Insulating Behavior of a Trapped Ideal Fermi Gas

We investigate theoretically and experimentally the center-of-mass motion of an ideal Fermi gas in a combined periodic and harmonic potential. We find a crossover from a conducting to an insulating regime as the Fermi energy moves from the first Bloch band into the band gap of the lattice. The conducting regime is characterized by an oscillation of the cloud about the potential minimum, while in the insulating case the center of mass remains on one side of the potential.

Figure 1

Phase trajectories for a trapped 1D Fermi gas in a lattice at $T=0$, just before and after the displacement of the trap [(a) and (b), respectively], and their dynamical evolution [(c) and (d)]. The ordinate and abscissa are in units of ${\tilde{p}}_z\equiv p_{z}d/2\hslash$ and $\tilde{z}\equiv \sqrt{m{\omega }_z^2{z}^2/4\delta }$, respectively.

Figure 2

Dipole oscillations of the Fermi gas of ${}^{40}\mathrm{K}$ atoms at $T=0.3T_F$ in the presence (filled circles and full line) and in the absence (empty circles and dotted line) of a lattice with height $s=3$. The lines are the theoretical predictions, and the circles are the experimental results. The horizontal dot-dashed line represents the trap minimum.

Figure 3

Relative offset of the oscillations of a Fermi gas in the lattice (normalized to the initial displacement) as a function of the lattice height. The circles are the experimental data and the continuous line is the theoretical prediction for $3\times {10}^4$ atoms at $T=100\mathrm{n}\mathrm{K}$. The dashed line is the prediction for a Fermi gas of $2.5\times {10}^3$ atoms at $T=0$.

Figure 4

(a) Comparison between theory (line) and experiments (circles) for the damping rate of the dipole oscillations of the Fermi gas as a function of the lattice height. (b) Oscillation frequency of the Fermi gas as a function of the lattice height. The line is the expectation for a particle oscillating at the band bottom.