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We develop a non-Gaussian variational approach that enables us to study bothequilibrium and far-from-equilibrium physics of the two-dimensional Fermipolaron. This method provides an unbiased analysis of the polaron-to-moleculephase transition without relying on truncations in the total number ofparticle-hole excitations. Our results -- which include the ground state energyand quasiparticle residue -- are in qualitative agreement with the known MonteCarlo calculations. The main advantage of the non-Gaussian states compared toconventional numerical methods is that they enable us to explore long-timepolaron evolution and, in particular, study various spectral propertiesaccessible to both solid-state and ultracold atom experiments. We design twotypes of radiofrequency spectroscopies to measure polaronic and molecularspectral functions. Depending on the parameter regime, we find that thesespectral functions and fermionic density profiles near the impurity displayeither long-lived oscillations between the repulsive and attractive polaronbranches or exhibit fast relaxational dynamics to the molecular state.

Efficient variational approach to the Fermi polaron problem in two dimensions, both in and out of equilibrium