Bloch-Zener oscillations of atoms inside an optical cavity

Cold atoms in an optical lattice execute Bloch-Zener oscillations when they are accelerated. We investigate the corresponding behavior of the atoms and the light when the optical lattice is provided by the intra-cavity field of a driven Fabry-Perot resonator. When the atoms oscillate inside the resonator, we find that their back-action modulates the phase and intensity of the light transmitted through the cavity. We solve the coupled atom-light equations self-consistently and show that, remarkably, the Bloch period is unaffected by this back-action. The transmitted light provides a way to observe the atomic oscillation continuously, allowing very high precision measurements to be derived from a single cloud of atoms.