  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 derived an analytical formula that
quantitatively describes the relationship between the decoherence rate and
laser frequency fluctuation. The formula was experimentally verified by using
the $\Lambda$-type EIT system of laser-cooled $^{87}$Rb atoms, in which one can
either completely eliminate or controllably introduce the effect of laser
frequency fluctuation. We also included the effect of Doppler shift caused by
the atomic thermal motion in the formula, which can be negligible in the
$\Lambda$-type EIT experiment but significant in the Rydberg-EIT experiment.
Utilizing the atoms of 350 $\mu$K, we studied the decoherence rate in the
Rydberg-EIT system involving with the state of $|32D_{5/2}\rangle$. The
experimental data are consistent with the predictions from the formula. We were
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.
