Ramsey spectroscopy of CPT resonances on the $D_1$ line of alkali metal atoms in miniature cells in the field of counterpropagating waves with opposite circular polarizations

In this study, the Ramsey spectroscopy of coherent population trapping resonances excited on the D$_1$ line of alkali metal atoms in miniature vapor cells has been studied theoretically and experimentally. The configuration of the field produced by two counterpropagating waves with opposite circular polarizations has been considered. A counterpropagating wave is formed as a result of reflection from a partially transmitting output mirror, while the signal from the initial wave transmitted through the mirror is detected. It is shown that such a scheme is characterized by the optimal mirror reflection coefficient, for which the short-term stability can be substantially improved relative to the standard scheme without the counterpropagating wave. The three-fold improvement of the short-term stability of the atomic clock based on the coherent population trapping resonance in a vapor cell with $^{87}$Rb atoms has been demonstrated experimentally.