Work

Error bounds for the Floquet-Magnus expansion and their application to the semiclassical quantum Rabi model

Year: 2025

Type: article

Abstract: We present a general, nonperturbative method for deriving effective Hamiltonians of arbitrary order for periodically driven systems based on an iterated integration-by-parts technique. The resulting family of effective Hamiltonians reproduces the well-known Floquet-Magnus expansion, now enhanced with explicit error bounds that quantify the distance between the exact and approximate dynamics at each order, even in cases where the Floquet-Magnus series fails to converge. We apply the method to the semiclassical Rabi model and provide explicit error bounds for both the Bloch-Siegert Hamiltonian and its third-order refinement. Our analysis shows that, while the rotating-wave approximation more accurately captures the true dynamics than the Bloch-Siegert Hamiltonian in most regimes, the third-order approximation ultimately outperforms both.

Source: Physical Review A

DOI: 10.1103/6bgj-s987

Authors: Anirban Dey, Davide Lonigro, Kazuya Yuasa, Daniel Burgarth

Institutions: ARC Centre of Excellence for Engineered Quantum Systems, Macquarie University, Friedrich-Alexander-Universität Erlangen-Nürnberg, Waseda University

Language: English

Topic: Strong Light-Matter Interactions

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: Friedrich-Alexander-Universität Erlangen-Nürnberg, Ministry of Education, Culture, Sports, Science and Technology, Japan Society for the Promotion of Science

Award: Quantum Adiabatic Theorems for Quantum Information Technologies