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We propose to investigate the full counting statistics of nonequilibrium spintransport with an ultracold atomic quantum gas. The setup makes use of the spincontrol available in atomic systems to generate spin transport induced by animpurity atom immersed in a spin-imbalanced two-component Fermi gas. Incontrast to solid-state realizations, in ultracold atoms spin relaxation andthe decoherence from external sources is largely suppressed. As a consequence,once the spin current is turned off by manipulating the internal spin degreesof freedom of the Fermi system, the nonequilibrium spin population remainsconstant. Thus one can directly count the number of spins in each reservoir toinvestigate the full counting statistics of spin flips, which is notoriouslychallenging in solid state devices. Moreover, using Ramsey interferometry, thedynamical impurity response can be measured. Since the impurity interacts witha many-body environment that is out of equilibrium, our setup provides a way torealize the non-equilibrium orthogonality catastrophe. Here, even for spinreservoirs initially prepared in a zero-temperature state, the Ramsey responseexhibits an exponential decay, which is in contrast to the conventionalpower-law decay of Anderson's orthogonality catastrophe. By mapping our systemto a multi-step Fermi sea, we are able to derive analytical expressions for theimpurity response at late times. This allows us to reveal an intimateconnection of the decay rate of the Ramsey contrast and the full countingstatistics of spin flips.

Atomtronics with a spin: statistics of spin transport and non-equilibrium orthogonality catastrophe in cold quantum gases