Semiclassical many-mode floquet theory

A. N. Poertner, J. D. D. Martin

Georg Engelhardt, JunYan Luo, V. M. Bastidas +1 more

Floquet theory and other established semiclassical approaches are widely used methods to predict the state of externally driven quantum systems, yet they do not allow the prediction of the state of the photonic driving field. To overcome this shortcoming, the photon-resolved Floquet theory (PRFT) was developed recently [], which deploys concepts from full-counting statistics to predict the statistics of the photon flux between several coherent driving modes. In this paper, we study in detail the scaling properties of the PRFT in the semi-classical regime. We find that there is an ambiguity in the definition of the moment-generating function, such that different versions of this function produce the same photonic probability distribution in the semiclassical limit, and generate the same leading-order terms of the moments and cumulants. Using this ambiguity, we establish a simple expression for the Kraus operators, which describe the decoherence dynamics of the driven quantum system appearing as a consequence of the light-matter interaction. The PRFT will pave the way for improved quantum sensing methods, e.g., for spectroscopic quantum sensing protocols, reflectometry in semiconductor nanostructures, and other applications, where the detailed knowledge of the photonic probability distribution is necessary. Published by the American Physical Society 2024

Tak‐San Ho, Shih‐I Chu

The SU(3) dynamical evolution of three-level systems at two-photon resonance induced by two strong linearly polarized monochromatic fields is studied exactly by means of the semiclassical many-mode Floquet theory (MMFT) recently developed by the authors. Within the rotating-wave approximation (RWA), Hioe and Eberly have recently shown that the eight-dimensional SU(3) coherent vector S\ensuremath{\rightarrow} characterizing the time evolution of three-level systems can be factored into three independent vectors of dimensions three, four, and one, at appropriate two-photon resonance conditions. In practice, however, if the laser-atom interactions occur away from the two-photon resonance, or if the RWA is not valid, etc., this Gell-Mann--type SU(3) dynamical symmetry will be broken. It is shown in this paper that instead of solving the time-dependent generalized Bloch equations, the SU(3) dynamical evolution of the coherent vector S\ensuremath{\rightarrow} as well as various symmetry-breaking effects can be expediently studied by the use of the MMFT and expressed in terms of a few time-independent quasienergy eigenvalues and eigenvectors. Furthermore, we have extended the generalized Van Vleck (GVV) nearly degenerate perturbation theory to an analytical treatment of the two-mode Floquet Hamiltonian. This reduces the infinite-dimensional time-independent Floquet Hamiltonian into a 3\ifmmode\times\else\texttimes\fi{}3 effective Hamiltonian, from which useful analytical properties of the SU(3) coherent vector can be easily obtained. The combination of the MMFT and the GVV method thus greatly facilitates the study of the dynamical evolution. Pictorial comparison of the exact and the RWA results of the time evolution of the eight-dimensional coherent vector under several different physical conditions is presented and discussed at length.

Kwanghsi Wang, Tak‐San Ho, Shih‐I Chu

The authors present an exact treatment of two- and multiquantum transitions in three-level systems driven by two intense linearly polarised monochromatic fields based on the semiclassical many-mode Floquet theory developed recently. Further they extend the almost degenerate perturbation theory of Salwen (1955-6) to the two-mode Floquet Hamiltonian and obtain approximate analytical formulae for multiphoton transition probabilities, resonance bichromatic shifts and widths, and absorption lineshapes beyond the conventional rotating-wave approximation (RWA). Detailed comparison of the analytical, the RWA, and the exact results is given. Several novel features of multiphoton lineshape characteristics are pointed out.

Christian Grosche, Frank Steiner