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General solution of the time evolution of two interacting harmonic oscillators

General solution of the time evolution of two interacting harmonic oscillators
General solution of the time evolution of two interacting harmonic oscillators
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
1050-2947
Bruschi, David Edward
6b839b6e-2a84-428a-bb60-0a76397228df
Paraoanu, G.S.
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Fuentes Guridi, Ivette
c6d65a4c-feac-44c1-9097-e0f6a9e0cf44
Wilhelm, Frank K.
42176e01-4809-4c1d-bced-2ffb01ef1955
Schell, Andreas W.
e8a5f725-4ece-4313-8c00-2cd31b202422
Bruschi, David Edward
6b839b6e-2a84-428a-bb60-0a76397228df
Paraoanu, G.S.
bad624bd-c50a-40d1-aabf-29013fc10aee
Fuentes Guridi, Ivette
c6d65a4c-feac-44c1-9097-e0f6a9e0cf44
Wilhelm, Frank K.
42176e01-4809-4c1d-bced-2ffb01ef1955
Schell, Andreas W.
e8a5f725-4ece-4313-8c00-2cd31b202422

Bruschi, David Edward, Paraoanu, G.S., Fuentes Guridi, Ivette, Wilhelm, Frank K. and Schell, Andreas W. (2021) General solution of the time evolution of two interacting harmonic oscillators. Physical Review A. (In Press)

Record type: Article

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

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General solution of the time evolution of two interacting harmonic oscillators - Accepted Manuscript
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Accepted/In Press date: 15 January 2021
Additional Information: arxiv is am

Identifiers

Local EPrints ID: 448071
URI: http://eprints.soton.ac.uk/id/eprint/448071
ISSN: 1050-2947
PURE UUID: 0183c4c8-99a3-4a7e-b991-24af2e3034e3

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Date deposited: 01 Apr 2021 15:41
Last modified: 01 Apr 2021 15:51

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Contributors

Author: David Edward Bruschi
Author: G.S. Paraoanu
Author: Frank K. Wilhelm
Author: Andreas W. Schell

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