  Synthetic photonic materials are an emerging platform for exploring the
interface between microscopic quantum dynamics and macroscopic material
properties[1-5]. Photons experiencing a Lorentz force develop handedness,
providing opportunities to study quantum Hall physics and topological quantum
science[6-8]. Here we present an experimental realization of a magnetic field
for continuum photons. We trap optical photons in a multimode ring resonator to
make a two-dimensional gas of massive bosons, and then employ a non-planar
geometry to induce an image rotation on each round-trip[9]. This results in
photonic Coriolis/Lorentz and centrifugal forces and so realizes the
Fock-Darwin Hamiltonian for photons in a magnetic field and harmonic trap[10].
Using spatial- and energy-resolved spectroscopy, we track the resulting
photonic eigenstates as radial trapping is reduced, finally observing a
photonic Landau level at degeneracy. To circumvent the challenge of trap
instability at the centrifugal limit[10,11], we constrain the photons to move
on a cone. Spectroscopic probes demonstrate flat space (zero curvature) away
from the cone tip. At the cone tip, we observe that spatial curvature increases
the local density of states, and we measure fractional state number excess
consistent with the Wen-Zee theory, providing an experimental test of this
theory of electrons in both a magnetic field and curved space[12-15]. This work
opens the door to exploration of the interplay of geometry and topology, and in
conjunction with Rydberg electromagnetically induced transparency, enables
studies of photonic fractional quantum Hall fluids[16,17] and direct detection
of anyons[18-19].
