$^{31}$P NMR study of discrete time-crystalline signatures in an ordered crystal of ammonium dihydrogen phosphate

Abstract

The rich dynamics and phase structure of driven systems includes the recently described phenomenon of the "discrete time crystal" (DTC), a robust phase which spontaneously breaks the discrete time translation symmetry of its driving Hamiltonian. Experiments in trapped ions and diamond nitrogen vacancy centers have recently shown evidence for this DTC order. Here, we show nuclear magnetic resonance (NMR) data of DTC behavior in a third, strikingly different system: a highly ordered spatial crystal in three dimensions. We devise a DTC echo experiment to probe the coherence of the driven system. We examine potential decay mechanisms for the DTC oscillations, and demonstrate the important effect of the internal Hamiltonian during nonzero duration pulses.