  We propose to investigate the full counting statistics of nonequilibrium spin
transport with an ultracold atomic quantum gas. The setup makes use of the spin
control available in atomic systems to generate spin transport induced by an
impurity atom immersed in a spin-imbalanced two-component Fermi gas. In
contrast to solid-state realizations, in ultracold atoms spin relaxation and
the decoherence from external sources is largely suppressed. As a consequence,
once the spin current is turned off by manipulating the internal spin degrees
of freedom of the Fermi system, the nonequilibrium spin population remains
constant. Thus one can directly count the number of spins in each reservoir to
investigate the full counting statistics of spin flips, which is notoriously
challenging in solid state devices. Moreover, using Ramsey interferometry, the
dynamical impurity response can be measured. Since the impurity interacts with
a many-body environment that is out of equilibrium, our setup provides a way to
realize the non-equilibrium orthogonality catastrophe. Here, even for spin
reservoirs initially prepared in a zero-temperature state, the Ramsey response
exhibits an exponential decay, which is in contrast to the conventional
power-law decay of Anderson's orthogonality catastrophe. By mapping our system
to a multi-step Fermi sea, we are able to derive analytical expressions for the
impurity response at late times. This allows us to reveal an intimate
connection of the decay rate of the Ramsey contrast and the full counting
statistics of spin flips.
