Floquet polaritons in optically driven materials

Polaritons are coupled collective modes of light and matter in quantum materials. In modern pump-probe experiments, a pump light pulse may dramatically alter the properties of the polaritons, rendering them Floquet polaritons that can be detected by a probe pulse. We present a practical framework to describe Floquet polaritons in terms of the linear and nonlinear optical properties of the material. The central quantity that yields the spectra of Floquet polaritons is an effective linear optical susceptibility contributed by the pump through nonlinear optical susceptibilities. We apply this method to graphene and show that via its third-order optical nonlinearity, infrared pump leads to Floquet plasmon bands. Notably, near plasmonic band crossings, parametric instability leads to flat bands with unstable modes and exceptional points that closely resemble those of non-Hermitian systems. As a second example, we show that in hexagonal boron nitride pumped by mid-infrared laser, the pump induces Floquet phonon polariton bands via phononic nonlinearity, which can be detected with either far-field or near-field optical technique. Finally, in layered superconductors pumped by THz light polarized along the out-of-plane direction, the Josephson-type optical nonlinearity leads to Floquet Josephson plasmons, which manifest as new peaks in the THz reflectivity of a probe pulse.