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Physica Scripta

Interaction between the Kravchuck and Meixner oscillators coherent states and the coherent radiation field

Gheorghe Eugen Drăgănescu

Published Mar 1, 2013• 0 citations
Publisher

Abstract

To describe a series of phenomena that occur in micro- and nano-systems, we have used the discrete variable Kravchuk and Meixner oscillators for which some sets of coherent states and some squeezed states were established. For a system consisting of molecular oscillators interacting with the coherent radiation field, an oscillatory variation of the refractive index was established.

DOI
10.1088/0031-8949/2013/t153/014019

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To describe a series of phenomena that occur in micro- and nano-systems, we have used the discrete variable Kravchuk and Meixner oscillators for which some sets of coherent states and some squeezed states were established. For a system consisting of molecular oscillators interacting with the coherent radiation field, an oscillatory variation of the refractive index was established.
In this work we study different types of coherent and squeezed states for the Charlier, Kravchuk and Meixner oscillators. We calculate the average values of different observables corresponding to the coherent states. We found that the coherent and squeezed states of the Kravchuk oscillator are unstable. There are also coherent and squeezed states that are similar to the coherent and squeezed states of the harmonic oscillator. We have introduced a discrete variable model for the biophoton coherent radiation, and the coherent thermal and squeezed thermal states.
The coherent states for the Kratzer-Fues potential, which are eigenstates of the annihilation operator and minimize the generalized position-momentum uncertainty relation, are constructed using the algebraic approach. The method is extended to include the rotating Kratzer-Fues oscillator. Construction of such states is important in the theory of molecular interactions with coherent electromagnetic fields, for example, in calculation of the dynamic alternation of the refractive index due to the interactions of the laser pulse with the coherent vibration-rotational states of the diatomic molecule.
For the one-dimensional Morse oscillator we have built a set of creation and annihilation operators and established the corresponding coherent states. The average values of some observables in these coherent states have been calculated and their time evolution established. In order to study the strong vibrations of di-atomic molecules we use a three-dimensional Morse oscillator model and its dynamic group. For this system we have built the coherent states and calculated the dynamic modifications of the refractive index of the molecules, as the result of interaction with a laser beam.
We extend our approach to constmction of coherent states for oscillator-like systems connected with given system of orthogonal polynomials to the case of the classical orthogonal polynomials of a discrete variable. In this paper we consider oscillntmor-liksey stem associated with the Meixnct polynomials and compare associated Hamiltonian with the Hamiltonian of the relativistic linear oscillator obtained by the other point of view. We also construct generalized coherent states both Rarut-Girardello and Perelomov types €or this system.
The photon distribution function of a discrete series of excitations of squeezed coherent states is given explicitly in terms of Hermite polynomials of two variables. The Wigner and the coherent-state quasiprobabilities are also presented in closed form through the Hermite polynomials and their limiting cases. Expectation values of photon numbers and their dispersion are calculated. Some three-dimensional plots of photon distributions for different squeezing parameters demonstrating oscillatory behaviour are given.