Quantum chaotic electron transport in superlattices

We introduce semiconductor superlattices as a new type of quantum chaotic system that is accessible to experiment. In contrast to previous physical systems that have been used to study quantum chaos, the classical Hamiltonian for the superlattices has an intrinsically quantum–mechanical origin. For low electric fields, superlattices have well-defined minibands which originate from the quantum–mechanical coupling of electron states in a periodic array of potential wells. The energy-wave-vector dispersion curves define an effective Hamiltonian that can be used to calculate semiclassical orbits for electrons confined to a single miniband. We show that applying a tilted magnetic field induces a controllable transition from stable regular motion to strong classical chaos. The onset of chaos delocalizes both the classical orbits and the corresponding quantum wave functions, and is therefore expected to produce a sharp increase in the current flow measured in electron transport experiments. We show that magnetically confined atoms in a periodic optical potential exhibit similar chaotic dynamics at ultra-low (μK) temperatures.