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Physical Review A

Squeezed states and the Franck-Condon overlap

L. Sandoval, Manuel Martín, Juan Francisco Rivas-Silva, Alberto José Palma

Published Nov 1, 1992• 7 citations
Publisher

Abstract

A simple and direct approach to studying squeezed states is proposed. It is based on treating the corresponding differential equations and their solutions directly on the Fock-Bargmann space. The method is exemplified by giving quite general solutions to the case of amplitude-squared squeezed states. We show the importance of this approach by deriving the overlap between these solutions and connecting them with the overlap integral associated with the Franck-Condon principle.

DOI
10.1103/physreva.46.6095

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A simple and direct approach to studying squeezed states is proposed. It is based on treating the corresponding differential equations and their solutions directly on the Fock-Bargmann space. The method is exemplified by giving quite general solutions to the case of amplitude-squared squeezed states. We show the importance of this approach by deriving the overlap between these solutions and connecting them with the overlap integral associated with the Franck-Condon principle.
Abstract A central problem in quantum mechanics is the calculation of the overlap, that is, the scalar product between two quantum states. In the semiclassical limit (Bohr's correspondence principle) we visualize this quantity as the area of overlap between two bands in phase space. In the case of more than one overlap the contributing amplitudes have to be combined with a phase difference again determined by an area in phase space. In this sense the familiar double‐slit interference experiment is generalized to an interference in phase space. We derive this concept by the WKB approximation, illustrate it by the example of Franck‐Condon transitions in diatomic molecules, and compare it with and contrast it to Wigner's concept of pseudo‐probabilities in phase space.