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Quantum Electronics and Laser Science Conference

Recovery of classically chaotic behaviour with noise in the quantum kicked rotor

D. Steck, Valery Milner, Windell H. Oskay, Mark G. Raizen

Published Jan 1, 2000• 0 citations
OpenAlex

Abstract

Summary form only given. We use the tools of atom optics to study the effects of noise in a quantum system that is classically chaotic. We prepare cold cesium atoms in a magneto-optic trap, and after the trap is extinguished, they are kicked by a pulsed standing wave of far-detuned light.

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Journal of Physics B Atomic Molecular and Optical Physics•May 28, 1998•12 citations
This thesis presents an account of experimental and numerical investigations of two quantum systems whose respective classical analogues are chaotic. These are the delta-kicked rotor, a paradigm in classical chaos theory, and the novel delta-kicked accelerator, created by application of a constant external acceleration or torque to the rotor. The experimental realisation of these systems has been achieved by the exposure of laser-cooled caesium atoms to approximate delta-kicks from a pulsed, high-intensity, vertical standing wave of laser light. Gravity’s effect on the atoms can be controlled by appropriate shifting of the profile of the standing wave. Numerical simulations of the systems are based on a diffractive model of the potential’s effect. Each system’s dynamics are characterised by the final form of the momentum distribution and the dependence of the atoms’ mean kinetic energy on the number and time period of the delta-kicks. The phenomena of dynamical localisation and quantum resonances in the delta-kicked rotor, which have no counterparts in the system’s classical analogue, are observed and investigated. Similar experiments on the delta-kicked accelerator reveal the striking phenomenon of the quantum accelerator mode, in which a large momentum is transferred to a substantial fraction of the atomic ensemble. This feature, absent in the system’s classical analogue, is characterised and an analytic explanation is presented. The effect on each quantum system of decoherence, introduced through spontaneous emission in the atoms, is examined and comparison is made with the results of classical simulations. While having little effect on the classical systems, the level of decoherence used is found to degrade quantum signatures of behaviour. Classical-like behaviour is, to some extent, restored, although significant quantum features remain. Possible applications of the quantum accelerator mode are discussed. These include use as a tool in atom optics and interferometry, a technique for measuring gravity, and a method of preparing atoms in a particular region of phase space. This may allow measurement of quantum phase space stability, and hence investigation of quantum chaos and quantum-classical correspondence.
Summary form only given. Atom optics has proven to be a fruitful testbed for the experimental study of quantum dynamics in classically chaotic systems. However, the quantum behavior in a mixed classical phase space, where both stable and chaotic regions are present, remains an interesting and challenging subject, with much left to understand. To probe local dynamics in mixed phase space, the atomic sample must be prepared such that it is localized in phase space. To accomplish this, cesium atoms are first prepared in a standard magneto-optic trap. They are then further cooled in a 3-D far-detuned optical lattice. A model system for the study of mixed phase space is realized when the atoms are subjected to an amplitude-modulated standing wave, where the intensity varies as sin/sup 2/ (/spl pi/t/T) (T is the pulse duration). There are three primary resonances in this system; one is at zero momentum, and the other two are located symmetrically about p = 0. As the intensity of the standing wave increases, the resonances overlap, and the resonances appear as islands of stability surrounded by bands of chaos. We have used our method of state preparation to center the atomic distribution at various positions and at the same momentum as one of the "side" resonances. We observe trapping of the atoms in the resonance when the atomic distribution is centered on the island, but not when the atoms are centered away from the resonance, since they instead diffuse through the chaotic region.
We report on the experimental observation of environment induced decoherence in the quantum delta-kicked rotor. Ultracold cesium atoms are subjected to a pulsed standing wave of near resonant light. Spontaneous scattering of photons destroys dynamical localization thereby giving rise to a quantum diffusion, which approaches the classical diffusion with an increasing degree of decoherence. This tendency is enhanced by a stronger stochasticity in the underlying classical system. A comparison with theoretical predictions is presented.