Projects per year
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 ultrastrongcoupling regime with additional singlemode squeezing on both oscillators, as well as higherorder 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 secondorder 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 higherorder interactions.
Original language  English 

Article number  023707 
Number of pages  13 
Journal  Physical Review A 
Volume  103 
Issue number  2 
DOIs  
Publication status  Published  11 Feb 2021 
MoE publication type  A1 Journal articlerefereed 
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Dive into the research topics of 'General solution of the time evolution of two interacting harmonic oscillators'. Together they form a unique fingerprint.Projects
 3 Finished

QuantumEnhanced Detection
Paraoanu, G., Björkman, I., McCord, J. & Sultanov, A.
01/01/2020 → 31/12/2022
Project: Academy of Finland: Other research funding

QUARTET: Quantum readout techniques and technologies
Paraoanu, G., Khalifa, H., Petrovnin, K. & Rapinoja De Carvalho, A.
15/10/2019 → 30/04/2023
Project: EU: Framework programmes funding

Finnish Centre of Excellence in Quantum Technology
Paraoanu, G., Dogra, S., Petrovnin, K., Lan, D., McCord, J. & Cattaneo, M.
01/01/2018 → 31/12/2020
Project: Academy of Finland: Other research funding