Spin-charge separation with tunable interaction strength*

We report on the observation of spin-charge separation in a Tomonaga-Luttinger liquid (TLL) with tunable interaction strength. We measure the dynamic structure factor (DSF) for both the spin and charge modes for various strengths of repulsive interaction, and compare these to calculations using Bethe ansatz results and the local density approximation. Our experiment employs fermionic ultracold ⁶Li atoms confined in an array of quasi-one-dimensional tubes produced using a two-dimensional optical lattice. The gas is a spin-balanced mixture of two hyperfine sublevels, which constitute a spin-1/2 system. Using Bragg spectroscopy we separately excite low-energy spin and charge waves in order to obtain the DSFs for each mode. Our measurements are in good agreement with our calculations, indicating an increasing charge-mode velocity and a decreasing spin-mode velocity with increasing interaction strength, as expected according to TLL theory. Furthermore, our spin-mode measurements for strong interactions show a high-frequency tail that we show is a result of the nonlinear Luttinger liquid.