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arXiv:quant-ph/0503167 · Physical Review A

Phase-space reconstruction of an atomic chaotic system

Hugo L. D. de S. Cavalcante, Carlos R. de Carvalho, Jean Claude Garreau

Published Sep 16, 2005• 3 citations
arXivHTMLPDF

Abstract

We consider the dynamics of a single atom submitted to periodic pulses of a far-detuned standing wave generated by a high-finesse optical cavity, which is an atomic version of the well-known ``kicked rotor.'' We show that the classical phase-space map can be ``reconstructed'' by monitoring the transmission of the cavity. We also studied the effect of spontaneous emission on the reconstruction and put limits to the maximum acceptable spontaneous emission rate.

DOI
10.1103/physreva.72.033814

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We consider the dynamics of a single atom submitted to periodic pulses of a far-detuned standing wave generated by a high-finesse optical cavity, which is an atomic version of the well-known kicked rotor.'' We show that the classical phase-space map can be reconstructed'' by monitoring the transmission of the cavity. We also studied the effect of spontaneous emission on the reconstruction and put limits to the maximum acceptable spontaneous emission rate.
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.
We use an atom interferometer to investigate the dynamics of matter waves in a periodically pulsed optical standing wave: an atom optics realization of the quantum kicked rotor that exhibits chaotic classical dynamics. We experimentally show that a measure of the coherence between the interferometer diffraction orders can revive after a quick initial loss, and can approach a finite asymptote as the number of kicks increases. This observation demonstrates that quantum fidelity of a classically chaotic system can survive strong perturbations over long times without decay.
A new effect of chaotic motion of the center of mass of a cold atom in the coherent field of a standing light wave in a high-finesse Fabry-Pérot cavity is theoretically predicted and numerically implemented in the absence of any random fluctuations due to spontaneous emission. Numerical experiments demonstrate that the Hamiltonian chaos arises near resonance in the range of parameters characteristic of the strong coupling regime that was implemented in recent experiments. The effect is of interest in studying the quantum-classical correspondence and quantum chaos in atomic optics.
We consider continuous observation of the nonlinear dynamics of single atom trapped in an optical cavity by a standing wave with intensity modulation. The motion of the atom changes the phase of the field which is then monitored by homodyne detection of the output field. We show that the conditional Hilbert space dynamics of this system, subject to measurement-induced perturbations, depends strongly on whether the corresponding classical dynamics is regular or chaotic. If the classical dynamics is chaotic, the distribution of conditional Hilbert space vectors corresponding to different observation records tends to be orthogonal. This is a characteristic feature of hypersensitivity to perturbation for quantum chaotic systems.