# Effect of laser frequency fluctuation on the decay rate of Rydberg coherence

## TL;DR

This study investigates how laser frequency fluctuations affect the decoherence rate of Rydberg coherence in EIT systems, deriving and experimentally verifying a formula that accounts for these fluctuations and Doppler effects.

## Contribution

The paper presents a new analytical formula linking laser frequency fluctuation to Rydberg coherence decay, validated through experiments with cold rubidium atoms including Doppler effects.

## Key findings

- Decoherence rate can be quantitatively predicted by the derived formula.
- Experimental verification shows consistency with theoretical predictions.
- Achieved low decoherence rate of 2π×48 kHz in Rydberg-EIT system.

## Abstract

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.