Details
| Originalsprache | Englisch |
|---|---|
| Aufsatznummer | 023707 |
| Fachzeitschrift | Physical Review A |
| Jahrgang | 103 |
| Ausgabenummer | 2 |
| Publikationsstatus | Veröffentlicht - 11 Feb. 2021 |
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.
ASJC Scopus Sachgebiete
- Physik und Astronomie (insg.)
- Atom- und Molekularphysik sowie Optik
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in: Physical Review A, Jahrgang 103, Nr. 2, 023707, 11.02.2021.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - General solution of the time evolution of two interacting harmonic oscillators
AU - Bruschi, David Edward
AU - Paraoanu, G. S.
AU - Fuentes, Ivette
AU - Wilhelm, Frank K.
AU - Schell, Andreas W.
N1 - Funding Information: We thank Pablo Tieben and Anna Okopińska for useful comments and suggestions. G.S.P. acknowledges support from Foundational Questions Institute, from the European Commission project Quantum readout techniques and technologies (Grant No. 862644, FET Open, Horizon 2020), and from the Academy of Finland through Project No. 328193 and through the “Finnish Center of Excellence in Quantum Technology Quantum Technology Finland” Project No. 312296. D.E.B. acknowledges the Central European Institute of Technology Nano RI for partial support. A.W.S. was partly funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy EXC-2123 QuantumFrontiers 390837967.
PY - 2021/2/11
Y1 - 2021/2/11
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85101867763&partnerID=8YFLogxK
U2 - 10.1103/PhysRevA.103.023707
DO - 10.1103/PhysRevA.103.023707
M3 - Article
AN - SCOPUS:85101867763
VL - 103
JO - Physical Review A
JF - Physical Review A
SN - 2469-9926
IS - 2
M1 - 023707
ER -