General solution of the time evolution of two interacting harmonic oscillators

authored by
David Edward Bruschi, G. S. Paraoanu, Ivette Fuentes, Frank K. Wilhelm, Andreas W. Schell
Abstract

We study the time evolution of an ideal system composed of two harmonic oscillators coupled through a quadratic Hamiltonian with arbitrary interaction strength. We solve its dynamics analytically by employing tools from symplectic geometry. In particular, we use this result to completely characterize the dynamics of the two oscillators interacting in the ultrastrong-coupling regime with additional single-mode squeezing on both oscillators, as well as higher-order terms. Furthermore, we compute quantities of interest, such as the average number of excitations and the correlations that are established between the two subsystems due to the evolution. We find that this model predicts a second-order phase transition and we compute the critical exponents and the critical value. We also provide an exact decoupling of the time evolution in terms of simple quantum optical operations, which can be used for practical implementations and studies. Finally, we show how our techniques can be extended to include more oscillators and higher-order interactions.

Organisation(s)
Institute of Solid State Physics
QuantumFrontiers
External Organisation(s)
Saarland University
Brno University of Technology
Aalto University
University of Nottingham
University of Southampton
National Metrology Institute of Germany (PTB)
Type
Article
Journal
Physical Review A
Volume
103
ISSN
2469-9926
Publication date
11.02.2021
Publication status
Published
Peer reviewed
Yes
ASJC Scopus subject areas
Atomic and Molecular Physics, and Optics
Electronic version(s)
https://doi.org/10.1103/PhysRevA.103.023707 (Access: Closed)