Infinite-range interactions in atomic spin systems

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The goal of the present project is the investigation of large and small spin systems with cavity mediated all-to-all interactions. We will perform detailed theoretical studies of the so-called Dicke-Ising model, experimentally implemented in Project 1 of this Research Unit. Here, the infinite-range interactions induced by the collective coupling of a large atomic gas to a cavity coexist with Ising-type long-range interatomic interactions induced by off-resonant laser excitation of Rydberg states. We will explore the novel phases and phase transitions in this model and analyze its potential to create highly correlated many-body quantum states. We will then turn to the study of a few-spin system with infinite-range exchange or Ising-type interactions. This system will be realised experimentally in this project using highly-excited Rydberg atoms coupled to a microwave cavity field that plays the role of a "quantum bus". Strong dipole-dipole interactions between the nearby Rydberg atoms will permit the formation of Rydberg superatoms that can accommodate at most one collective excitation. Individual superatoms would represent single spins, which in turn can interact with each other via the cavity-mediated infinite-range interactions. The development of such few- and many-body quantum systems with highly-tunable arbitrary-range interactions will be of paramount importance for scalable implementations of quantum logic gates and the realization of dynamically controlled and configurable quantum simulators.