2019/12/05 by A. N. Poertner, J. D. D. Martin · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Computer science #Floquet theory #Mathematics #Mode (computer interface) #Nonlinear Photonic Systems #Nonlinear system #Photonic and Optical Devices #Physics #Quantum electrodynamics #Quantum mechanics #Statistical physics #Topological Materials and Phenomena #physics.atom-ph #quant-ph
paper · pdf · doi:10.1103/physreva.101.032116
published as Phys. Rev. A 101, 032116 (2020) · 16 pages, 2 figures
arxiv created 2019/12/05 · openalex created_date 2019/12/13 · openalex publication_date 2020/03/25 · arxiv updated 2020/04/01 · openalex updated_date 2026/08/05
Many-mode Floquet theory [T.-S. Ho, S.-I. Chu, and J. V. Tietz, Chem. Phys. Lett. 96, 464 (1983)] is a technique for solving the time-dependent Schr"odinger equation in the special case of multiple periodic fields, but its limitations are not well understood. We show that for a Hamiltonian consisting of two time-periodic couplings of commensurate frequencies (integer multiples of a common frequency), many-mode Floquet theory provides a correct expression for unitary time evolution. However, caution must be taken in the interpretation of the eigenvalues and eigenvectors of the corresponding many-mode Floquet Hamiltonian, as only part of its spectrum is directly relevant to time evolution. We give a physical interpretation for the remainder of the spectrum of the Hamiltonian. These results are relevant to the engineering of quantum systems using multiple controllable periodic fields.