Dual-Frequency Absorption Spectroscopy in Laser-Cooled Rubidium Atoms: Theoretical Modeling and Experiment

We demonstrate dual-frequency absorption spectroscopy (DFAS) using laser-cooled 87Rb and 85Rb atoms. Doppler-free resonances with high-contrast are produced, which suggest the suitability of using dual-frequency absorption spectroscopy (DFAS) for laser stabilization in a cold-atom-based coherent population trapping (CPT) clock, and for developing a compact, high-performance optical frequency standard using an integrated magneto-optical trap (MOT). We developed a model using density-matrix equations to accurately simulate DFAS in the atomic medium without applying any simplifying approximations. Comprehensive simulations are performed using our multi-level system model to analyze dual-frequency spectra produced in cold atom ensembles under different experimental conditions, including the effect of magnetic field, and two-photon detuning. The simulations accurately yield amplitudes, linewidths, frequency shifts, and lineshapes of DFAS resonances under these experimental conditions. We also demonstrate a simple mechanism for performing CPT spectroscopy by implementing a DFAS laser lock using trapped atoms in the MOT. Additionally, we have extended our model to accurately model the dual-frequency spectrum produced in rubidium cell, which is a medium of practical interest for vapor-cell-based quantum sensing applications.