Signatures of strong correlations in one-dimensional ultracold atomic Fermi gases

Recent success in manipulating ultracold atomic systems allows one to probe different strongly correlated regimes in one dimension. Regimes such as the (spin-coherent) Luttinger liquid and the spin-incoherent Luttinger liquid can be realized by tuning the interatomic interaction strength and trap parameters. We identify the noise correlations of density fluctuations as a robust observable (uniquely suitable in the context of trapped atomic gases) to discriminate between these two regimes. Finally, we address the prospects of realizing and probing these phenomena experimentally using optical lattices.

Figure 1

(Color online) Schematic sketch of the 3D cigar-shaped cloud (upper) and array of 1D tubes (lower) formed by optical trap lattice potentials. Yellow (tube-center) regions represent the spin-coherent Luttinger liquid regime, while blue (tube-edge) regions indicate its spin-incoherent counterpart.

Figure 2

Qualitative behavior of ${\overline{G}}_{\uparrow \downarrow }∕\mid {\overline{G}}_c\mid$ as a function of the 3D scattering length $a_{3\mathrm{D}}$ in a harmonic trap for ${}^6\mathrm{Li}$ atoms ($N={10}^5$, ${\omega }_{\perp }=2160\pi \mathrm{Hz}$, ${\omega }_0=14\pi \times {10}^5\mathrm{Hz}$, and ${\omega }_z=470\pi \mathrm{Hz}$) for the central tube (dashed line) and the array of tubes (solid line). As the interaction strength is increased, the response changes to negative, indicating the crossover from the spin-coherent Luttinger liquid regime to its spin-incoherent counterpart. Inset: “phase diagram” of a 1D ultracold atomic Fermi gas; the dashed curve is a crossover line between the two regimes.