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Two-mode quantum systems: Invariant classification of squeezing transformations and squeezed states

Arvind, * and Dutta, B and Mukunda, N and Simon, R (1995) Two-mode quantum systems: Invariant classification of squeezing transformations and squeezed states. In: Physical Review A, 52 (2). 1609-1620 .

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Official URL: http://pra.aps.org/abstract/PRA/v52/i2/p1609_1


A general analysis of squeezing transformations for two-mode systems is given based on the four-dimensional real symplectic group Sp(4, R). 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 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: 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)
Division of Physical & Mathematical Sciences > Physics
Date Deposited: 26 Apr 2011 06:51
Last Modified: 26 Apr 2011 06:51
URI: http://eprints.iisc.ac.in/id/eprint/36895

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