Stabilizing two-photon frequency to reduce the decoherence rate of Rydberg-state electromagnetically induced transparency

Two-photon frequency stabilization is a critical step for experiments related to the Rydberg-state electromagnetically induced transparency (EIT) effect, as it exploits both the high optical nonlinearity of the EIT effect and the strong electric dipole-dipole interaction among Rydberg-state atoms. Fluctuations in the two-photon frequency cause decoherence in the Rydberg-EIT system, degrading its optical nonlinearity. Here, we propose and experimentally demonstrate a counterintuitive method to enhance the stability of the two-photon frequency of probe and coupling using atomic transitions. This method leverages increased probe power or intensity beyond the power broadening threshold. This improvement in the two-photon frequency stability consequently reduces the decoherence rate of Rydberg-EIT in laser-cooled atoms. By employing the double-resonance scheme with a moderate 480-nm coupling power of 64 mW or a Rabi frequency of $2\ensuremath{\pi}\ifmmode\times\else\texttimes\fi{}4.1$ MHz, the resulting fluctuation of the two-photon frequency lock was 170 kHz at an optimum 780 nm probe Rabi frequency of $2\ensuremath{\pi}\ifmmode\times\else\texttimes\fi{}15.6$ MHz. Concurrently, the observed frequency fluctuation-induced decoherence rate was $2\ensuremath{\pi}\ifmmode\times\else\texttimes\fi{}12$ kHz at a moderate coupling Rabi frequency of $2\ensuremath{\pi}\ifmmode\times\else\texttimes\fi{}4.8$ MHz for the Rydberg-EIT transition with cold atoms. This work represents a pivotal advancement, as it furnishes sufficient stability in the two-photon frequency to meet the demands of most Rydberg-EIT applications.