Orthogonality catastrophe as a consequence of qubit embedding in an ultracold Fermi gas

We investigate the behavior of a two-level atom coupled to a one-dimensional, ultracold Fermi gas. The sudden switching on of the scattering between the two entities leads to the loss of any coherence in the initial state of the impurity and we show that the exact dynamics of this process is strongly influenced by the effect of the orthogonality catastrophe within the gas. We highlight the relationship between the Loschmidt echo and the retarded Green's function---typically used to formulate the dynamical theory of the catastrophe---and demonstrate that the effect is reflected in the impurity dynamics. We show that the expected nonexponential decay of the spectral function can be observed using Ramsey interferometry on the two-level atom and comment on finite temperature effects.