Observation of Discrete-Time-Crystal Signatures in an Ordered Dipolar Many-Body System*

The rich dynamics and phase structure of driven systems include 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 report nuclear magnetic resonance (NMR) observations of DTC signatures in a third, strikingly different, system: an ordered spatial crystal. This system is expected to be even farther from the regime of many-body localization (MBL) than those studied in the earlier experiments. We study the 100% occupied crystal lattice of spin-1/2 ³¹P nuclei in ammonium dihydrogen phosphate (ADP), with chemical formula NH4H2PO4. ADP also contains spin-1/2 ¹H nuclei (99.98% abundant) and spin-1 ¹⁴N nuclei (99.64% abundant). Implementing the DTC pulse sequence on the ³¹P spins, we observe robust oscillations at half the drive frequency (“DTC oscillations” for brevity) across orders of magnitude in interaction time. We also study the decay mechanism of the DTC oscillations, with two results. First, we show by generating a time-reversed DTC echo that the density matrix is more coherent than the original DTC sequence reveals. Second, we show that the effect of interactions during the nonzero pulse duration of the DTC sequence limits our ability to observe the intrinsic lifetime of the DTC oscillations [1,2]. In this work, we exploited both the long coherence times of our sample, and our ability to use NMR pulse sequences to edit the spin Hamiltonian. This suggests that NMR can be a useful probe of the physics of out-of-equilibrium, driven many-body systems.

[1] J. Rovny, R.L. Blum, and S.E. Barrett, Phys. Rev. Lett. 120, 180603 (2018)
[2] J. Rovny, R.L. Blum, and S.E. Barrett, Phys. Rev. B 97, 184301 (2018)