  We present a simple model for multiphoton transitions between the quasi-bound
states of a current-driven Josephson junction. The transitions are induced by
applying an ac voltage with controllable frequency and amplitude across the
junction. The voltage induces transitions when the ac frequency equals n times
the splitting between the ground and first excited quasi-bound state of the
junction. We calculate the transition matrix elements as functions of the dc
bias current I, and the frequency and amplitude of the ac voltage, for
representative junction parameters. We also calculate the frequency-dependent
absorption coefficient by solving the relevant Bloch equations when the ac
amplitude is sufficiently small. In this regime, the absorption coefficient is
a sum of Lorentzian lines centered at the n-photon absorption frequency, of
strength proportional to the squared matrix elements. For fixed ac voltage
amplitude, the n-photon transition rate usually decreases with increasing n. We
also find a characteristic even-odd effect: The absorption coefficient
typically increases with I for n even but decreases for n odd. Our results
agree qualitatively with recent experiments.
