  We consider the supercurrent flow through gated mesoscopic semiconductor
hetrostructures in which a two-dimensional normal constriction is confined
between superconducting electrodes. We show that for these structures the
Josephson current, carried by quantized electron modes, can be strongly
affected by an electromagnetic field. Photon-assisted Landau-Zener transitions
between Andreev bound states in the constriction manifest themselves in one of
two ways: (i) If the phase difference between the superconducting elements is
fixed a series of reversals in the direction of supercurrent flow occurs
(Somersault effect). (ii) If instead the junction is current biased a series of
voltage spikes is seen. Both manifestations are a direct consequence of the
discrete energy spectrum of the mesoscopic junction. We discuss necessary
conditions for the described phenomena to be experimentally observable.
