  Recent experimental realization of strongly imbalanced mixtures of ultracold
atoms opens new possibilities for studying impurity dynamics in a controlled
setting. We discuss how the techniques of atomic physics can be used to explore
new regimes and manifestations of Anderson's orthogonality catastrophe (OC),
which could not be accessed in solid state systems. We consider a system of
impurity atoms localized by a strong optical lattice potential and immersed in
a sea of itinerant Fermi atoms. Ramsey interference experiments with impurity
atoms probe OC in the time domain, while radio-frequency (RF) spectroscopy
probes OC in the frequency domain. The OC in such systems is universal for all
times and is determined by the impurity scattering length and Fermi wave vector
of itinerant fermions. We calculate the universal Ramsey response and RF
absorption spectra. In addition to the standard power-law contribution, which
corresponds to the excitation of multiple particle-hole pairs near the Fermi
surface, we identify a novel contribution to OC that comes from exciting one
extra particle from the bottom of the itinerant band. This gives rise to a
non-analytic feature in the RF absorption spectra, which evolves into a true
power-law singularity with universal exponent 1/4 at the unitarity.
Furthermore, we discuss the manifestations of OC in spin-echo experiments, as
well as in the energy counting statistic of the Fermi gas following a sudden
quench of the impurity state. Finally, systems in which the itinerant fermions
have two or more hyperfine states provide an even richer playground for
studying non-equilibrium impurity physics, allowing one to explore
non-equilibrium OC and to simulate quantum transport through nano-structures.
This provides a useful connection between cold atomic systems and mesoscopic
quantum transport.
