Collective modes in a bilayer dipolar fermi gas and the dissipationless drag effect

We consider the collective modes of a bilayer dipolar Fermi system in which the particles interact via long range (∼1/r 3) interaction. Assuming that each layer has a background flow which varies little and that the dynamics of the superfluid near T=0 is the same as that of a normal fluid, we obtain the dispersion relations for the collective modes in the presence of background flow. Decomposing the background flow into two parts, the center-of-mass flow and counterflow, we focus on the properties of the counterflow. We first find an estimate of the change in the zero-point energy ΔE ZP due to counterflow for a unit area of bilayer. Combining this with the free energy F of the system and taking the partial derivatives with respect to background velocities in the layers, we determine the current densities which reveal the fact that current in one layer does not only depend on the velocity in the same layer but also on the velocity of the other layer. This is the drag effect and we calculate the drag coefficient.