  We experimentally implement the Harper Hamiltonian for neutral particles in
optical lattices using laser-assisted tunneling and a potential energy gradient
provided by gravity or magnetic field gradients. This Hamiltonian describes the
motion of charged particles in strong magnetic fields. Laser-assisted tunneling
processes are characterized by studying the expansion of the atoms in the
lattice. The band structure of this Hamiltonian should display Hofstadter's
butterfly. For fermions, this scheme should realize the quantum Hall effect and
chiral edge states.
