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arXiv:2109.01063 · Reviews of Modern Physics

Long-range interacting quantum systems

Nicolò Defenu, Tobias Donner, Tommaso Macrì, Guido Pagano, Stefano Ruffo, Andrea Trombettoni

Published Aug 29, 2023• 326 citations
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Abstract

Many-body quantum physics with long-range interactions of variable range and strength can be studied in experiments with Rydberg atom arrays, dipolar systems, trapped ions, and cold atoms in cavities. This review identifies common and universal features induced by the long-range interactions such as the extensive or nonextensive character of the total energy and features that deviate from the case of short-range interactions. A comparison with the corresponding results for classical systems is presented.

DOI
10.1103/revmodphys.95.035002

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The fields of quantum simulation with cold atoms and quantum optics are currently being merged. In a set of recent pathbreaking experiments with atoms in optical cavities , lattice quantum many-body systems with both, a short-range interaction and a strong interaction potential of infinite range –mediated by a quantized optical light field– were realized. A theoretical modelling of these systems faces considerable complexity at the interface of: (i) spontaneous symmetry-breaking and emergent phases of interacting many-body systems with a large number of atoms N\rightarrow \infty N → ∞ , (ii) quantum optics and the dynamics of fluctuating light fields, and (iii) non-equilibrium physics of driven, open quantum systems. Here we propose what is possibly the simplest, quantum-optical magnet with competing short- and long-range interactions, in which all three elements can be analyzed comprehensively: a Rydberg-dressed spin lattice coherently coupled to a single photon mode. Solving a set of coupled even-odd sublattice master equations for atomic spin and photon mean-field amplitudes, we find three key results. (R1): Superradiance and a coherent photon field appears in combination with spontaneously broken magnetic translation symmetry. The latter is induced by the short-range nearest-neighbor interaction from weakly admixed Rydberg levels. (R2): This broken even-odd sublattice symmetry leaves its imprint in the light via a novel peak in the cavity spectrum beyond the conventional polariton modes. (R3): The combined effect of atomic spontaneous emission, drive, and interactions can lead to phases with anomalous photon number oscillations. Extensions of our work include nano-photonic crystals coupled to interacting atoms and multi-mode photon dynamics in Rydberg systems.