Many-body-localized discrete time crystal with a programmable spin-based quantum simulator

Disorder-induced many-body-localization (MBL) is the only known mechanism by which to stabilize discrete-time-crystalline (DTC) order across the many-body spectrum. However, an experimental observation of this robust order has remained elusive due to the need for disordered interactions, varied state preparation, site-selective read-out and long coherence times. In this work, we use the electron spin of a single nitrogen-vacancy centre to perform dynamic-nuclear-polarization and selective spin-read-out of naturally interacting 13C spins in diamond [1]. Using selective radio-frequency controls [2], we isolate and manipulate a 1D chain of 9 spins from a precisely characterized 27-spin cluster [3]. We create a DTC via a Floquet unitary and observe long-lived period-doubled oscillations of the system autocorrelation up to N=800 Floquet cycles, and confirm its robustness for generic initial states, a hallmark of the MBL DTC. Our results are consistent with the realization of an out-of-equilibrium Floquet phase of matter and introduce a programmable quantum simulator based on solid-state spins for exploring many-body physics.

[1] J. Randall et al., arXiv:2107.00736 (2021) 

[2] C. E. Bradley et al., Phys. Rev. X 9, 031045 (2019)

[3] M. H. Abobeih et al., Nature, 576, 411-415 (2019)