Recoil Effects in Microwave Ramsey Spectroscopy

TL;DR

This paper develops a theoretical framework for recoil effects in microwave Ramsey spectroscopy with laser cooled atoms, revealing partial cancellation of recoil shifts and guiding future experimental tests for improved microwave frequency standards.

Contribution

It introduces a Gaussian wave packet-based model for recoil effects, providing analytical and numerical results that predict partial cancellation of recoil shifts in microwave fountain clocks.

Findings

Recoil frequency shift can be partially canceled depending on experimental conditions.

Predicted shifts are up to ten times smaller due to partial cancellation.

Observation of recoil shifts is feasible with specific experimental adjustments.

Abstract

We present a theory of recoil effects in two zone Ramsey spectroscopy, particularly adapted to microwave frequency standards using laser cooled atoms. We describe the atoms by a statistical distribution of Gaussian wave packets which enables us to derive and quantify effects that are related to the coherence properties of the atomic source and that have not been considered previously. We show that, depending on the experimental conditions, the expected recoil frequency shift can be partially cancelled by these effects which can be significant at microwave wavelengths whilst negligible at optical ones. We derive analytical expressions for the observed interference signal in the weak field approximation, and numerical results for realistic caesium fountain parameters. In the near future Cs and Rb fountain clocks are expected to reach uncertainties which are of the same order of magnitude (10^{-16}) as first estimates of the recoil shift at microwave frequencies. We show, however, that the partial cancellation predicted by the complete theory presented here leads to frequency shifts which are up to an order of magnitude smaller. Nonetheless observation of the microwave recoil shift should be possible under particular experimental conditions (increased microwave power, variation of atomic temperature and launching height etc.). We hope that the present paper can provide some guidance for such experiments that would test the underlying theory and its assumptions, which in turn is essential for the next generation of microwave frequency standards.