  We theoretically study the driven-dissipative Harper-Hofstadter model on a 2D
square lattice in the presence of a weak harmonic trap. Without pumping and
loss, the eigenstates of this system can be understood, in certain limits, as
momentum-space toroidal Landau levels, where the Berry curvature, a geometrical
property of an energy band, acts like a momentum-space magnetic field. We show
that key features of these eigenstates can be observed in the steady-state of
the driven-dissipative system under a monochromatic coherent drive, and present
a realistic proposal for an optical experiment using state-of-the-art coupled
cavity arrays. We discuss how such spectroscopic measurements may be used to
probe effects associated both with the off-diagonal elements of the
matrix-valued Berry connection and with the synthetic magnetic gauge.
