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Journal of Optics B Quantum and Semiclassical Optics

Quantum statistical properties of the generalized excited even and odd coherent states

Wei Wu, Ling-An Wu

Published Jul 23, 2003• 7 citations
Publisher

Abstract

We construct mathematically two new types of quantum state which we call the generalized excited even and odd coherent states of the radiation field. They are created by repeatedly applying the pseudo-creation operator b † = ν ∗ a + μ ∗ a † to the even and odd coherent states m times, respectively. Analytic expressions for the quantum statistical properties are derived, and through numerical computation it is found that these states can exhibit highly nonclassical behaviour depending on the degree of excitation m and other parameters. These states may have interesting significance if they can be realized experimentally.

DOI
10.1088/1464-4266/5/4/307

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We construct mathematically two new types of quantum state which we call the generalized excited even and odd coherent states of the radiation field. They are created by repeatedly applying the pseudo-creation operator b † = ν ∗ a + μ ∗ a † to the even and odd coherent states m times, respectively. Analytic expressions for the quantum statistical properties are derived, and through numerical computation it is found that these states can exhibit highly nonclassical behaviour depending on the degree of excitation m and other parameters. These states may have interesting significance if they can be realized experimentally.
Two new classes of nonclassical states are defined by exciting Hillery's even and odd coherent states. Their physical properties are investigated numerically. It is found that they do not exhibit the squeezing effect but exhibit remarkable characteristics of sub-Poissonian distribution and antibunching. In sharp contrast to the case of excited Glauber coherent states, it is observed that the uncertainty of the field quadrature in excited even and odd coherent states increases with the degree of excitation. It is also seen that the Wigner functions associated with them take negative values for wider regions of parameters compared to those of Hillery's even and odd coherent states.
By applying higher powers of Bogoliubov’s transformation operator b†=ν*a+μ*a† to the even and odd coherent states we construct mathematically two new types of quantum states. Various special functions and mathematical formulations are used to obtain the matrix elements for the states in the coherent state representation. The nonclassical nature of these states is found to be related to their quantum coherence in phase space. The interference effects can also be regarded as a consequence of the oscillatory behavior of the special functions in the structure of the states.
By applying higher powers of the Bogoliubov transformation operator bdagger = v*a + mu*adagger to the two-photon coherent states (or minimum uncertainty squeezed states) we construct a new type of quantum state which we call the generalized excited two-photon coherent states. Analytic expressions for the quantum statistical properties are derived, and through numerical computation the phase space quasi-probability distributions are found. These states can exhibit highly nonclassical behaviour depending on the degree of excitation m and other parameters. For particular values of two parameters lambda and rho, these generalized states reduce to other classes of coherent states formerly reported. Our theory thus presents a much broader approach to these types of quantum states.