Role of generalized parity in the symmetry of the fluorescence spectrum from two-level systems under periodic frequency modulation

Abstract

We study the origin of the symmetry of the fluorescence spectrum from the two-level system subjected to a low-frequency periodic modulation and a near-resonant high-frequency monochromatic excitation by using the analytical and numerical methods based on the Floquet theory. We find that the fundamental origin of symmetry of the spectrum can be attributed to the presence of the generalized parity of the Floquet states, which depends on the driving parameters. The absence of the generalized parity can lead to the asymmetry of the spectrum. Based on the generalized parity, the conditions for the symmetry and asymmetry of the spectrum can be derived, which succeeds in predicting symmetry and asymmetry of the spectrum for the harmonic, biharmonic, and multiharmonic modulations. Moreover, we find that the secular approximation widely used in the analytical calculation may lead to artifact symmetry of the spectrum that vanishes when such approximation is avoided. The present study provides a significant perspective on the origin of the symmetry of the spectrum.

Dynamical Symmetries and Symmetry-Protected Selection Rules in Periodically Driven Quantum Systems

“…Inversion symmetry results in selection rules for dipole transitions; particle-hole, chiral, and time-reversal symmetries establish the so-called periodic table, a classification scheme for topological insulators [16][17][18], and symmetries have an essential impact on transport properties [19][20][21][22][23][24][25]. For periodically driven systems, these spatial symmetries can be generalized to dynamical symmetries that can give rise to a generalized periodic table for topological insulators [26,27] and a new control mechanism [28][29][30][31][32][33][34][35]. Dynamical symmetries have been used to control the coherent destruction of tunneling [36] and induce selection rules for high harmonic generation [37][38][39][40].…”

Observation of the Influence of Generalized Parity on the Alignment Spectra in the Periodically Modulated Warm Atomic Ensemble

“…Consequently, under the restriction of condition (6), the Floquet states that are acted by the generalized parity operator 𝒫(F) are either odd or even parity states. According to the Van Vleck perturbation theory, [32,42] the Hamiltonian (2) is perturbed to the second order in the dressed state representation. The Floquet Hamiltonian with the rotating frequency ±(𝛿 p − l𝜔 z ) is…”

“…[ 46,49 ] Compared with the resonance fluorescence emission spectra, there is no central peak. [ 38,39,42,50 ] Based on the spectra (), if the condition $$|\Omega _{p\pm }^{(l )}|= |\Omega _{p\mp }^{(-l )}|$$ is established, the alignment spectra are symmetric in detuning $$\delta _p=0$$.…”

Unified Light-Matter Floquet Theory and its Application to Quantum Communication

“…In recent years, periodic driving has emerged as a powerful tool for the coherent control of many-body systems. This has led to the realization of novel quantum phases of matter like dynamical topological states [1-15] and discrete time crystals [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31] as well as breakthroughs in applications like spectroscopy [32][33][34][35], metrology [36][37][38], and quantum simulation [39][40][41][42][43][44][45][46][47][48][49][50]. These non-equilibrium quantum systems are generally analyzed using Floquet theory -a method first developed by Jon Shirley in 1965 [51].…”