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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).

Pure spin currents are simultaneously generated and detected electrically through sub-terahertz magnons in the antiferromagnetic insulator Cr2O3, demonstrating the potential of magnon excitations in antiferromagnets for high-frequency spintronic devices.

Spin dynamics in antiferromagnets has much shorter timescales than in ferromagnets, offering attractive properties for potential applications in ultrafast devices(1-3). However, spin-current generation via antiferromagnetic resonance and simultaneous electrical detection by the inverse spin Hall effect in heavy metals have not yet been explicitly demonstrated(4-6). Here we report sub-terahertz spin pumping in heterostructures of a uniaxial antiferromagnetic Cr2O3 crystal and a heavy metal (Pt or Ta in its beta phase). At 0.240 terahertz, the antiferromagnetic resonance in Cr2O3 occurs at about 2.7 tesla, which excites only right-handed magnons. In the spin-canting state, another resonance occurs at 10.5 tesla from the precession of induced magnetic moments. Both resonances generate pure spin currents in the heterostructures, which are detected by the heavy metal as peaks or dips in the open-circuit voltage. The pure-spin-current nature of the electrically detected signals is unambiguously confirmed by the reversal of the voltage polarity observed under two conditions: when switching the detector metal from Pt to Ta, reversing the sign of the spin Hall angle(7-9), and when flipping the magnetic-field direction, reversing the magnon chirality(4,5). The temperature dependence of the electrical signals at both resonances suggests that the spin current contains both coherent and incoherent magnon contributions, which is further confirmed by measurements of the spin Seebeck effect and is well described by a phenomenological theory. These findings reveal the unique characteristics of magnon excitations in antiferromagnets and their distinctive roles in spin-charge conversion in the high-frequency regime.