  Exponential decay laws describe systems ranging from unstable nuclei to
fluorescent molecules, in which the probability of jumping to a lower-energy
state in any given time interval is static and history-independent. These
decays, involving only a metastable state and fluctuations of the quantum
vacuum, are the most fundamental nonequilibrium process, and provide a
microscopic model for the origins of irreversibility. Despite the fact that the
apparently universal exponential decay law has been precisely tested in a
variety of physical systems, it is a surprising truth that quantum mechanics
requires that spontaneous decay processes have non-exponential time dependence
at both very short and very long times. Cold-atom experiments both classic and
recent have proven to be powerful probes of fundamental decay processes; in
this paper, we propose the use of Bose condensates in Floquet-Bloch bands as a
probe of long-time non-exponential decay in single isolated emitters. We
identify a range of parameters that should enable observation of long-time
deviations, and experimentally demonstrate a key element of the scheme: tunable
decay between quasienergy bands in a driven optical lattice.
