Quantum chaos for cold atoms in an optical lattice with a tilted harmonic trap

We show how ultracold (sub-muK temperature) atoms in a one-dimensional peri odic optical potential with a harmonic trap can provide a new quantum chaot ic system that is accessible to experiment. Provided that the harmonic pote ntial varies slowly over a lattice period, the optical lattice has well def ined energy bands. The energy-wavevector dispersion curves define an effect ive Hamiltonian that can be used to calculate classical orbits for atoms co nfined to a single band. We show that tilting the harmonic trap relative to the optical lattice induces a controllable transition from stable regular motion to classical chaos. The onset of chaos strongly delocalizes the atom orbits and should be manifest in both the classical and quantum properties of the trapped atoms. We also consider how the transition to chaos might a ffect the collective time-dependent dynamics of interacting atoms in Bose-E instein condensates.