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Abstract

Optical drives at terahertz and mid-infrared frequencies in quantum materials
are increasingly used to reveal the nonlinear dynamics of collective modes in
correlated many-body systems and their interplay with electromagnetic waves.
Recent experiments demonstrated several surprising optical properties of
transient states induced by driving, including the appearance of photo-induced
edges in the reflectivity in cuprate superconductors, observed both below and
above the equilibrium transition temperature. Furthermore, in other driven
materials, reflection coefficients larger than unity have been observed. In
this paper we demonstrate that unusual optical properties of photoexcited
systems can be understood from the perspective of a Floquet system; a system
with periodically modulated system parameters originating from pump-induced
oscillations of a collective mode. We present a general phenomenological model
of reflectivity from Floquet materials, which takes into account parametric
generation of excitation pairs. We find a universal phase diagram of drive
induced features in reflectivity which evidence a competition between driving
and dissipation. To illustrate our general analysis we apply our formalism to
two concrete examples motivated by recent experiments: a single plasmon band,
which describes Josephson plasmons in layered superconductors, and a
phonon-polariton system, which describes upper and lower polaritons in
materials such as insulating SiC. Finally we demonstrate that our model can be
used to provide an accurate fit to results of phonon-pump - terahertz-probe
experiments in the high temperature superconductor YBa₂Cu₃O_6.5. Our
model explains the appearance of a pump-induced edge, which is higher in energy
than the equilibrium Josephson plasmon edge, even if the interlayer Josephson
coupling is suppressed by the pump pulse.