  The Fermi edge singularity and the Anderson orthogonality catastrophe
describe the universal physics which occurs when a Fermi sea is locally
quenched by the sudden switching of a scattering potential, leading to a brutal
disturbance of its ground state. We demonstrate that the effect can be seen in
the controllable domain of ultracold trapped gases by providing an analytic
description of the out-of-equilibrium response to an atomic impurity, both at
zero and at finite temperature. Furthermore, we link the transient behavior of
the gas to the decoherence of the impurity, and, in particular to the amount of
non-markovianity of its dynamics.
