The effect of electromagnetically induced transparency (EIT) combined with Rydberg-state atoms provides high optical nonlinearity to efficiently mediate the photon-photon interaction. However, the decay rate of Rydberg coherence, i.e., the decoherence rate, plays an important role in optical nonlinear efficiency and can be largely influenced by laser frequency fluctuation. In this work, we carried out a systematic study of the effect of laser frequency fluctuation on the decoherence rate. We derive an analytical formula that quantitatively describes the relationship between the decoherence rate and laser frequency fluctuation. The formula is experimentally verified by using the $\mathrm{\Lambda }$-type EIT system of laser-cooled ${}^{87}\mathrm{Rb}$ atoms, in which one can either completely eliminate or controllably introduce the effect of laser frequency fluctuation. We also include the effect of Doppler shift caused by the atomic thermal motion in the formula, which can be negligible in the $\mathrm{\Lambda }$-type EIT experiment but significant in the Rydberg-EIT experiment. Utilizing the atoms of 350 $\mu \mathrm{K}$, we study the decoherence rate in the Rydberg-EIT system involving the state of $|32D_{5/2}\rangle$. The experimental data are consistent with the predictions from the formula. We are able to achieve a rather low decoherence rate of $2\pi \times 48$ kHz at a moderate coupling Rabi frequency of $2\pi \times 4.3$ MHz.

• Received 20 February 2019

DOI:https://doi.org/10.1103/PhysRevA.100.013815