Multiphoton-resonance-induced fluorescence of a strongly driven two-level system under frequency modulation

We study the fluorescence spectrum of a strongly driven two-level system (TLS) with modulated transition frequency, which is a bichromatically driven TLS and has multiple resonance frequencies. We are aiming to provide a reliable description of the fluorescence in a regime that is difficult to tackle with perturbation theory and the rotating-wave approximation (RWA), and illustrate the spectral features of the fluorescence under off- and multiphoton-resonance conditions. To go beyond the RWA, we use a semianalytical counter-rotating-hybridized rotating-wave method that combines a unitary transformation and Floquet theory to calculate the two-mode Floquet states and quasienergies for the bichromatically driven TLS. We then solve the master equation accounting for the spontaneous decay in the bases of the two-mode Floquet states, and derive a physically transparent fluorescence spectrum. In comparison with the numerically exact spectrum from the generalized Floquet-Liouville approach, the present spectrum is found to be applicable in a wide range of the parameters where the RWA and the secular approximation may break down. We find that the counter-rotating (CR) terms of the transverse field omitted in the RWA have non-negligible contributions to the spectrum under certain conditions. Particularly, at the multiphoton resonance the width of which is comparable with the Bloch-Siegert shift, the RWA and non-RWA spectra markedly differ from each other because of the CR-induced shift. We also analyze the symmetry of the spectrum in terms of the transition matrix elements between the two-mode Floquet states. We show that the strict symmetry of the spectrum cannot be expected without the RWA but the almost symmetric spectrum can be obtained at the single-photon resonance that takes the Bloch-Siegert shift into account if the driving is moderately strong and at the multiphoton resonance with a sufficiently weak transverse field.