Interaction-Controlled Transport of an Ultracold Fermi Gas

We explore the transport properties of an interacting Fermi gas in a three-dimensional optical lattice. The center of mass dynamics of the atoms after a sudden displacement of the trap minimum is monitored for different interaction strengths and lattice fillings. With increasingly strong attractive interactions the weakly damped oscillation, observed for the noninteracting case, turns into a slow relaxational drift. Tuning the interaction strength during the evolution allows us to dynamically control the transport behavior. Strong attraction between the atoms leads to the formation of local pairs with a reduced tunneling rate. The interpretation in terms of pair formation is supported by a measurement of the number of doubly occupied lattice sites. This quantity also allows us to determine the temperature of the noninteracting gas in the lattice to be as low as $(27\pm 2)\%$ of the Fermi temperature.

Figure 1

Dynamic control of transport by tuning the collisional interaction. The graph shows the center of mass motion of a two-component Fermi gas of $(2.9\pm 0.3)\times {10}^4$ atoms in a lattice of $5E_R$ depth. At $t=0$, the equilibrium position of the underlying harmonic trap is displaced vertically. After 9 ms of evolution without interaction (•), the magnetic field is changed linearly in 1 ms so that the interaction is strongly attractive ($\circ$) for 10 ms. Then the magnetic field is changed to its original value again within 0.5 ms (•). The two noninteracting cases • are each fit by a damped cosine and an offset, while the evolution with attractive interaction $\circ$ is fit by an exponential decay and an offset. Error bars denote the standard deviation of at least 4 measurements.

Figure 2

Evolution of the center of mass position for different interaction strengths and fillings. The circles $\circ$ (•) denote samples in the half-filled (band insulating) regime. For each data point the position of the cloud with and without displacement was compared to eliminate long term drifts. The error bars denote the standard deviation of at least 4 measurements.

Figure 3

Relaxation rate $\Gamma$ as a function of interaction strength. The data points and error bars are fit results to center of mass evolutions of $(3.8\pm 0.4)\times {10}^4$ atoms. The empirical power law $h\Gamma =CJ(J/U{)}^{\nu }$ with $\nu =1.61\pm 0.03$ and $C=2.95\pm 0.17$ fits the data well. The inset shows the dependence of the relaxation rate on the atom number.

Figure 4

The fraction of molecules formed in the optical lattice increases with attractive interaction, demonstrating a higher number of doubly occupied lattice sites. Error bars denote the statistical errors of at least 4 measurements. The line serves as a guide to the eye.