Inducing exceptional points, enhancing plasmon quality and creating correlated plasmon states with modulated Floquet parametric driving

The control of low frequency collective modes in solids by light presents important challenges and opportunities for condensed matter physics. We propose a method to parametrically drive low THz range collective modes in an interacting many body system using Floquet driving at optical frequencies with a modulated amplitude. We demonstrate that it can be used to design plasmonic time-varying media with singular dispersions. Plasmons near resonance with half the modulation frequency exhibit two lines of exceptional points connected by dispersionless states. Above a critical driving strength, resonant plasmon modes become unstable and undergo a continuous transition towards a crystal-like structure stabilized by interactions and nonlinearities. This new state breaks the discrete time translational symmetry of the drive as well as the translational and rotational spatial symmetries of the system and exhibits soft, Goldstone-like phononic excitations. Below the instability threshold, our method can be used to enhance the quality of plasmon resonances.