Wigner function for SU(1,1)

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.

arXiv commentVersion accepted in Quantum

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Cited by in corpus (11)

• Overview of the phase space formulation of quantum mechanics with application to quantum technologies
• Four-mode squeezed states: two-field quantum systems and the symplectic group $\mathrm{Sp}(4,\mathbb{R})$
• Signatures of excited state quantum phase transitions in quantum many body systems: Phase space analysis
• Sub-Planck phase-space structure and sensitivity for SU(1,1) compass states
• Sub-Planck structures: Analogies between the Heisenberg-Weyl and SU(2) groups
• Spectrally multimode integrated SU(1,1) interferometer
• $SU(1,1)$ covariant $s$-parametrized maps
• Quantum heat engine based on quantum interferometry: the SU(1,1) Otto cycle
• Intensity correlations in the Wigner representation
• Stimulated parametric down-conversion for spatiotemporal metrology
• Understanding Squeezed States of Light Through Wigner's Phase-Space