Sub-Doppler spectroscopy of atoms excited in the regime of Rabi oscillations in a thin gas cell

We carried out theoretical investigation about velocity-selective atomic excitation on long-lived (metastable) levels of an atomic vapour in a thin cell by a monochromatic laser beam, running in the normal direction. The regime of coherent Rabi oscillations is considered on the light-induced transition from a sublevel of the ground quantum term to a metastable atomic level. On the basis of density matrix equations for the two-level system, we analysed the atomic population density of the metastable level, when the sample is irradiated by resonant monochromatic laser beam with an annular cross-section versus atomic velocities and versus the detuning, the amplitude, and the geometry of the laser beam. It is shown that, in the centre of the annular region, it can be obtained a population distribution on the metastable level as a function of the laser detuning, characterized by a sharp narrow resonance profile, whose width is reduced with respect to the thermal Doppler width roughly by the ratio between the diameter of the irradiated region and the inner thickness of the cell. We suggest high-sensitive schemes, in order to detect these sub-Doppler resonances, by probing the population of the metastable state with a second laser beam, resonant with a transition leaving from the metastable level. The case of ¹S₀ → ³P₁ spin-forbidden transition of Ca is discussed in more detail