  Motivated by recent pump-probe experiments indicating enhanced coherent
$c$-axis transport in underdoped YBCO, we study Josephson junctions
periodically driven by optical pulses. We propose a mechanism for this
observation by demonstrating that a parametrically driven Josephson junction
shows an enhanced imaginary part of the low-frequency conductivity when the
driving frequency is above the plasma frequency, implying an effectively
enhanced Josephson coupling. We generalize this analysis to a bilayer system of
Josephson junctions modeling YBCO. Again, the Josephson coupling is enhanced
when the pump frequency is blue-detuned to either of the two plasma frequencies
of the material. We show that the emergent driven state is a genuine,
non-equilibrium superconducting state, in which equilibrium relations between
the Josephson coupling, current fluctuations, and the critical current no
longer hold.
