Umklapp Collisions and Center-of-Mass Oscillations of a Trapped Fermi Gas

Starting from the Boltzmann equation, we study the center-of-mass oscillation of a harmonically trapped normal Fermi gas in the presence of a one-dimensional periodic potential. We show that for values of the Fermi energy above the first Bloch band the center of mass motion is overdamped in the collisional regime due to umklapp processes. This should be contrasted with the behavior of a superfluid where one instead expects the occurrence of persistent Josephson-like oscillations.

Figure 1

Ratio of umklapp over normal collisional rates [see Eq. (5)] as a function of $t=T/T_F$ for the values $T_F/2\delta =5$ (solid line), $2$ (dashed line), $1$ (dotted line).

Figure 2

Dipole relaxation function $F$ [see Eq. (16)] as a function of the reduced temperature $t=T/T_F$ for the values $T_F/2\delta =5$ (solid line), $2$ (dashed line), $1$ (dotted line).