Polar molecules in bilayers with high population imbalance

We investigate a dilute Fermi gas of polar molecules confined into a bilayer setup with dipole moments polarized perpendicular to the layers. In particular, we consider the extreme case of population imbalance, where we have only one particle in one layer and many particles in the other one. The single molecule is attracted by the dilute Fermi gas through the interlayer dipole-dipole force, presenting an interesting impurity problem with long-range anisotropic interaction. We characterize the quasiparticle, calculating its chemical potential with a Brueckner-Hartree-Fock approach. Moreover, we determine the momentum relaxation rate for finite momentum and temperature. The latter is reminiscent of Coulomb drag in bilayer electronic systems. For a confined system we relate the results for the chemical potential with the measurement of the oscillation frequency of the impurity. The momentum relaxation rate provides instead an estimate on how quickly the oscillations are damped.

Figure 1

Scheme of the system under consideration.

Figure 2

Polaron energy as a function of the inverse interlayer distance for a dipolar strength of $r^{*}{k}_{F,B}=0.5$ calculated in second-order perturbation theory (black dashed line) and in ladder approximation (red crosses). Inset: Zoom onto the weakly interacting regime, where second-order perturbation theory is a good approximation.

Figure 3

Polaron energy in log scale as a function of the inverse interlayer distance for a dipolar strength of $r^{*}{k}_{F,B}=0.5$ calculated from Eq. (9) (red crosses) and from Eq. (10) (black dashed line). The blue dash-dotted line indicates the two-body binding energy ${\epsilon }_b$ for the interlayer DDI potential Eq. (3) as calculated in [9].