  We study the dynamics of many atoms in the recently proposed Single Atom
Transistor setup [A. Micheli, A. J. Daley, D. Jaksch, and P. Zoller, Phys. Rev.
Lett. 93, 140408 (2004)] using recently developed numerical methods. In this
setup, a localised spin 1/2 impurity is used to switch the transport of atoms
in a 1D optical lattice: in one state the impurity is transparent to probe
atoms, but in the other acts as a single atom mirror. We calculate
time-dependent currents for bosons passing the impurity atom, and find
interesting many body effects. These include substantially different transport
properties for bosons in the strongly interacting (Tonks) regime when compared
with fermions, and an unexpected decrease in the current when weakly
interacting probe atoms are initially accelerated to a non-zero mean momentum.
We also provide more insight into the application of our numerical methods to
this system, and discuss open questions about the currents approached by the
system on long timescales.

Quantum Physics;Soft Condensed Matter