SAMOP 2023 – scientific programme
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QI: Fachverband Quanteninformation
QI 16: Concepts and Methods I
QI 16.2: Talk
Wednesday, March 8, 2023, 11:15–11:30, B302
On the validity of the rotating wave approximation for interacting harmonic oscillators — •Paul Lageyre1, Alessandro Ferreri1, G. S. Paraoanu2, Frank K. Wilhelm1,3, Andreas W. Schell4,5, and David Edward Bruschi1,3 — 1Forschungzentrum Jülich, 52425 Jülich, Germany — 2Aalto University School of Science, FI-00076 AALTO, Finland — 3Universität des Saarlandes, 66123 Saarbrücken, Germany — 4Leibniz Universität Hannover, 30167 Hannover, Germany — 5Physikalisch-Technische Bundesanstalt, 38116 Braunschweig, Germany
The rotating wave approximation (RWA) is widely used in the study of the dynamics of quantum systems. Within the interaction picture, terms in the Hamiltonian modelling two (or more) coupled quantum system acquire a phase factor. The RWA prescribes that terms rotating faster in phase with time tend to average out, and thus can be neglected in respect to slower rotating ones, which dominate the dynamics. The RWA is particularly easier to prove valid if the coupling is weak enough. Regardless of the success in applying this approximation, a deeper understanding of its domains of validity and the degree of error introduced otherwise would be greatly beneficial.
In this work we quantify the deviation from the full dynamics of coupled harmonic oscillators if the RWA is applied. We employ techniques from symplectic geometry and are able to directly relate the error introduced to the squeezing-like terms in the Hamiltonian that are dropped. We compute analytical expressions for the set of pure Gaussian states and discuss further applications.