Spectral density analysis for light excitation of alkali–metal vapors with variant time-dependent chirping

The spectroscopic phenomena, such as electromagnetically induced transparency (EIT) and electromagnetically induced absorption (EIA), as well as switching between them, have been extensively studied in the steady-state regime for stationary excitations. The stationary line shape is understood through the imaginary part of the atomic polarization, which accounts for absorption, and the real part, which corresponds to atomic dispersion. In this paper, we adopt a time-dependent approach that allows for varying chirp mechanics through a weak probe field in the Y-type configuration of alkali vapors with two control fields. In this scenario, the absorption power spectrum (APSD) as well as the emission power spectral density (EPSD) of the atomic coherences and populations exhibit distinctive features that are beyond the traditional stationary spectrum. For weak chirping as sigmoid functions, the APSD shows a double-double EIT-like spectrum with a single EIA-like spike at the line center. For short interaction times and controlled active-chirping times, the APSD for coherence between upper levels shows a rich mixed EIA-like and EIT-like spectrum. The EPSD is analyzed through the variation of populations. Finally, the spectrum is analyzed for gain media where the atomic coherences are temporally negative at most times. We provided a fast estimation technique for APSD and EPSD based on the periodogram of signals with chirping, which might be an alternative approach to the quantum regression hypothesis and the physical spectrum.