Spin-charge separation in a strongly interacting 1D Fermi gas

We propose to measure the response of a 1D Fermi gas to both density- and spin-mode excitations as a function of interaction strength via Bragg spectroscopy. We realize a pseudospin-1/2 system with two ground-state hyperfine levels of $^6$Li. We confine the atoms in an array of 1D tubes created by a 2D optical lattice and use a Feshbach resonance to tune the interactions between atoms in different spin-states. In a previous work\footnote{ T. Yang et al., Physical Review Letters \textbf{121}, 103001 (2018).} the excitation spectrum for the density-mode in this system was successfully measured. Spontaneous emission poses the largest challenge to measure the spin-mode excitations. We address this issue by performing Bragg spectroscopy on the narrow-linewidth 2S-3P transition as well as by probing a mixture of the lowest- and third-to-lowest, $|1 \rangle$-$|3\rangle$, hyperfine states. With these improvements we expect to directly observe the difference in the propagation speeds for the density and the spin modes as a function of the interaction strength, as predicted by the Tomonaga-Luttinger liquid theory.