  The strength of the (Rashba-type) spin-orbit coupling in mesoscopic
semiconductor rings can be tuned with external gate voltages. Here we consider
the case of a periodically changing spin-orbit interaction strength as induced
by sinusoidal voltages. In a closed one dimensional quantum ring with weak
spin-orbit coupling, Rabi oscillations are shown to appear. We find that the
time evolution of initially localized wave packets exhibits a series of
collapse and revival phenomena. Partial revivals -- that are typical in
nonlinear systems -- are shown to correspond to superpositions of states
localized at different spatial positions along the ring. These "spintronic
Schrodinger-cat sates" appear periodically, and similarly to their counterparts
in other physical systems, they are found to be sensitive to environment
induced disturbances. The time dependent spin transport problem, when leads are
attached to the ring, is also solved. We show that the "sideband currents"
induced by the oscillating spin-orbit interaction strength can become the
dominant output channel, even in the presence of moderate thermal fluctuations
and random scattering events.
