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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).

Strongly correlated insulating Mott and generalized Wigner phases are detected in WSe2/WS2 moire superlattices, and their electrical properties and excited spin states are studied using an optical technique.

Moire superlattices can be used to engineer strongly correlated electronic states in two-dimensional van der Waals heterostructures, as recently demonstrated in the correlated insulating and superconducting states observed in magic-angle twisted-bilayer graphene and ABC trilayer graphene/boron nitride moire superlattices(1-4). Transition metal dichalcogenide moire heterostructures provide another model system for the study of correlated quantum phenomena(5) because of their strong light-matter interactions and large spin-orbit coupling. However, experimental observation of correlated insulating states in this system is challenging with traditional transport techniques. Here we report the optical detection of strongly correlated phases in semiconducting WSe2/WS2 moire superlattices. We use a sensitive optical detection technique and reveal a Mott insulator state at one hole per superlattice site and surprising insulating phases at 1/3 and 2/3 filling of the superlattice, which we assign to generalized Wigner crystallization on the underlying lattice(6-11). Furthermore, the spin-valley optical selection rules(12-14) of transition metal dichalcogenide heterostructures allow us to optically create and investigate low-energy excited spin states in the Mott insulator. We measure a very long spin relaxation lifetime of many microseconds in the Mott insulating state, orders of magnitude longer than that of charge excitations. Our studies highlight the value of using moire superlattices beyond graphene to explore correlated physics.

At the historic Shelter Island Conference on the Foundations of Quantum Mechanics in 1947, Willis Lamb reported an unexpected feature in the fine structure of atomic hydrogen: a separation of the 2S(1/2) and 2P(1/2) states(1). The observation of this separation, now known as the Lamb shift, marked an important event in the evolution of modern physics, inspiring others to develop the theory of quantum electrodynamics(2-5). Quantum electrodynamics also describes antimatter, but it has only recently become possible to synthesize and trap atomic antimatter to probe its structure. Mirroring the historical development of quantum atomic physics in the twentieth century, modern measurements on anti-atoms represent a unique approach for testing quantum electrodynamics and the foundational symmetries of the standard model. Here we report measurements of the fine structure in the n = 2 states of antihydrogen, the antimatter counterpart of the hydrogen atom. Using optical excitation of the 1S-2P Lyman-alpha transitions in antihydrogen(6), we determine their frequencies in a magnetic field of 1 tesla to a precision of 16 parts per billion. Assuming the standard Zeeman and hyperfine interactions, we infer the zero-field fine-structure splitting (2P(1/2)-2P(3/2)) in antihydrogen. The resulting value is consistent with the predictions of quantum electrodynamics to a precision of 2 per cent. Using our previously measured value of the 1S-2S transition frequency(6,7), we find that the classic Lamb shift in antihydrogen (2S(1/2)-2P(1/2) splitting at zero field) is consistent with theory at a level of 11 per cent. Our observations represent an important step towards precision measurements of the fine structure and the Lamb shift in the antihydrogen spectrum as tests of the charge-parity-time symmetry(8) and towards the determination of other fundamental quantities, such as the antiproton charge radius(9,10), in this antimatter system.

Precision measurements of the 1S-2P transition in antihydrogen that take into account the standard Zeeman and hyperfine effects confirm the predictions of quantum electrodynamics.