  We suggest to subject anharmonically trapped Bose-Einstein condensates to
sinusoidal forcing with a smooth, slowly changing envelope, and to measure the
coherence of the system after such pulses. In a series of measurements with
successively increased maximum forcing strength one then expects an adiabatic
return of the condensate to its initial state as long as the pulses remain
sufficiently weak. In contrast, once the maximum driving amplitude exceeds a
certain critical value there should be a drastic loss of coherence, reflecting
significant heating induced by the pulse. This predicted experimental signature
is traced to the loss of an effective adiabatic invariant, and to the ensuing
breakdown of adiabatic motion of the system's Floquet state when the many-body
dynamics become chaotic. Our scenario is illustrated with the help of a
two-site model of a forced bosonic Josephson junction, but should also hold for
other, experimentally accessible configurations.
