Fermi polaron in two dimensions: Importance of the two-body bound state

We investigate a single impurity interacting with a free two-dimensional atomic Fermi gas. The interaction between the impurity and the gas is characterized by an arbitrary attractive short-range potential, which, in two dimensions, always admits a two-particle bound state. We provide analytical expressions for the energy and the effective mass of the dressed impurity by including the two-body bound state, which is crucial for strong interactions, in the integral equation for the effective interaction. Using the same method, we also give the results for the polaron parameters in one and three dimensions and find good agreement with previous results. Thus, our relations can be used as a simple way to estimate the polaron parameters once the two-body bound state of the interaction potential is known.

Figure 1

Main: polaron energy as a function of the two-body binding energy ${\epsilon }_b$ as given by Eq. (6) (solid red line) in two dimensions. For completeness, we report also the weakly interacting (dashed green line) and the strongly interacting (dotted black line) results (see text). Inset: ratio $m^{*}/m$ between the effective and the bare mass as given by Eq. (9).

Figure 2

Interaction energy (main panel) and effective mass (inset) as a function of the two-body binding energy ${\epsilon }_b$ in one dimension. The approximate result [Eq. (11)] (solid red line) is compared with the exact expression [Eq. (10)] given by McGuire [9].

Figure 3

Interaction energy as a function of the inverse 3D scattering length $1/\left(k_{F}a\right)$ (red line) in comparison with the results obtained from Monte Carlo calculations [5] in the polaron regime and at unitarity (black diamonds). In the molecule regime ($|{\epsilon }_b|\gg {\epsilon }_F$), we compare the expected result ${\epsilon }_p^0=-\left|{\epsilon }_b\right|-{\epsilon }_F$ (blue line). Inset: zoom on the negative axis.