Delocalized and resonant quantum transport in nonlinear generalizations of the kicked rotor model

Rebuzzini, Laura; Wimberger, Sandro; Artuso, Roberto

doi:10.1103/physreve.71.036220

Cited by 18 publications

(14 citation statements)

References 33 publications

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“…On short time scales, however, the perturbation induced by the nonlinearity cannot accumulate a large enough dephasing, because even for the small kick strength k < 0:5 it is at least 1 order of magnitude smaller than the kinetic energy. Our results are consistent with a simplified 1D model analysis of the QR, in the presence of a small nonlinear perturbation [18]. This analysis, however, could not account for the exact nonlinear wave packet evolution including the harmonic confinement.…”

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confidence: 92%

Resonant Nonlinear Quantum Transport for a Periodically Kicked Bose Condensate

et al. 2005

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confidence: 92%

Resonant Nonlinear Quantum Transport for a Periodically Kicked Bose Condensate

et al. 2005

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“…(1), has shown differences on a short time scale, but the same asymptotic behavior in the rotor energy [20]. At the same time, this model allows for more efficient and faster numerical computation.…”

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Interactions destroy dynamical localization with strong and weak chaos

Gligorić

Bodyfelt

Flach

2011

EPL

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-Bose-Einstein condensates loaded into kicked optical lattices can be treated as quantum kicked rotor systems. Noninteracting rotors show dynamical localization in momentum space. The experimentally tunable condensate interaction is included in a qualitative Gross-Pitaevskii type model based on two-body interactions. We observe strong and weak chaos regimes of wave packet spreading in momentum space. In the intermediate strong chaos regime the condensate energy grows as t 1/2 . In the asymptotic weak chaos case the growth crosses over into a t 1/3 law. The results do not depend on the details of the kicking.Introduction. -There is much interest in quantum behavior of systems that are chaotic in the classical limit. The hallmark model used in many such studies is the kicked rotor [1, 2], which was observed to exhibit a parametric transition from integrable dynamical behavior to a fully chaotic one. In physical terms, this corresponds to an unbounded diffusive increase of the rotor energy in the chaotic regime, as opposed to energies bounded by invariant tori in the integrable case. Once quantized, the kicked rotor disrespects the classical chaotic energy increase -a highly interesting phenomenon known as dynamical localization, similar to Anderson localization in disordered tight-binding models [3,4]. Dynamical localization has been observed in laboratory experiments with atoms in microwave fields [5,6], and in ultracold dilute gases condensed within kicked optical lattices [7][8][9]. In particular, the latter realization with a Bose-Einstein condensate, where the magnitude and the sign of the interactions between atoms can be tuned via Feshbach resonance by an additional magnetic field, has greatly opened opportunities to study dynamical systems in the presence of many-body interactions. In the mean-field approximation, these interactions can be modeled by adding a nonlinear cubic term in the Schrödinger equation, giving the well-known Gross-Pitaevskii equation. This can also be extended to the quantum kicked rotor model, result-

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“…However, the mean field energy might be significantly increased using a Feshbach resonance to tune the scattering length, or by tight confinement of the BEC along the direction perpendicular to the optical standing wave. Both dynamical localization and quantum resonances are expected to show the effects of sufficiently strong interactions [19][20][21].…”

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High-Order Quantum Resonances Observed in a Periodically Kicked Bose-Einstein Condensate

et al. 2006

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We have observed high-order quantum resonances in a realization of the quantum delta-kicked rotor, using Bose-condensed Na atoms subjected to a pulsed standing wave of laser light. These resonances occur for pulse intervals that are rational fractions of the Talbot time, and are characterized by ballistic momentum transfer to the atoms. The condensate's narrow momentum distribution not only permits the observation of the quantum resonances at 3/4 and 1/3 of the Talbot time, but also allows us to study scaling laws for the resonance width in quasimomentum and pulse interval.

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Delocalized and resonant quantum transport in nonlinear generalizations of the kicked rotor model

Cited by 18 publications

References 33 publications

Resonant Nonlinear Quantum Transport for a Periodically Kicked Bose Condensate

Resonant Nonlinear Quantum Transport for a Periodically Kicked Bose Condensate

Interactions destroy dynamical localization with strong and weak chaos

High-Order Quantum Resonances Observed in a Periodically Kicked Bose-Einstein Condensate

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