Jan Gelhausen, Michael Buchhold, Achim Rosch, Philipp Strack
SciPost Phys. 1, 004 (2016) ·
published 23 October 2016

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The fields of quantum simulation with cold atoms [1] and quantum optics [2]
are currently being merged. In a set of recent pathbreaking experiments with
atoms in optical cavities [3,4] lattice quantum manybody systems with both, a
shortrange 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 symmetrybreaking and emergent phases of interacting manybody
systems with a large number of atoms $N\rightarrow\infty$, (ii) quantum optics
and the dynamics of fluctuating light fields, and (iii) nonequilibrium physics
of driven, open quantum systems. Here we propose what is possibly the simplest,
quantumoptical magnet with competing short and longrange interactions, in
which all three elements can be analyzed comprehensively: a Rydbergdressed
spin lattice [5] coherently coupled to a single photon mode. Solving a set of
coupled evenodd sublattice Master equations for atomic spin and photon
meanfield amplitudes, we find three key results. (R1): Superradiance and a
coherent photon field can coexist with spontaneously broken magnetic
translation symmetry. The latter is induced by the shortrange nearestneighbor
interaction from weakly admixed Rydberg levels. (R2): This broken evenodd
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 nanophotonic crystals coupled to interacting atoms and multimode
photon dynamics in Rydberg systems.