Photonic metamaterial analogue of a continuous time crystal

Abstract

Time crystals are an eagerly sought phase of matter with broken time-translation symmetry. Quantum time crystals with discretely broken time-translation symmetry have been demonstrated in trapped ions, atoms and spins whereas continuously broken time-translation symmetry has been observed in an atomic condensate inside an optical cavity. Here we report that a classical metamaterial nanostructure, a two-dimensional array of plasmonic metamolecules supported on flexible nanowires, can be driven to a state possessing all of the key features of a continuous time crystal: continuous coherent illumination by light resonant with the metamolecules’ plasmonic mode triggers a spontaneous phase transition to a superradiant-like state of transmissivity oscillations, resulting from many-body interactions among the metamolecules, characterized by long-range order in space and time. The phenomenon is of interest to the study of dynamic classical many-body states in the strongly correlated regime and applications in all-optical modulation, frequency conversion and timing.