Realizing the Harper Hamiltonian with Laser-Assisted Tunneling in Optical Lattices

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.