Controlling collective modes with amplitude modulated Floquet drives

We propose a method to parametrically excite low frequency collective modes in an interacting many body system using a Floquet driving at optical frequencies with a modulated amplitude. We first apply the idea to plasmons and demonstrate that it can be used to design plasmonic time-varying media with singular dispersions. Above a critical driving strength, resonant plasmon modes become unstable and arrange themselves in 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. Finally, we discuss the extension of our ideas to Magnons.