Fourier analysis of Ramsey fringes observed in a continuous atomic fountain for in situ magnetometry

TL;DR

This paper uses Fourier analysis of Ramsey fringes in an atomic fountain to extract magnetic field profiles and atomic velocity distributions, improving in situ magnetometry accuracy.

Contribution

It introduces a method to analyze Ramsey fringes for retrieving magnetic field and velocity distribution information in atomic fountain experiments.

Findings

Successfully reconstructed Ramsey fringes using Fourier analysis.

Derived an analytical expression for the Ramsey pattern position.

Demonstrated in situ magnetometry capability in atomic fountains.

Abstract

Ramsey fringes observed in an atomic fountain are formed by the superposition of the individual atomic signals. Due to the atomic beam residual temperature, the atoms have slightly different trajectories and thus are exposed to a different average magnetic field, and a velocity dependent Ramsey interaction time. As a consequence, both the velocity distribution and magnetic field profile are imprinted in the Ramsey fringes observed on Zeeman sensitive microwave transitions. In this work, we perform a Fourier analysis of the measured Ramsey signals to retrieve both the time averaged magnetic field associated with different trajectories and the velocity distribution of the atomic beam. We use this information to reconstruct Ramsey fringes and establish an analytical expression for the position of the overall observed Ramsey pattern.