# Probing multiple-frequency atom-photon interactions with ultracold atoms

## TL;DR

This paper explores complex atom-photon interactions in ultracold atoms dressed with multiple radiofrequency fields, combining theoretical modeling with experimental spectroscopy to observe and verify high-order transitions.

## Contribution

It provides a comprehensive theoretical framework and experimental validation for multiple-frequency atom-photon interactions, including the first observation of high-order transitions.

## Key findings

- Observation of transitions up to sixth order in the probe field
- Excellent agreement between theory and experiment
- Verification of previously unobserved transitions

## Abstract

We dress atoms with multiple-radiofrequency fields and investigate the spectrum of transitions driven by an additional probe field. A complete theoretical description of this rich spectrum is presented, in which we find allowed transitions and determine their amplitudes using the resolvent formalism. Experimentally, we observe transitions up to sixth order in the probe field using radiofrequency spectroscopy of Bose-Einstein condensates trapped in single- and multiple-radiofrequency-dressed potentials. We find excellent agreement between theory and experiment, including the prediction and verification of previously unobserved transitions, even in the single-radiofrequency case.