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Banach Center Publications

Quasi-probability distribution of nonclassical states in interacting Fock space

Pradip Das, Arpita Ghosh

Published Jan 1, 2007• 0 citations
Publisher

Abstract

In this paper we study approximate quasi-probability distribution functions of nonclassical states such as incoherent states, Kerr states, squeezed states and $k$-photon coherent states in interacting Fock space.

DOI
10.4064/bc78-0-6

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In this paper we study approximate quasi-probability distribution functions of nonclassical states such as incoherent states, Kerr states, squeezed states and kkk-photon coherent states in interacting Fock space.
We consider the p-ordered characteristic function and its Fourier transform, the quasidistribution function, of squeezed coherent photons in a thermal state of photons and calculate the mean number and number variance of squeezed coherent photons. All the properties calculated from the previous characteristic function can be used to calculate said properties for photons in a thermal state of squeezed coherent photons via a parametric transformation. In particular, one can obtain the mean number and number variance via the parametric transformation.
Nonlinear extensions of the single-mode squeezed vacuum and squeezed coherent states are constructed. Nonlinear squeezed coherent states (NLSCSs) are defined and special cases of these states are discussed. Two cases of the definition are considered for the unitary and non-unitary deformation operator functions. Some nonclassical properties of these states are discussed. The Glauber second-order coherence function is calculated. Analytical and numerical results for the quadrature component distributions for the NLSCSs are presented. The s -parameterized quasi-probability function, especially the Wigner function, is discussed.
Displaced and squeezed Fock states have recently been thoroughly investigated. Application of these states as the input of a Kerr nonlinear medium reveals many nonclassical effects. We solve this problem analytically and demonstrate results by numerical examples. We introduce a phase distribution for the antinormal quasidistribution ${\mathrm{\ensuremath{\varphi}}}_{\mathit{s}\mathit{c}\mathit{r}\mathit{A}}$ and show that the ``phase'' of the new states can be sharply localized at some values. This happens when revivals appear in the field. If the states are shifted by a reference wave, photon-number distributions clearly detect the structure of ${\mathrm{\ensuremath{\varphi}}}_{\mathrm{scrA}}$. Damping of the new states is briefly discussed.