  Topological quantum phases underpin many concepts of modern physics. While
the existence of disorder-immune topological edge states of electrons usually
requires magnetic fields, direct effects of magnetic field on light are very
weak. As a result, demonstrations of topological states of photons employ
synthetic fields engineered in special complex structures or external
time-dependent modulations. Here, we reveal that the quantum Hall phase with
topological edge states, spectral Landau levels and Hofstadter butterfly can
emerge in a simple quantum system, where topological order arises solely from
interactions without any fine-tuning. Such systems, arrays of two-level atoms
(qubits) coupled to light being described by the classical Dicke model, have
recently been realized in experiments with cold atoms and superconducting
qubits. We believe that our finding will open new horizons in several
disciplines including quantum physics, many-body physics, and nonlinear
topological photonics, and it will set an important reference point for
experiments on qubit arrays and quantum simulators.

Quantum Physics;Mesoscale and Nanoscale Physics;Pattern Formation and Solitons;Optics