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Interactions between light and an ensemble of strontium atoms in an optical cavity can serve as a testbed for studying dynamical phase transitions, which are currently not well understood.

Interactions between atoms and light in optical cavities provide a means of investigating collective (many-body) quantum physics in controlled environments. Such ensembles of atoms in cavities have been proposed for studying collective quantum spin models, where the atomic internal levels mimic a spin degree of freedom and interact through long-range interactions tunable by changing the cavity parameters(1-4). Non-classical steady-state phases arising from the interplay between atom-light interactions and dissipation of light from the cavity have previously been investigated(5-11). These systems also offer the opportunity to study dynamical phases of matter that are precluded from existence at equilibrium but can be stabilized by driving a system out of equilibrium(12-16), as demonstrated by recent experiments(17-22). These phases can also display universal behaviours akin to standard equilibrium phase transitions(8,23,24). Here, we use an ensemble of about a million strontium-88 atoms in an optical cavity to simulate a collective Lipkin-Meshkov-Glick model(25,26), an iconic model in quantum magnetism, and report the observation of distinct dynamical phases of matter in this system. Our system allows us to probe the dependence of dynamical phase transitions on system size, initial state and other parameters. These observations can be linked to similar dynamical phases in related systems, including the Josephson effect in superfluid helium(27), or coupled atomic(28) and solid-state polariton(29) condensates. The system itself offers potential for generation of metrologically useful entangled states in optical transitions, which could permit quantum enhancement in state-of-the-art atomic clocks(30,31).

Protein crystallization is important in structural biology, disease research and pharmaceuticals. It has recently been recognized that nonclassical crystallization involving initial formation of an amorphous precursor phase-occurs often in protein, organic and inorganic crystallization processes(1-5). A two-step nucleation theory has thus been proposed, in which initial low-density, solvated amorphous aggregates subsequently densify, leading to nucleation(4,6,7). This view differs from classical nucleation theory, which implies that crystalline nuclei forming in solution have the same density and structure as does the final crystalline state(1). A protein crystallization mechanism involving this classical pathway has recently been observed directly(8). However, a molecular mechanism of nonclassical protein crystallization(9-15) has not been established(9,11,14). To determine the nature of the amorphous precursors and whether crystallization takes place within them (and if so, how order develops at the molecular level), three-dimensional (3D) molecular-level imaging of a crystallization process is required. Here we report cryogenic scanning transmission microscopy tomography of ferritin aggregates at various stages of crystallization, followed by 3D reconstruction using simultaneous iterative reconstruction techniques to provide a 3D picture of crystallization with molecular resolution. As crystalline order gradually increased in the studied aggregates, they exhibited an increase in both order and density from their surface towards their interior. We observed no highly ordered small structures typical of a classical nucleation process, and occasionally we observed several ordered domains emerging within one amorphous aggregate, a phenomenon not predicted by either classical or two-step nucleation theories. Our molecular-level analysis hints at desolvation as the driver of the continuous order-evolution mechanism, a view that goes beyond current nucleation models, yet is consistent with a broad spectrum of protein crystallization mechanisms.

Redox-switchable chelation is demonstrated for a carborane cluster molecule, leading to controlled chemical or electrochemical capture and release of uranyl in monophasic or biphasic model solvent systems.