Atom optics: A new testing ground for quantum chaos

By using the techniques of laser cooling and trapping, the ability to control the momentum and position of atoms with light has improved drastically in the last 10 years. At the low temperatures that can be achieved, the deBroglie wavelength of an atom {dollar}lambdasb{lcub}dB{rcub}{dollar} = h/p becomes significant and the wave nature of the atom needs to be considered. "Atom optics" consists of acting on atoms to obtain effects analogous to what we know for light: reflection, refraction, diffraction, and interference. In general, however, interactions in atom optics need not have optical analogs. Light acting on atoms provides the initial state preparation and the time dependent interaction potentials that are necessary for the work described here.; The study of quantum mechanical systems that exhibit dynamical chaos in their classical limit is called "quantum chaos," and has attracted a great deal of interest in recent years. What is found are sharp deviations from classical physics, which are nonetheless fingerprints of classical chaos in the quantal behavior. The nature of these fingerprints has been explored in the atom optics experiments described here, involving the study of momentum transfer to a sample of ultra-cold sodium atoms by a time dependent standing wave of light.; An experimental realization of the periodically driven rotor is described, where the underlying classical phase space goes from stable to chaotic as the phase modulation of the standing wave is varied. Dynamical localization, the quantum suppression of diffusion in a system that is classically chaotic, is observed. The experimental results are in good absolute agreement with a quantum Floquet analysis and with a quantum simulation.; The first direct experimental realization of the quantum {dollar}delta{dollar}-kicked rotor is also described. A standing wave of light is pulsed. Momentum spread of the atoms increases diffusively with every pulse until the "quantum break time" after which exponentially localized distributions are observed. Quantum resonances are found for specific values of the pulse period.; A third experiment involves momentum transfer to atoms by a single pulse of a standing wave of light. The classical mechanism of resonance overlap is seen, and the results are in good agreement with theoretical predictions.