  We present a microscopic theory of the effect of a microwave field on the
supercurrent through a quantum point contact of arbitrary transmission. Our
theory predicts that: (i) for low temperatures and weak fields, the
supercurrent is suppressed at certain values of the superconducting phase, (ii)
at strong fields, the current-phase relation is strongly modified and the
current can even reverse its sign, and (iii) at finite temperatures, the
microwave field can enhance the critical current of the junction. Apart from
their fundamental interest, our findings are also important for the description
of experiments that aim at the manipulation of the quantum state of atomic
point contacts.
