Observation of the Wannier-Stark fan and the fractional ladder in an accelerating optical lattice

We report an experimental study of the Wannier-Stark fan and the fractional Wannier-Stark ladder using laser-cooled sodium atoms in an accelerating one-dimensional standing wave of light. We prepare the atoms in the lowest motional band of the optical lattice and then impose a constant acceleration. A weak oscillatory component is added to the acceleration in order to resonantly drive interband transitions, and the number of atoms that remain in the lowest band is measured as a function of the probe frequency. The spectrum is characterized by a ladder of resonances spaced by the atomic Bloch oscillation frequency ${\omega }_B.$ When an additional, strong ac component at frequency $\Omega$ is added, a fractional ladder is observed with a spacing related to the electric matching ratio $\Omega /{\omega }_B.$