Falling Atoms

TL;DR

This paper analyzes frequency shifts in atomic fountain clocks caused by gravity and motion, deriving a formula for net shift and corrections for rotational effects to improve clock accuracy.

Contribution

It provides a detailed derivation of the gravitational and Doppler frequency shifts in atomic fountain clocks, including corrections for Coriolis and centripetal effects.

Findings

Net frequency shift is g h/3 c^2 relative to launch point

Next correction to the shift is derived

Corrections for Coriolis and centripetal effects are shown to be necessary

Abstract

Atomic fountain clocks launch laser-cooled balls of atoms upwards to some height $h$ in the local gravitational field where they experience both second-order Doppler shifts and gravitational frequency shifts. It is shown in this paper that the net shift, relative to a reference at the launch point, is $ g h/3 c^2$. We derive the next most significant correction to this expression, and show that the value of $g$ should be corrected for Coriolis and centripetal effects.