Abstract
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 \inftyN→∞, (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.
Highlights
In reduced dimensions with confined electric fields, even small qubit-qubit interactions can have a huge effect. These systems generate a lot of complexity at the interface of three typically only weakly connected areas of physics: (i) emergent phases and spontaneous symmetry-breaking of interacting many-body systems in the thermodynamic limit (N → ∞ number of qubits) (ii) quantum optics and the dynamics of fluctuating light fields, and (iii) non-equilibrium physics of driven, open quantum systems, due to drive and multiple loss channels such as photon decay with rate κ and atomic spontaneous emission with rate γ
As the photonic sector alone couples to a dissipative channel, we numerically observe that when translational symmetry is restored as one goes from the (AFM+superradiant phase (SR)) into the SR phase as g → gc,2, two of the six poles approach the origin on the complex frequency plane
The point of this paper was to create a base case for a large array of self-interacting atomic qubits coupled to a single-mode optical light field
Summary
The fields of quantum simulation with cold atoms [1] and quantum optics [2] are currently being merged. In reduced dimensions with confined electric fields, even small qubit-qubit interactions can have a huge effect These systems generate a lot of complexity at the interface of three typically only weakly connected areas of physics: (i) emergent phases and spontaneous symmetry-breaking of interacting many-body systems in the thermodynamic limit (N → ∞ number of qubits) (ii) quantum optics and the dynamics of fluctuating light fields (from M = 1 to M = ∞ photon modes), and (iii) non-equilibrium physics of driven, open quantum systems, due to drive and multiple loss channels such as photon decay with rate κ and atomic spontaneous emission with rate γ. We extend such models by coupling the spin degrees of freedom to a quantum light field, which can be in a zero-photon vacuum state with undetermined phase.
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