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

Abstract

We show how ultracold (sub-µK temperature) atoms in a one-dimensional periodic optical potential with a harmonic trap can provide a new quantum chaotic system that is accessible to experiment. Provided that the harmonic potential varies slowly over a lattice period, the optical lattice has well defined energy bands. The energy-wavevector dispersion curves define an effective Hamiltonian that can be used to calculate classical orbits for atoms confined 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 affect the collective time-dependent dynamics of interacting atoms in Bose-Einstein condensates.