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

TL;DR

This study demonstrates discrete time-crystalline behavior in a three-dimensional ordered crystal of ammonium dihydrogen phosphate using NMR, revealing new insights into DTC coherence and decay mechanisms in solid-state systems.

Contribution

First observation of DTC signatures in a 3D ordered crystal via NMR, expanding understanding of DTC phenomena beyond previous systems.

Findings

DTC signatures observed in ammonium dihydrogen phosphate crystal.

The internal Hamiltonian significantly affects DTC coherence during pulses.

A DTC echo experiment was developed to probe system coherence.

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.