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arXiv · 1911.11703

Wigner function for SU(1,1)

U. Seyfarth·A. B. Klimov·H. de Guise·G. Leuchs·L. L. Sanchez-Soto
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Abstract

In spite of their potential usefulness, Wigner functions for systems with SU(1,1) symmetry have not been explored thus far. We address this problem from a physically-motivated perspective, with an eye towards applications in modern metrology. Starting from two independent modes, and after getting rid of the irrelevant degrees of freedom, we derive in a consistent way a Wigner distribution for SU(1,1). This distribution appears as the expectation value of the displaced parity operator, which suggests a direct way to experimentally sample it. We show how this formalism works in some relevant examples.

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U. Seyfarth, A. B. Klimov, H. de Guise, G. Leuchs, L. L. Sanchez-Soto. 2019-11-26. Wigner function for SU(1,1). https://doi.org/10.22331/q-2020-09-07-317

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