Observation of Dynamical Localization in Atomic Momentum Transfer: A New Testing Ground for Quantum Chaos

Moore, F. L.; Robinson, John C.; Bharucha, C. F.; Williams, P.; Raizen, Mark G.

doi:10.1103/physrevlett.73.2974

Cited by 367 publications

(341 citation statements)

References 13 publications

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“…This proposal was realized shortly after by the Raizen group [29]. Later on the paradigmatic quantum delta-kicked rotor model found an experimental realization with atom optics [30] (see [31] for a more recent discussion of the experimental and theoretical investigations into this model).…”

Section: Introductionmentioning

confidence: 99%

Statistical properties of spectra in harmonically trapped spin–orbit coupled systems

Marchukov¹,

Volosniev²,

Fedorov³

et al. 2014

J. Phys. B: At. Mol. Opt. Phys.

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We compute single-particle energy spectra for a one-body hamiltonian consisting of a twodimensional deformed harmonic oscillator potential, the Rashba spin-orbit coupling and the Zeeman term. To investigate the statistical properties of the obtained spectra as functions of deformation, spin-orbit and Zeeman strengths we examine the distributions of the nearest neighbor spacings. We find that the shapes of these distributions depend strongly on the three potential parameters. We show that the obtained shapes in some cases can be well approximated with the standard Poisson, Brody and Wigner distributions. The Brody and Wigner distributions characterize irregular motion and help identify quantum chaotic systems. We present a special choices of deformation and spin-orbit strengths without the Zeeman term which provide a fair reproduction of the fourth-power repelling Wigner distribution. By adding the Zeeman field we can reproduce a Brody distribution, which is known to describe a transition between the Poisson and linear Wigner distributions.

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Section: Introductionmentioning

confidence: 99%

Statistical properties of spectra in harmonically trapped spin–orbit coupled systems

Marchukov¹,

Volosniev²,

Fedorov³

et al. 2014

J. Phys. B: At. Mol. Opt. Phys.

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“…It is of significant experimental interest in quantum mechanics since it has been implemented in a number of studies [7,8,9,10,12] through the use of cold atom optics, particularly in investigations of multiple-state dynamical tunneling [12]. Theoretically, it provides a convenient framework for studying the avoided crossings of near-integrable systems since for λ → 0 the system is the integrable pendulum Hamiltonian.…”

Section: Introductionmentioning

confidence: 99%

Avoided crossings in driven systems

Holder

Reichl

2005

Phys. Rev. A

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We characterize the avoided crossings in a two-parameter, time-periodic system which has been the basis for a wide variety of experiments. By studying these avoided crossings in the near-integrable regime, we are able to determine scaling laws for the dependence of their characteristic features on the non-integrability parameter. As an application of these results, the influence of avoided crossings on dynamical tunneling is described and applied to the recent realization of multiple-state tunneling in an experimental system.

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“…Recent great advances in atom optics, the manipulation of atomic de Broglie waves, have also made it possible to study quantum dynamics by observing the center-of-mass motion of cold atoms [17,18]. Here, laboratory tests have allowed the direct observation of such phenomena as dynamical localization [19], quantum resonances [20], and chaos-assisted tunneling [21].Of particular interest is dynamical localization [22], a quantum suppression of classically chaotic (diffusive) motion. A prototypical system is the kicked rotor, or standard map, which has been a model system for the study of both classical and quantum chaos.…”

mentioning

confidence: 99%

Timing noise effects on dynamical localization

Oskay

Steck

Raizen

2003

Chaos, Solitons & Fractals

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The quantum kicked rotor is studied experimentally in an atom-optics setting, where we observe the center-of-mass motion of cold cesium atoms. Dynamical localization in this system typically suppresses classical diffusive motion, but is susceptible to the addition of various forms of noise. We study in detail the effects of timing noise, where variations are introduced to the times at which the kicks occur. This noise is particularly interesting because it does not directly induce momentum diffusion. However, it is found that the addition of timing noise efficiently destroys both the classical correlations that give rise to fluctuations in the classical diffusion rate as well as quantum coherences that lead to dynamical localization. Ó 2002 Elsevier Science Ltd. All rights reserved.The interface between quantum and classical dynamics serves as a testing ground for decoherence and is a central feature of mesoscopic physics. It is believed that decoherence, the destruction of quantum interferences, is necessary to reconcile the distinctly different behavior in the quantum and classical limits [1]. Experimental progress towards understanding decoherence has been made on a number of different fronts. One system that has the advantage of conceptual simplicity is a perturbed atom interferometer [2,3], where spontaneous scattering introduces dissipation into the system. Decoherence has also been observed with Rydberg atoms coupled to microwave cavities [4] and motional Schr€ o odinger cat states in an ion trap [5].One of the most interesting settings in which to study correspondence is a classically chaotic system, where quantum effects suppress classical diffusive motion [6]. While the majority of research in decohering effects on ''quantum chaos'' has been theoretical in nature [7][8][9][10][11], there has been a steadily growing body of experimental work in recent years. Some of the pioneering experiments in this field have been conducted by studying the internal dynamics of Rydberg atoms [12][13][14][15]. Mesoscopic condensed-matter systems have provided another important testing ground [16]. Recent great advances in atom optics, the manipulation of atomic de Broglie waves, have also made it possible to study quantum dynamics by observing the center-of-mass motion of cold atoms [17,18]. Here, laboratory tests have allowed the direct observation of such phenomena as dynamical localization [19], quantum resonances [20], and chaos-assisted tunneling [21].Of particular interest is dynamical localization [22], a quantum suppression of classically chaotic (diffusive) motion. A prototypical system is the kicked rotor, or standard map, which has been a model system for the study of both classical and quantum chaos. The kicked rotor is a particularly suitable system for experimental study because it can be directly realized by exposing cold atoms to a pulsed standing wave of light. Classical particles in such a chaotic potential tend to exhibit diffusive behavior, where the energy of the system grows linearly as a f...

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Observation of Dynamical Localization in Atomic Momentum Transfer: A New Testing Ground for Quantum Chaos

Cited by 367 publications

References 13 publications

Statistical properties of spectra in harmonically trapped spin–orbit coupled systems

Statistical properties of spectra in harmonically trapped spin–orbit coupled systems

Avoided crossings in driven systems

Timing noise effects on dynamical localization

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