Atom Optics Realization of the Quantum<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>δ</mml:mi></mml:math>-Kicked Rotor

Moore, F. L.; Robinson, John C.; Bharucha, C. F.; Sundaram, Bala; Raizen, Mark G.

doi:10.1103/physrevlett.75.4598

Cited by 588 publications

(669 citation statements)

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“…For the AOKR experiments [7,8], with an initially Gaussian momentum distribution with root mean square > 1, the distribution of quasimomenta f 0 (β) is nearly uniform [10]. Since β is a constant of motion, the fidelity is…”

Section: Analytical Results and Discussionmentioning

confidence: 99%

“…Specifically, we derive an analytic expression for the fidelity at the fundamental quantum resonances of the KR. At these resonances, a subclass of the experimental atomic ensemble [7,8,9] experiences an enhanced acceleration by the kicking field, at precisely defined kicking periods [5]. We show that this resonantly driven subclass induces a slow algebraic decay of fidelity, whilst the bulk of the initial atomic ensemble produces the novel phenomenon of a perfect saturation of fidelity at a finite and experimentally easily detectable level.…”

Section: Introductionmentioning

confidence: 93%

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Saturation of fidelity in the atom-optics kicked rotor

Wimberger

Buchleitner

2006

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

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Abstract.We show that the quantum fidelity is accessible to cold atom experiments for a large class of evolutions in periodical potentials, properly taking into account the experimental initial conditions of the atomic ensemble. We prove analytically that, at the fundamental quantum resonances of the Atom-Optics Kicked Rotor, the fidelity saturates at a constant, time-independent value after a small number of kicks. The latter saturation arises from the bulk of the atomic ensemble, whilst for the resonantly accelerated atoms the fidelity is predicted to decay slowly according to a power law.

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Section: Analytical Results and Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 93%

Saturation of fidelity in the atom-optics kicked rotor

Wimberger

Buchleitner

2006

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

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“…In addition, it suggests a new type of quantum motion in the QKR, evidencing again the dynamics wealth of this paradigmatic quantum chaos model. As various QKR systems have been realized with atom-optics setup [8,9], our result also suggests a possible way to experimental studies of the superballistic spreading.…”

Section: Introductionmentioning

confidence: 90%

Superballistic wavepacket spreading in double kicked rotors

Fang

Wang

2016

Sci. China Phys. Mech. Astron.

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We investigate possible ways in which a quantum wavepacket spreads. We show that in a general class of double kicked rotor system, a wavepacket may undergo superballistic spreading; i.e., its variance increases as the cubic of time. The conditions for the observed superballistic spreading and two related characteristic time scales are studied. Our results suggest that the symmetry of the studied model and whether it is a Kolmogorov-Arnold-Moser system are crucial to its wavepacket spreading behavior. Our study also sheds new light on the exponential wavepacket spreading phenomenon previously observed in the double kicked rotor system.

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“…In this section the decay of correlations in time will be studied for the kicked rotor, defined by the Hamiltonian (6), and its dynamics is given by the standard map (8) [1,3,7]. The phase space is presented in Fig.…”

Section: The Frobenius-perron Operator For the Kicked Rotormentioning

confidence: 99%

“…1. A variant of this map provides a good description of driven laser cooled atoms [8] and of beams deflected by dielectrics with a modulated index of refraction [9]. b.…”

Section: Introductionmentioning

confidence: 99%

Relaxation and Noise in Chaotic Systems

Fishman

Rahav

2002

Dynamics of Dissipation

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For a class of idealized chaotic systems (hyperbolic systems) correlations decay exponentially in time. This result is asymptotic and rigorous. The decay rate is related to the Ruelle-Pollicott resonances. Nearly all chaotic model systems, that are studied by physicists, are not hyperbolic. For many such systems it is known that exponential decay takes place for a long time. It may not be asymptotic, but it may persist for a very long time, longer than any time of experimental relevance. In this review a heuristic method for calculation of this exponential decay of correlations in time is presented. It can be applied to model systems, where there are no rigorous results concerning this exponential decay. It was tested for several realistic systems (kicked rotor and kicked top) in addition to idealized systems (baker map and perturbed cat map). The method consists of truncation of the evolution operator (Frobenius-Perron operator), and performing all calculations with the resulting finite dimensional matrix. This finite dimensional approximation can be considered as coarse graining, and is equivalent to the effect of noise. The exponential decay rate of the chaotic system is obtained when the dimensionality of the approximate evolution operator is taken to infinity, resulting in infinitely fine resolution, that is equivalent to vanishing noise. The corresponding Ruelle-Pollicott resonances can be calculated for many systems that are beyond the validity of the Ruelle-Pollicott theorem.

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Atom Optics Realization of the Quantumδ-Kicked Rotor

Cited by 588 publications

References 10 publications

Saturation of fidelity in the atom-optics kicked rotor

Saturation of fidelity in the atom-optics kicked rotor

Superballistic wavepacket spreading in double kicked rotors

Relaxation and Noise in Chaotic Systems

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