# Measurement of the Dynamical Structure Factor of a 1D Interacting Fermi Gas

## TL;DR

This paper reports measurements of the dynamical structure factor of a 1D interacting Fermi gas using Bragg spectroscopy, confirming theoretical predictions from Tomonaga-Luttinger theory.

## Contribution

First experimental measurement of $S(q,omega)$ in a 1D interacting Fermi gas with tunable interactions, validating Tomonaga-Luttinger theory.

## Key findings

- Measurements agree well with Tomonaga-Luttinger theory
- Spectra obtained for small excitation energies and momenta below Fermi momentum
- Demonstrates control and probing of 1D quantum gases

## Abstract

We present measurements of the dynamical structure factor $S(q,\omega)$ of an interacting one-dimensional (1D) Fermi gas for small excitation energies. We use the two lowest hyperfine levels of the $^6$Li atom to form a pseudo-spin-1/2 system whose s-wave interactions are tunable via a Feshbach resonance. The atoms are confined to 1D by a two-dimensional optical lattice. Bragg spectroscopy is used to measure a response of the gas to density ("charge") mode excitations at a momentum $q$ and frequency $\omega$. The spectrum is obtained by varying $\omega$, while the angle between two laser beams determines $q$, which is fixed to be less than the Fermi momentum $k_\textrm{F}$. The measurements agree well with Tomonaga-Luttinger theory.