Low Energy Excitations of a 1D Fermi Gas with Attractive Interactions

Abstract

The low-energy excitations of a two-component repulsive Fermi gas confined to one dimension are linear dispersing spin- and charge-density waves whose respective propagation velocities depend on the strength and sign of their interaction. Quasi-1D fermions with attractive interaction realize the Luther-Emery liquid, which exhibits a rich array of phenomena, many of which are qualitatively different from those exhibited by their repulsive counterpart. We use a Feshbach resonance to access attractive interactions with $^6$Li atoms. We measured the spin and charge dynamic structure factors using Bragg spectroscopy and find that, contrary to repulsive interactions, the spin wave propagates faster than the charge density wave, thus producing an inversion of the classic spin-charge separation. We also find that a small spin polarization strongly suppresses the spin gap in the measured Bragg spectra. Evidence for pairing are a reduction in spin correlations with increasing attraction and RF spectra consistent with an atom/molecule mixture.

Figures (5)

• Figure 1: Spin and charge velocities ($v_s$ and $v_c$) vs. the dimensionless interaction strength $\gamma$ for the spin-1/2 1D Fermi gas. The solid lines are the velocities obtained by numerically solving the Bethe-ansatz equations. The classic spin-charge separation is inverted in the attractive regime ($\gamma < 0$), where pairing is expected to cause $v_c$ to plateau at half the noninteracting value and the spin mode to disappear resulting from the onset of a gap. Figure adapted from Ref. Batchelor2006.
• Figure 2: Normalized Bragg spectra corresponding to $S_c(q,\omega)$ (red triangles) and $S_s(q,\omega)$ (blue circles). Each data point is the average of at least 20 separate experimental shots. Error bars represent the standard error obtained by bootstrapping Efron1979. Vertical lines show the extracted peak frequency $\omega_p$ for the non-interacting case (dashed black) and $\omega_p$ for $a_s = -500$$a_0$ in the case of spin (dotted blue line) and charge (dotted red line). The solid red (blue) lines are fits to the calculated charge-mode (spin-mode) spectra from the Bethe ansatz solution, with fitting parameters $T = 250$ nK and an overall scaling.
• Figure 3: Spin Bragg spectrum for $a_s=-300a_0$. The symbols are data and the solid line is the calculated spectrum by assuming a small polarization of $p=0.1$. These are reproduced from Fig. \ref{['fig:spectra']}. The dashed line is the calculated spectrum assuming perfect spin balance with $p=0$. This clearly demonstrates the significant effects on the spin DSF by small spin imbalance.
• Figure 4: Locations of frequencies, $\omega_p$, corresponding to the peak of the DSF's for charge (red triangles) and spin (blue circles) excitations extracted from Fig. \ref{['fig:spectra']}. $\omega_p$ values were determined through fits of a parabolic function to the data points above 50% of the maximum measured value, and error bars are statistical standard errors of the fit parameters. The corresponding speed of sound, $v_p=\omega_p/q$, is given by the right axis. The upper horizontal axis gives the interaction strength in terms of the interaction parameter $\gamma^*$, obtained from $\gamma$ evaluated at the center of a tube with an average occupancy of 35 atoms. The dashed lines show the calculated values of $\omega_p$ for the spin and charge modes from the Bethe ansatz solution. The point to point variations of $\omega_p$ arise from variations of the density profile for different interactions, see the Methods supp.
• Figure 5: Normalized peak height, $\alpha$, of the DSF obtained from a skew-Gaussian fit to the measured DSFs at different interactions. The error bars are obtained from statistical standard errors of the relevant fit parameters. The data points are normalized to $\alpha = 1$ for the measured DSF height at $0$$a_0$. The dashed blue (red) line is an exponential fit in $\gamma^*$ to the spin (charge) mode.