  Periodically driven systems exhibit resonance when the difference between an
excited state energy and the ground state energy is an integer multiple of
$\hbar$ times the driving frequency. On the other hand, when a superconducting
phase difference is maintained between two superconductors, subgap states
appear which carry a Josephson current. A driven Josephson junction therefore
opens up an interesting avenue where the excitations due to applied driving
affect the current flowing from one superconductor to the other. Motivated by
this, we study charge transport in a superconductor-normal metal-superconductor
(SNS) junction where oscillating potentials are applied to the normal metal
region. We find that for small amplitudes of the oscillating potential, driving
at one site reverses the direction of current at the superconducting phase
differences when difference between the subgap eigenenergies of the undriven
Hamiltonian is integer multiple of $\hbar$ times the driving frequency. For
larger amplitudes of oscillating potential, driving at one site exhibits richer
features. We show that even when the two superconductors are maintained at same
superconducting phase, a current can be driven by applying oscillating
potentials to two sites in the normal metal differing by a phase. We find that
when there is a nonzero Josephson current in the undriven system, the local
peaks and valleys in current of the system driven with an amplitude of
oscillating potential smaller than the superconducting gap indicates sharp
excitations in the system. In the adiabatic limit, we find that charge
transferred in one time period diverges as a powerlaw with pumping frequency
when a Josephson current flows in the undriven system. Our calculations are
exact and can be applied to finite systems. We discuss possible experimental
setups where our predictions can be tested.
