  We demonstrate the experimental implementation of an optical lattice that
allows for the generation of large homogeneous and tunable artificial magnetic
fields with ultracold atoms. Using laser-assisted tunneling in a tilted optical
potential we engineer spatially dependent complex tunneling amplitudes. Thereby
atoms hopping in the lattice accumulate a phase shift equivalent to the
Aharonov-Bohm phase of charged particles in a magnetic field. We determine the
local distribution of fluxes through the observation of cyclotron orbits of the
atoms on lattice plaquettes, showing that the system is described by the
Hofstadter model. Furthermore, we show that for two atomic spin states with
opposite magnetic moments, our system naturally realizes the time-reversal
symmetric Hamiltonian underlying the quantum spin Hall effect, i.e., two
different spin components experience opposite directions of the magnetic field.
