Quantum Simulation of a One-Dimensional Luther-Emery Liquid

We investigate the one-dimensional behavior of attractively interacting spin-1/2 fermions in optical lattices. With repulsive interactions, the continuum model as described by the Tomonaga-Luttinger theory has low energy excitations characterized by bosonic charge and spin excitations that propagate with different velocities. With attractive interaction, however, one expects pairing that leads to a gap in the spin sector, thus inducing a decay in the spin correlations- as explained by the Luther-Emery theory. We use a 2D optical lattice to realize an array of quasi-1D tubes. The tubes contain a pseudo-spin-1/2 system consisting of the lowest and third-to-lowest hyperfine sublevels of ⁶Li. We tune the interspecies interactions with a magnetic Feshbach resonance and use radiofrequency (RF) spectroscopy to probe dimer formation in the attractively interacting liquid. Furthermore, we implement Bragg spectroscopy to obtain low-energy excitation spectra for the charge and spin modes. Our work aims to better understand the equivalent of the “BCS-BEC crossover” in 1D.