Static dipolar impurity in a Fermi gas

Abstract

We consider a static dipolar impurity immersed in a Fermi gas and show how dipolar interactions shape both the few-body scattering properties and the resulting polaron physics. Using Fumi's theorem, we connect the anisotropic phase shifts directly to the ground-state energy, and compute the exact impurity spectrum via the functional determinant approach. The resulting spectrum is a convolution of independent even- and odd-wave contributions, giving rise to a ground state with simultaneously occupied even- and odd-wave bound states whose separation is tunable via the dipole length. A variational ansatz limited to one particle-hole excitation fails to capture this doubly occupied ground state. We further find that long-range dipolar interactions weaken Anderson's orthogonality catastrophe, reducing the power-law decay of the quasiparticle weight. These effects can be tested with ultracold polar molecules, where microwave shielding and independent tunability of interactions enable experimental access to the predicted regimes.

The paper asks how anisotropic, long-range dipolar scattering affects the energy, spectrum, and orthogonality catastrophe of an infinitely heavy impurity in a three-dimensional, non-interacting Fermi gas. It treats aligned and sign-reversed (“anti-dipolar”) interactions using a short-range-regularized dipolar potential. Coupled-channel scattering calculations supply bound-state energies and eigenphase shifts; generalized Fumi’s theorem gives the ground-state energy, and a functional determinant calculation gives the impurity spectrum. Even- and odd-parity sectors decouple, so their Ramsey overlaps multiply and their spectra convolve. When both sectors support bound states, the ground state occupies them simultaneously. The first odd-parity bound state has $m=0$ for aligned dipoles, versus two degenerate $m=\pm1$ states for anti-dipolar interactions. A one-particle–hole Chevy ansatz misses the jointly occupied ground-state branch. At fixed $k_Fa$, increasing $k_F|a_d|$ suppresses scattering phase shifts at the Fermi energy and reduces the orthogonality-catastrophe exponent relative to contact interactions. This exponent is checked against finite-size overlap scaling. Finite-temperature spectra resolve the parity branches at $T/T_F=0.1$ but barely distinguish them at $0.3$. The results assume a static impurity and negligible bath interactions. Finite impurity mass would couple the otherwise independent sectors and is left for future work. The odd-wave binding threshold depends on short-range regularization, and non-universal finite-range corrections matter in the studied regime $k_Fa_d\sim1$. Microwave-shielded molecules are proposed as a realization, with collisional losses and spectroscopic constraints noted.