Squeezed states, metaplectic group, and operator möbius transformations

Arvind, * and Dutta, Biswadeb and Mehta, CL and Mukunda, N (1994) Squeezed states, metaplectic group, and operator möbius transformations. In: Physical Review A, 50 (1). pp. 39-61.

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Abstract

We present an analysis, based on the metaplectic group Mp(2), of the recently introduced single-mode inverse creation and annihilation operators and of the associated eigenstates of different two-photon annihilation operators. We motivate and obtain a quantum operator form of the classical Mobius or fractional linear transformation. The subtle relation to the two unitary irreducible representations of Mp(2) is brought out. For problems involving inverse operators the usefulness of the Bargmann analytic function representation of quantum mechanics is demonstrated. Squeezing, bunching, and photon-number distributions of the four families of states that arise in this context are studied both analytically and numerically

Item Type:	Journal Article
Publication:	Physical Review A
Publisher:	The american physical society
Additional Information:	Copyright of this article belongs to The american physical society.
Department/Centre:	Division of Physical & Mathematical Sciences > Centre for Theoretical Studies (Ceased to exist at the end of 2003)
Date Deposited:	13 Apr 2011 07:24
Last Modified:	13 Apr 2011 07:24
URI:	http://eprints.iisc.ac.in/id/eprint/36824

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