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Resonance fluorescence of strongly driven two-level system coupled to multiple dissipative baths

We present a theoretical formalism for resonance fluorescence radiating from a two-level system (TLS) driven by any periodic driving and coupled to multiple reservoirs. The formalism is derived analytically based on the combination of Floquet theory and Born-Markov master equation. The formalism allows us to calculate the spectrum when the Floquet states and quasienergies are analytically or numerically solved for simple or complicated driving fields. We can systematically explore the spectral features by implementing the present formalism. To exemplify this theory, we apply the unified formalism to comprehensively study a generic model that a harmonically driven TLS is simultaneously coupled to a radiative reservoir and a dephasing reservoir. We demonstrate that the significant features of the fluorescence spectra, the driving-induced asymmetry and the dephasing-induced asymmetry, can be attributed to the violation of detailed balance condition, and explained in terms of the driving-related transition quantities between Floquet-states and their steady populations. In addition, we find the distinguished features of the fluorescence spectra under the biharmonic and multiharmonic driving fields in contrast with that of the harmonic driving case. In the case of the biharmonic driving, we find that the spectra is significantly different from the result of the rotating-wave approximation (RWA) under the multiple resonance conditions. By the three concrete applications, we illustrate that the present formalism provides a routine tool for comprehensively exploring the fluorescence spectrum of periodically strongly driven TLSs.