Understanding quantum dynamics away from equilibrium is an outstanding challenge in the modern physical sciences. It is well known that out-of-equilibrium systems can display a rich array of phenomena, ranging from self-organized synchronization to dynamical phase transitions1,2. More recently, advances in the controlled manipulation of isolated many-body systems have enabled detailed studies of non-equilibrium phases in strongly interacting quantum matter3-6. As a particularly striking example, the interplay of periodic driving, disorder, and strong interactions has recently been predicted to result in exotic "time-crystalline" phases7, which spontaneously break the discrete time-translation symmetry of the underlying drive8-11. Here, we report the experimental observation of such discrete time-crystalline order in a driven, disordered †

International audienceWe implemented two-photon scanned light-sheet microscopy, combining nonlinear excitation with orthogonal illumination of light-sheet microscopy, and showed its excellent performance for in vivo, cellular-resolution, three-dimensional imaging of large biological samples. Live imaging of fruit fly and zebrafish embryos confirmed that the technique can be used to image up to twice deeper than with one-photon light-sheet microscopy and more than ten times faster than with point-scanning two-photon microscopy without compromising normal biology. Cop. 2011 Nature America, Inc. All rights reserved

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Statistical mechanics underlies our understanding of macroscopic quantum systems. It is based on the assumption that out-of-equilibrium systems rapidly approach their equilibrium states, forgetting any information about their microscopic initial conditions. This fundamental paradigm is challenged by disordered systems, in which a slowdown or even absence of thermalization is expected. We report the observation of critical thermalization in a three dimensional ensemble of ∼10^{6} electronic spins coupled via dipolar interactions. By controlling the spin states of nitrogen vacancy color centers in diamond, we observe slow, subexponential relaxation dynamics and identify a regime of power-law decay with disorder-dependent exponents; this behavior is modified at late times owing to many-body interactions. These observations are quantitatively explained by a resonance counting theory that incorporates the effects of both disorder and interactions.

We study the depolarization dynamics of a dense ensemble of dipolar interacting spins, associated with nitrogen-vacancy centers in diamond. We observe anomalously fast, density-dependent, and non-exponential spin relaxation. To explain these observations, we propose a microscopic model where an interplay of long-range interactions, disorder, and dissipation leads to predictions that are in quantitative agreement with both current and prior experimental results. Our results pave the way for controlled many-body experiments with long-lived and strongly interacting ensembles of solid-state spins.Experiments-To probe the depolarization dynamics of strongly interacting NV ensembles, we utilize the pulse sequence illustrated in Fig. 1c. This sequence allows one