The Fermi polaron is a mobile impurity interacting with a sea of fermions. Together with Andrey Mishchenko, Nikolay Prokof’ev and Boris Svistunov I studied the polaron spectral function, which is directly linked to many of its physical properties and can be probed in experiments. Our controlled numerical approach allows us to make reliable statements about the properties of the spectrum. For example, we have established the existence of a region of anomalously low spectral weight between the polaron peak and the rest of the spectrum, which we call the dark continuum. This suppression of the spectrum is surprising, as it develops in the absence of any small interaction related parameter.

Extracting the spectral function from the imaginary-time Green’s function is numerically ill-defined, because there is an infinite number of possible solutions that are consistent with the Green’s function data within its error bars. Most of these solutions are noisy, so one challenge is to find a smooth physical solution that fits the data. But as we discovered (in collaboration also with Lode Pollet ) this is only a small part of the problem, because there can be several qualitatively different smooth spectra that agree with the data. We developed a method that allows us to tell explicitly what features of the spectrum can be recovered reliably and what features are ambiguous. Our method is very general and applicable to any numerical analytic continuation technique.