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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).

Solid-state lithium metal batteries require accommodation of electrochemically generated mechanical stress inside the lithium: this stress can be(1,2) up to 1 gigapascal for an overpotential of 135 millivolts. Maintaining the mechanical and electrochemical stability of the solid structure despite physical contact with moving corrosive lithium metal is a demanding requirement. Using in situ transmission electron microscopy, we investigated the deposition and stripping of metallic lithium or sodium held within a large number of parallel hollow tubules made of a mixed ionic-electronic conductor (MIEC). Here we show that these alkali metals-as single crystals-can grow out of and retract inside the tubules via mainly diffusional Coble creep along the MIEC/metal phase boundary. Unlike solid electrolytes, many MIECs are electrochemically stable in contact with lithium (that is, there is a direct tie-line to metallic lithium on the equilibrium phase diagram), so this Coble creep mechanism can effectively relieve stress, maintain electronic and ionic contacts, eliminate solid-electrolyte interphase debris, and allow the reversible deposition/stripping of lithium across a distance of 10 micrometres for 100 cycles. A centimetre-wide full cell-consisting of approximately 10(10) MIEC cylinders/solid electrolyte/LiFePO4-shows a high capacity of about 164 milliampere hours per gram of LiFePO4, and almost no degradation for over 50 cycles, starting with a 1x excess of Li. Modelling shows that the design is insensitive to MIEC material choice with channels about 100 nanometres wide and 10-100 micrometres deep. The behaviour of lithium metal within the MIEC channels suggests that the chemical and mechanical stability issues with the metal-electrolyte interface in solid-state lithium metal batteries can be overcome using this architecture.

By containing lithium metal within oriented tubes of a mixed ionic-electronic conductor, a 3D anode for lithium metal batteries is produced that overcomes chemomechanical stability issues at the electrolyte interface.