Poincaré disk as a model of squeezed states of a harmonic oscillator

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jun 2025Embargo end date: 01 Jan 2024 English Publisher:AIP PublishingJournal:Journal of Mathematical Physics, volume 66 (issn: 0022-2488, eissn: 1089-7658,

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Authors: Ian Chi; Martin Fraas; Tina Tan;

doi: 10.1063/5.0252902 , 10.48550/arxiv.2404.07905

arXiv: 2404.07905

Poincaré disk as a model of squeezed states of a harmonic oscillator

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Abstract

Single-mode squeezed states exhibit a direct correspondence with points on the Poincaré disk. In this study, we delve into this correspondence and describe the motions of the disk generated by a quadratic Hamiltonian. This provides a geometric representation of squeezed states and their evolution. We discuss applications in bang-bang and adiabatic control problems involving squeezed states.

Related Organizations

University of California, Davis
United States

Keywords

Quantum Physics, Quantum theory, FOS: Physical sciences, Mathematical Physics (math-ph), Quantum Physics (quant-ph), Partial differential equations, Mathematical Physics

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