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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.

Keywords

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