Spin-charge separation in an atomic Luttinger liquid

Strong correlations that occur in many electronic materials are responsible for some of the most remarkable phenomena in condensed matter physics, such as novel forms of superconductivity and topological quasi-particles, but at the same time, they present vexing challenges for theoretical description. Strong correlations are generally found in low-dimensional materials where low energy excitations are most likely collective. A paradigm for these strongly correlated materials is the one-dimensional (1D) Luttinger liquid. The low energy excitations are bosonic sound waves that correspond to either spin-density or charge-density waves that, remarkably, propagate at different speeds, thus realizing a spin-charge separation. This phenomena has been observed in electronic materials, but a quantitative analysis of these data has proved challenging because of the complexity of the electronic structure and the unavoidable presence of impurities and defects.

We have studied an artificial one-dimensional (1D) material in which the electrons are replaced by ⁶Li, a composite fermion. A 2D optical lattice confines the atoms to an array of 1D tubes. Quantum simulation with ultracold atoms takes advantage of the capability to adhere to a theoretical model, and the tunability of the model parameters to enable quantitative comparison with theory. Our experiment uses Bragg spectroscopy to measure the momentum and energy resolved structure factor, S(q,ω), from which the two speeds of sound are determined. In collaboration with our theory colleagues, we made a direct theory/experiment comparison and found excellent agreement as a function of interaction strength [1]. We found that it was necessary to include nonlinear corrections to the spin-wave dispersion arising from back-scattering, thus going beyond the Luttinger model. More recently, we explored the disruption of spin correlations with increasing temperature [2], an effect that destroys spin-charge separation.

1. R. Senaratne*, D. Cavazos-Cavazos* et al, “Spin-charge separation in a 1D Fermi gas with tunable interactions”, Science 376, 1305 (2022).

2. D. Cavazos-Cavazos, R. Senaratne, A. Kafle, and R.G. Hulet, “Realization of a spin-incoherent Luttinger liquid”, arXiv:2210.06306 (2022).