Oppenheim Award: Excitations in space-time periodic systems beyond Floquet theory

The periodic modulation of local parameters in space and time provides a tunable route to active manipulation of waves across electronic, photonic, and phononic systems. The standard mathematical framework for describing such systems is Floquet theory, which describes the evolution of linear systems with parameters that are modulated periodically in time. I will describe recent progress in understanding exotic excitations in systems that require extensions to standard Floquet analysis to account for intertwined spatial and temporal translational symmetries and/or nonlinear effects. Examples include space-time crystals with topologically quantized transport; nonlinear resonator assemblies that exhibit chiral steady states for signal switching and amplification; and broadband temporal beam splitters. These phenomena, which span quantum and classical systems, highlight the versatility of space-time modulation as a design strategy for signal manipulation and motivate new theoretical approaches that go beyond standard Floquet analysis.