Bounding the rotating wave approximation for coupled harmonic oscillators

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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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Date

2025-04-28

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Department of Applied Physics

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Mcode

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Language

en

Pages

55

Series

Journal of Physics A: Mathematical and Theoretical, Volume 58, issue 17, pp. 1-55

Abstract

In this work we study the validity of the rotating wave approximation of an ideal system composed of two harmonic oscillators evolving with a quadratic Hamiltonian and arbitrarily strong interaction. We prove its validity for arbitrary states by bounding the error introduced. We then restrict ourselves to the dynamics of Gaussian states and are able to fully quantify the deviation of arbitrary pure Gaussian states that evolve through different dynamics from a common quantum state. We show that this distance is fully determined by the first and second moments of the statistical distribution of the number of excitations created from the vacuum during an appropriate effective time-evolution. We use these results to completely control the dynamics for this class of states, therefore providing a toolbox to be used in quantum optics and quantum information. Applications and potential physical implementations are also discussed.

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Publisher Copyright: © 2025 The Author(s). Published by IOP Publishing Ltd.

Keywords

quantum dynamics, quantum harmonic oscillators, quantum optics, rotating wave approximation

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DOI

10.1088/1751-8121/adcd16

Citation

Heib, T, Lageyre, P, Ferreri, A, Wilhelm, F K, Paraoanu, G S, Burgarth, D, Schell, A W & Edward Bruschi, D 2025, 'Bounding the rotating wave approximation for coupled harmonic oscillators', Journal of Physics A: Mathematical and Theoretical, vol. 58, no. 17, 175304, pp. 1-55. https://doi.org/10.1088/1751-8121/adcd16

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https://urn.fi/URN:NBN:fi:aalto-202505143629

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[article-cris] Perustieteiden korkeakoulu / SCI