  The combined action of a DC bias and a microwave drive on the transport
characteristic of a superconductor-quantum dot-superconductor junction is
investigated. To cope with time dependent non-equilibrium effects and
interactions in the quantum dot, we develop a general formalism for the
dynamics of the density operator based on a particle conserving approach to
superconductivity. Without invoking a broken U (1) symmetry, we identify a
dynamical phase connected to the coherent transfer of Cooper pairs across the
junction. In the weak coupling limit, we show that besides quasiparticle
transport, proximity induced superconducting correlations manifest in anomalous
pair tunneling involving the transfer of a Cooper pair. The resulting
generalized master equation in presence of the microwave drive showcases the
characteristic bichromatic response due to the combination of the AC Josephson
effect and an AC voltage. Analytical expressions for all harmonics in the
driving frequency of both the current and the reduced dot operator are given
for arbitrary driving strength. For the net DC current the resulting photon
assisted processes give rise to rich current-voltage characteristics. In
addition to photon assisted subgap transport we find regions of total current
inversion in the stability diagram. There, the junction acts as a pump with the
net DC current flowing against the applied DC bias. The first harmonic of the
current, being closely related to the nonlinear dynamic susceptibility of the
junction, is discussed at finite applied DC bias.
