Title: Transiently enhanced interlayer tunneling in optically driven high $T_c$ superconductors,
Abstract: Recent pump-probe experiments reported an enhancement of superconducting
transport along the $c$-axis of underdoped YBa$_2$Cu$_3$O$_{6+\delta}$ (YBCO),
induced by a mid-infrared optical pump pulse tuned to a specific lattice
vibration. To understand this transient non-equilibrium state, we develop a
pump-probe formalism for a stack of Josephson junctions, and we consider the
tunneling strengths in presence of modulation with an ultrashort optical pulse.
We demonstrate that a transient enhancement of the Josephson coupling can be
obtained for pulsed excitation and that this can be even larger than in a
continuously driven steady-state. Especially interesting is the conclusion that
the effect is largest when the material is parametrically driven at a frequency
immediately above the plasma frequency, in agreement with what is found
experimentally. For bilayer Josephson junctions, an enhancement similar to that
experimentally is predicted below the critical temperature $T_c$. This model
reproduces the essential features of the enhancement measured below $T_c$. To
reproduce the experimental results above $T_c$, we will explore extensions of
this model, such as in-plane and amplitude fluctuations, elsewhere.