  We consider sweeping a system through a Landau-Zener avoided-crossing, when
that system is also coupled to an environment or noise. Unsurprisingly, we find
that decoherence suppresses the coherent oscillations of quantum superpositions
of system states, as superpositions decohere into mixed states. However, we
also find an effect we call "Lamb-assisted coherent oscillations", in which a
Lamb shift exponentially enhances the coherent oscillation amplitude. This
dominates for high-frequency environments such as super-Ohmic environments,
where the coherent oscillations can grow exponentially as either the
environment coupling or temperature are increased. The effect could be used as
an experimental probe for high-frequency environments in such systems as
molecular magnets, solid-state qubits, spin-polarized gases (neutrons or He3)
or Bose-condensates.
