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 †

The ideas of topology have found tremendous success in Hermitian physical systems, but even richer properties exist in the more general non-Hermitian framework. Here, we theoretically propose and experimentally demonstrate a new topologically-protected bulk Fermi arc which-unlike the well-known surface Fermi arcs arising from Weyl points in Hermitian systems-develops from non-Hermitian radiative losses in photonic crystal slabs. Moreover, we discover half-integer topological charges in the polarization of far-field radiation around the Fermi arc. We show that both phenomena are direct consequences of the non-Hermitian topological properties of exceptional points, where resonances coincide in their frequencies and linewidths. Our work connects the fields of topological photonics, non-Hermitian physics and singular optics, and paves the way for future exploration of non-Hermitian topological systems.In recent years, topological physics has been widely explored in closed and lossless Hermitian systems, revealing novel phenomena such as topologically non-trivial band structures [1][2][3][4][5][6][7][8][9] and promising applications including backscattering-immune transport [10][11][12][13][14][15][16][17][18][19][20][21]. However, most systems, particularly in photonics, are generically non-Hermitian due to radiation into open space or material gain/loss. NonHermiticity enables even richer topological properties, often with no counterpart in Hermitian frameworks [22][23][24][25]. One such example is the emergence of a new class of degeneracies, commonly referred to as exceptional points (EPs), where two or more resonances of a system coalesce in both eigenvalues and eigenfunctions [26][27][28]. So far, isolated EPs in parameter space [29][30][31][32][33][34][35] and continuous rings of EPs in momentum space [36][37][38] have been studied across different wave systems due to their intriguing properties, such as unconventional transmission/reflection [39][40][41], relations to parity-time symmetry [42][43][44][45][46][47][48], as well as their unique applications in sensing [49,50] and single-mode lasing [51][52][53].Here, we theoretically design and experimentally realize a new configuration of isolated EP pairs in momentum space, which allows us to reveal the unique topological signatures of EPs in the band structure and far-field polarization, and to extend topological band theory into the realm of non-Hermitian systems. Specifically, we demonstrate that a Dirac point (DP) with nontrivial Berry phase can split into a pair of EPs [54][55][56] when radiation loss-a form of non-Hermiticity-is added to a 2D-periodic photonic crystal (PhC) structure. The EPpair generates a distinct double-Riemann-sheet topology in the complex band structure, which leads to two novel consequences: bulk Fermi arcs and polarization half charges. First, we discover and experimentally demonstrate that this pair of EPs is connected by an open-ended isofrequency contourwe refer to it as a bulk Fermi arc-in direct contrast to the common intuiti...

Classifications of symmetry-protected topological (SPT) phases provide a framework to systematically understand the physical properties and potential applications of topological systems. While such classifications have been widely explored in the context of Hermitian systems, a complete understanding of the roles of more general non-Hermitian symmetries and their associated classification is still lacking. Here, we derive a periodic table for non-interacting SPTs with general non-Hermitian symmetries. Our analysis reveals novel non-Hermitian topological classes, while also naturally incorporating the entire classification of Hermitian systems as a special case of our scheme. Building on top of these results, we derive two independent generalizations of Kramers theorem to the non-Hermitian setting, which constrain the spectra of the system and lead to new topological invariants. To elucidate the physics behind the periodic table, we provide explicit examples of novel non-Hermitian topological invariants, focusing on the symmetry classes in zero, one and two dimensions with new topological classifications (e.g. Z in 0D, Z2 in 1D, 2D). These results thus provide a framework for the design and engineering of non-Hermitian symmetry-protected topological systems. arXiv:1812.10490v2 [cond-mat.mes-hall]

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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.

The energy damping time in a mechanical resonator is critical to many precision metrology applications, such as timekeeping and force measurements. We present measurements of the phonon lifetime of a microwave-frequency, nanoscale silicon acoustic cavity incorporating a phononic bandgap acoustic shield. Using pulsed laser light to excite a colocalized optical mode of the cavity, we measured the internal acoustic modes with single-phonon sensitivity down to millikelvin temperatures, yielding a phonon lifetime of up to τph,0≈1.5 seconds (quality factor Q=5×1010) and a coherence time of τcoh,0≈130 microseconds for bandgap-shielded cavities. These acoustically engineered nanoscale structures provide a window into the material origins of quantum noise and have potential applications ranging from tests of various collapse models of quantum mechanics to miniature quantum memory elements in hybrid superconducting quantum circuits.

Exceptional points in non-Hermitian systems have recently been shown to possess nontrivial topological properties, and to give rise to many exotic physical phenomena. However, most studies thus far have focused on isolated exceptional points or one-dimensional lines of exceptional points. Here, we substantially expand the space of exceptional systems by designing two-dimensional surfaces of exceptional points, and find that symmetries are a key element to protect such exceptional surfaces. We construct them using symmetry-preserving non-Hermitian deformations of topological nodal lines, and analyze the associated symmetry, topology, and physical consequences. As a potential realization, we simulate a parity-time-symmetric 3D photonic crystal and indeed find the emergence of exceptional surfaces. Our work paves the way for future explorations of systems of exceptional points in higher dimensions.

Understanding the coordination of cell-division timing is one of the outstanding questions in the field of developmental biology. One active control parameter of the cell-cycle duration is temperature, as it can accelerate or decelerate the rate of biochemical reactions. However, controlled experiments at the cellular scale are challenging, due to the limited availability of biocompatible temperature sensors, as well as the lack of practical methods to systematically control local temperatures and cellular dynamics. Here, we demonstrate a method to probe and control the cell-division timing inCaenorhabditis elegansembryos using a combination of local laser heating and nanoscale thermometry. Local infrared laser illumination produces a temperature gradient across the embryo, which is precisely measured by in vivo nanoscale thermometry using quantum defects in nanodiamonds. These techniques enable selective, controlled acceleration of the cell divisions, even enabling an inversion of division order at the two-cell stage. Our data suggest that the cell-cycle timing asynchrony of the early embryonic development inC. elegansis determined independently by individual cells rather than via cell-to-cell communication. Our method can be used to control the development of multicellular organisms and to provide insights into the regulation of cell-division timings as a consequence of local perturbations.