dorsal/arxiv
View SchemaTwo Mode Quantum Systems: Invariant Classification of Squeezing Transformations and Squeezed States
| Authors | Arvind, B. Dutta, N. Mukunda, R. Simon |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9412011 |
| URL | https://arxiv.org/abs/quant-ph/9412011 |
| DOI | 10.1103/PhysRevA.52.1609 |
| Journal | Phys. Rev. A 52, 1609 (1995) |
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.
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"abstract": "A general analysis of squeezing transformations for two mode systems is given\nbased on the four dimensional real symplectic group $Sp(4,\\Re)\\/$. Within the\nframework of the unitary metaplectic representation of this group, a\ndistinction between compact photon number conserving and noncompact photon\nnumber nonconserving squeezing transformations is made. We exploit the\n$Sp(4,\\Re)-SO(3,2)\\/$ local isomorphism and the $U(2)\\/$ invariant squeezing\ncriterion to divide the set of all squeezing transformations into a two\nparameter family of distinct equivalence classes with representative elements\nchosen for each class. Familiar two mode squeezing transformations in the\nliterature are recognized in our framework and seen to form a set of measure\nzero. Examples of squeezed coherent and thermal states are worked out. The need\nto extend the heterodyne detection scheme to encompass all of $U(2)\\/$ is\nemphasized, and known experimental situations where all $U(2)\\/$ elements can\nbe reproduced are briefly described.",
"arxiv_id": "quant-ph/9412011",
"authors": [
"Arvind",
"B. Dutta",
"N. Mukunda",
"R. Simon"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.52.1609",
"journal_ref": "Phys. Rev. A 52, 1609 (1995)",
"title": "Two Mode Quantum Systems: Invariant Classification of Squeezing Transformations and Squeezed States",
"url": "https://arxiv.org/abs/quant-ph/9412011"
},
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