Characterizing spin-charge separation using Bragg spectroscopy*

One dimensional systems of fermions are predicted by Luttinger liquid theory to have different dispersion relations for the spin and charge excitations. Spin-charge separation has been previously seen in quantum wire tunneling experiments.\footnote{O. M. Auslaender et al., Science \textbf{308}, 88 (2005).}\textsuperscript{,}\footnote{Y. Jompol et al., Science \textbf{325}, 597 (2009).} Ultracold atoms, however, provide a highly tunable and precise system to directly observe this phenomenon. We propose to realize such a system with fermionic $^{6}$Li in a 2-D optical lattice, measuring the spin and charge dispersion relations using Bragg spectroscopy.\footnote{S. Hoinka et al., Phys. Rev. Lett. \textbf{109}, 050403 (2012).} Bragg spectroscopy offers the ability to probe a large region of the excitation spectrum, since it does not change the internal state of the atoms and total momentum transfer is adjustable. By exploiting the tunability of interactions, via a Feshbach resonance, and the adjustability of the optical potential, we will characterize spin-charge separation under a wide range of experimental parameters.