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

Ian Chi, Martin Fraas, Tina Tan

Published 2024-04-11Version 1

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.