Poincar\'{e} disk as a model of squeezed states of a harmonic oscillator
Mathematical Physics
2024-04-12 v1 math.MP
Quantum Physics
Abstract
Single-mode squeezed states exhibit a direct correspondence with points on the Poincar\'e 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.
Cite
@article{arxiv.2404.07905,
title = {Poincar\'{e} disk as a model of squeezed states of a harmonic oscillator},
author = {Ian Chi and Martin Fraas and Tina Tan},
journal= {arXiv preprint arXiv:2404.07905},
year = {2024}
}
Comments
16 pages, 5 figures