Two Mode Quantum Systems: Invariant Classification of Squeezing Transformations and Squeezed States

Arvind, * and Dutta, B and Mukunda, N and Simon, R (1994) Two Mode Quantum Systems: Invariant Classification of Squeezing Transformations and Squeezed States. [Preprint]

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Abstract

A general analysis of squeezing transformations for two mode systems is given based on the four dimensional real symplectic group $Sp(4,\Re)\/$. Within the framework of the unitary metaplectic representation of this group, a distinction between compact photon number conserving and noncompact photon number nonconserving squeezing transformations is made. We exploit the $Sp(4,\Re)-SO(3,2)\/$ local isomorphism and the $U(2)\/$ invariant squeezing criterion to divide the set of all squeezing transformations into a two parameter family of distinct equivalence classes with representative elements chosen for each class. Familiar two mode squeezing transformations in the literature are recognized in our framework and seen to form a set of measure zero. Examples of squeezed coherent and thermal states are worked out. The need to extend the heterodyne detection scheme to encompass all of $U(2)\/$ is emphasized, and known experimental situations where all $U(2)\/$ elements can be reproduced are briefly described.

Item Type:	Preprint
Additional Information:	Phys. Rev. A 52, 1609 (1995)
Department/Centre:	Division of Physical & Mathematical Sciences > Physics Division of Physical & Mathematical Sciences > Centre for Theoretical Studies (Ceased to exist at the end of 2003)
Date Deposited:	31 Jul 2004
Last Modified:	19 Sep 2010 04:13
URI:	http://eprints.iisc.ac.in/id/eprint/909

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