  Coherent optical excitation of certain phonon modes in YBa$_2$Cu$_3$O$_{6+x}$
has been shown to induce superconducting-like interlayer coherence at
temperatures higher than $T_c$. Recent work has associated these phenomena to a
parametric excitation and amplification of Josephson plasma polaritons, which
are overdamped above $T_c$ but are made coherent by the phonon drive. However,
the dissipative response of uncondensed quasiparticles, which do not couple in
the same way to the phonon drive, has not been addressed. Here, we investigate
both the enhancement of the superfluid density, $\omega\sigma_2(\omega)$, and
the dissipative response of quasiparticles, $\sigma_1(\omega)$, by
systematically tuning the duration and energy of the mid-infrared pulse while
keeping the peak field fixed. We find that the photo-induced superfluid density
saturates to the zero-temperature equilibrium value for pulses made longer than
the phonon dephasing time, whilst the dissipative component continues to grow
with increasing pulse duration. We show that superfluid and dissipation remain
uncoupled as long as the drive is on, and identify an optimal regime of pump
pulse durations for which the superconducting response is maximum and
dissipation is minimized.
