Collisionally Induced Transport in Periodic Potentials

We study the transport of ultracold atoms in a tight optical lattice. For identical fermions the system is insulating under an external force while for bosonic atoms it is conducting. This reflects the different collisional properties of the particles and reveals the role of interparticle collisions in establishing a macroscopic transport in a perfectly periodic potential. Also in the case of fermions we can induce a transport by creating a collisional regime through the addition of bosons. We investigate the transport as a function of the collisional rate and observe a transition from a regime in which the mobility increases with increasing collisional rate to one in which it decreases. We compare our data with a theoretical model for electron transport in solids introduced by Esaki and Tsu.

Figure 1

(a) Sketch of the experimental sequence. (b) Evolution of the c.m. position of a cloud of fermions. A pure fermionic sample (circles) does not move to the trap center, whereas an identical sample with an admixture of bosons reveals a current through the potential (squares). The data are fitted with a sum of an exponential decay and an initial damped oscillation as described in the text (continuous lines). The expansion time of the cloud is 8 ms and the lattice height is $s=3$. The temperature and the atom number of the fermions are $T=300\mathrm{nK}$ and $N=5\times {10}^4$; the number of admixed bosons is $N_{\mathrm{B}}=1\times {10}^5$.

Figure 2

Decay time $\tau$ of a cloud of fermions in a mixture with bosons in dependence on the collisional rate (dots). The first data point at zero collisional rate was taken for a pure fermionic sample. The number of fermions is $N=50000$ with a temperature of 350 nK. The number of bosons was changed from 25 000 to 300 000 corresponding to a change in the interspecies collisional rate between 40 and $550{\mathrm{s}}^{-1}$ [14]. The lattice height for the two species was $s_{\mathrm{K}}=3$ and $s_{\mathrm{Rb}}=9$; the initial displacement was $x_{\mathrm{d}}=35\mu \mathrm{m}$. The solid line is a drift time, calculated from Eq. (1) for a linear potential with Bloch oscillation frequency ${\omega }_{\mathrm{BO}}=2\pi \times 35{\mathrm{s}}^{-1}$ (see text).

Figure 3

Decay time of a cloud of bosons for different lattice heights. The initial displacement was $x_{\mathrm{d}}=10\mu m$. The continuous line is an exponential fit to the data. The exponent is given by $e^{-s/1.6}$.