Quantum Stat Mech in a Programmable Spin Chain of Trapped Ions

Trapped atomic ions are a versatile and very clean platform for the quantum programming of interacting spin models and the study of quantum nonequilibrium phenomena. When spin-dependent optical dipole forces are applied to a collection of trapped ions, an effective long-range quantum magnetic interaction arises, with reconfigurable and tunable graphs. Following earlier work on many-body spectroscopy\footnote{C. Senko, et al., \textbf{Science 345}, 430 (2014).} and quench dynamics\footnote{P. Richerme, et al., \textbf{Nature 511}, 198 (2014).}, we have recently studied many body non-thermalization processes in this system. Frustrated Hamiltonian dynamics can lead to prethermalization\footnote{B. Neyenhuis, et al., \textbf{arXiv 1608.00681} (2016).}, and by adding programmable disorder between the sites, we have observed the phenomenon of many body localization (MBL)\footnote{J. Smith, et al., \textbf{Nature Physics 12}, 907 (2016).}. Finally, by applying a periodically driven Floquet Hamiltonian tempered by MBL, we report the observation of a discrete ``time crystal” in the stable appearance of a subharmonic response of the system to the periodic drive\footnote{J. Zhang, et al., \textbf{arXiv 1609.08684} (2016).}