Raman-Ramsey resonances in atomic vapor cells: Rabi pulling and optical-density effects

Raman-Ramsey interference has proved a very effective technique to implement compact and high performing vapor cell frequency standards. In this paper, we theoretically characterize Raman-Ramsey resonances in an optically thick atomic vapor. Specifically, some parameters of interest for frequency standards applications, like contrast and linewidth of the central Raman-Ramsey fringe, are evaluated at different temperatures for Cs-133 and Rb-87 vapor cells with buffer gas. Density narrowing and broadening effects are described and explained in terms of a three-level theory where laser field propagation through the atomic medium is taken into account. Also, we investigate light shift both in low and high atomic density regimes. Light shift, which potentially degrades the medium-to long-term stability of Raman-Ramsey clocks, is composed of two contributions. The first is a pulling effect exerted by the wide Rabi profile enclosing the interference pattern on the central Raman-Ramsey fringe. The second light-shift term is strictly related to the detection time. Calculations derived from our model well describe already existing experimental results and new behaviors are predicted.