Direct Observation of Spin-Charge Separation in a Tomonaga-Luttinger Liquid

We demonstrate the first observation of spin-charge separation in a Tomonaga-Luttinger Liquid (TLL) with tunable interaction strength. We measured the low-energy dynamic density response in the charge- and spin-modes by selectively exciting these modes using Bragg spectroscopy. By adjusting the detuning of the Bragg light, we selected whether this spectroscopy was spin-independent (charge-mode), or spin-sensitive (spin-mode). We prepared an effective spin-1/2 system consisting of the lowest and third-to-lowest hyperfine sublevels of ⁶Li, trapped in a 2D optical lattice, which created an array of quasi-1D tubes. Repulsive inter-species interactions were tuned via a magnetic Feshbach resonance. We observed distinct spectra for the two modes in the strongly interacting regime, which implies that the two modes have distinct propagation speeds. The speed of the charge-mode increased with interaction strength, whereas that of the spin-mode decreased, as predicted for a TLL via exact results for a homogenous gas using Bethe ansatz methods. In the weakly interacting limit, we observed similar excitation spectra for the two modes, and therefore no evidence of spin-charge separation. This disagreement with TLL theory perhaps indicates that the system has effectively 3D behavior for weak interactions.