E(2)-symmetric two-mode sheared states

Y. S. Kim*, Leehwa Yeh

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


It is noted that the symmetry of two-mode squeezed states of light is governed by the group Sp(4) that is locally isomorphic to O(3,2). This group has subgroups that are locally isomorphic to the two-dimensional Euclidean group. Two-mode states having the E(2) symmetry are constructed. The translation-like transformations of this symmetry group shear the Wigner distribution function defined over the four-dimensional phase space consisting of two pairs of canonical variables. Sheared states are constructed in the Schrödinger picture of quantum mechanics and in the Fock space for photon numbers. It is shown that the Wigner phase-space picture is a convenient representation of quantum mechanics for calculating measurable quantities of the sheared states.

Original languageEnglish
Pages (from-to)1237-1246
Number of pages10
JournalJournal of Mathematical Physics
Issue number4
StatePublished - 1992

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