General solution of the time evolution of two interacting harmonic oscillators

journal article in Web of Science

English

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.

harmonic oscillators; ultrastrong-coupling regime ; phase transition

BRUSCHI, D.; PARAOANU, G.; FUENTES, I.; WILHELM, F.; SCHELL, A.

11. 2. 2021

AMER PHYSICAL SOC

COLLEGE PK

2469-9934

PHYSICAL REVIEW A

103

2

United States of America

023707-1

023707-13

13

https://journals.aps.org/pra/abstract/10.1103/PhysRevA.103.023707