photon states

The concept of mode locking in laser is applied to a two-photon state with frequency entanglement. Cavity enhanced parametric down conversion is found to produce exactly such a state. The mode-locked two-photon state exhibits a comblike correlation function. An unbalanced Hong-Ou-Mandel type interferometer is used to measure the correlation function. A revival of the typical interference dip is observed. We will discuss a scheme for engineering of quantum states in time domain.     

Photon statistics of a two-photon laser

The steady state quantum statistical properties of a two-photon laser are presented for the case when the cavity loss mechanism is simulated by a single-photon process.     

Preparation and control of entangled states in the two-mode coherent fields interacting with a moving atom via two-photon process

We investigate the preparation and the control of entangled states in a system with the two-mode coherent fields interacting with a moving two-level atom via the two-photon transition. We discuss entanglement properties between the two-mode coherent fields and a moving two-level atom by using the quantum reduced entropy, and those between the two-mode coherent fields by using the quantum relative entropy. In addition, we examine the influences of the atomic motion and field-mode structure parameter $p$ on the quantum entanglement of the system. Our results show that the period and the duration of the prepared maximal atom-field entangled states and the frequency of maximal two-mode field entangled states can be controlled, and that a sustained entangled state of the two-mode field, which is independent of atomic motion and the evolution time, can be obtained, by choosing appropriately the parameters of atomic motion, field-mode structure, initial state and interaction time of the system.     

简并双光子激光的光子统计

从原子和场模的密度算符的主方程出发,应用Haake和Lewenstein所发展的原子变量绝热消除的算符方法,导出了简并双光子激光光场Wigner函数的福克-普朗克(Fokker-Planck)方程及其稳态解.利用稳态解的高斯近似,求得了在不同泵浦强度下,光子统计的解析结果如数值结果,并与前人的结果作了比较.     

Quanta and coherent states

The quantum harmonic oscillator can be considered as a composite system of indistinguishable Bose-Einstein symmetric two-level-systems (quanta). In analogy to the classical Poisson limit theorem, we show that a coherent state is the limit of a sequence of homogeneous product states (coherent spin states) and discuss statistical properties of the quanta in classical and nonclassical states.