Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0704.1382 · Physical Review A

Effects of atomic interactions on quantum accelerator modes

Laura Rebuzzini, Roberto Artuso, Shmuel Fishman, Italo Guarneri

Published Sep 26, 2007• 20 citations
arXivHTMLPDF

Abstract

We consider the influence of the inclusion of interatomic interactions on the $\ensuremath{\delta}$-kicked accelerator model. Our analysis concerns in particular quantum accelerator modes, namely quantum ballistic transport near quantal resonances. The atomic interaction is modeled by a Gross-Pitaevskii cubic nonlinearity, and we address both attractive (focusing) and repulsive (defocusing) cases. The most remarkable effect is enhancement or damping of the accelerator modes, depending on the sign of the nonlinear parameter. We provide arguments showing that the effect persists beyond mean-field description, and lies within the experimentally accessible parameter range.

DOI
10.1103/physreva.76.031603

Related papers

Theoretical aspects of Quantum Accelerator Modes.

Laura Rebuzzini

This thesis is devoted to the study of some theoretical aspects of the problem of Quantum Accelerator Modes (QAMs), which has received considerable interest in recent years both by experimentalists and theorists in the fields of Quantum Chaos, Quantum Optics and cold-ultracold atomic physics.\nQAMs, recently observed in cold atom optics, are formed by exposing cold alkali atoms to periodic kicks in the direction of the gravitational field. The kicks are generated by a pulsed standing wave of light. A QAM is characterized by a momentum transfer, which increases linearly with the number of pulses, to a substantial fraction of the atoms. QAMs arise for values of the pulse period close to a integer multiple of half of a characteristic time TB (the Talbot time), typical of the kind of atoms used.\nA detailed theoretical explanation of this quantum effect is presented. The system can be modelled by a variant of the well-known quantum Kicked Rotator, in which the effects of a static force, produced by the earth gravitational field, are taken into account. A pseudo-classical theory has been formulated, in which the role of Planck constant is played by the detuning of the kicking period from the resonant value: in the asymptotic limit for a vanishing detuning, QAMs are described by the stable periodic orbit of a “formally” classical map on the 2-torus. An analysis of parametric dependence of the map is performed perturbatively; the parameter regions where the motion is stable and periodic exhibit Arnol’d tongues-like structures. The ordering of Arnol’d tongues and hence the classification of experimentally observed accelerator modes is provided by a number-theoretic construction known as the Farey Tree.\nQuantum decay of the modes from classical stable islands immersed in a chaotic sea is analysed and its relations to the famous Wannier-Stark problem are investigated. Theoretical estimates for the lifetimes of the metastable states as a function of the effective Planck constant are obtained.\nQAM dynamics in a Bose-Einstein condensate is then considered. Modifications on transport phenomena, imposed by nonlinearities of Gross-Pitaevskii type, which describe the atomic interactions in a mean-field approach, are examined by computer-assisted analysis.\nFinally, the problem of QAMs in the vicinity of a generic quantum resonance, namely for kicking period sufficiently close to any rational multiple of the Talbot time, is studied.\nThe theoretical framework is nontrivially generalized in terms of spinor dynamics: an ansatz of the Born-Oppenheimer type allows to decouple the dynamics of spinor and orbital degrees of freedom and a description of the orbital motion by means of “formally” classical equations is achieved. New rich families of experimental observable QAMs are predicted.

•Jan 1, 2008•0 citations

Nonlinearity effects in the kicked oscillator

Roberto Artuso, Laura Rebuzzini

The quantum kicked oscillator is known to display a remarkable richness of dynamical behavior, from ballistic spreading to dynamical localization. Here we investigate the effects of a Gross-Pitaevskii nonlinearity on quantum motion, and provide evidence that the qualitative features depend strongly on the parameters of the system.

arXiv:nlin/0203020•Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Jul 19, 2002•12 citations

Nonlinear tunneling in two-dimensional lattices

Valeriy A. Brazhnyi, V. V. Konotop, Vladimír Kuzmiak +1 more

We present a thorough analysis of the nonlinear tunneling of Bose-Einstein condensates in static and accelerating two-dimensional lattices within the framework of the mean-field approximation. We deal with nonseparable lattices, considering different initial atomic distributions in highly symmetric states. For an analytical description of the condensate before instabilities develop, we derive several few-mode models, analyzing essentially both nonlinear and quasilinear regimes of tunneling. By direct numerical simulations, we show that two-mode models provide an accurate description of tunneling when either initially two states are populated or tunneling occurs between two stable states. Otherwise, a two-mode model may give only useful qualitative hints for understanding tunneling, but does not reproduce many features of the phenomenon. This reflects the crucial role of instabilities developed due to two-body interactions resulting in a non-negligible population of the higher bands. This effect becomes even more pronounced in the case of accelerating lattices. In the latter case we show that the direction of the acceleration is a relevant physical parameter which affects the tunneling by changing the atomic rates at different symmetric states and by changing the numbers of bands involved in the atomic transfer.

arXiv:0709.3900•Physical Review A•Aug 20, 2007•9 citations

Quantum Accelerator Modes Near Higher-Order Resonances

Italo Guarneri, Laura Rebuzzini

Quantum accelerator modes have been experimentally observed, and theoretically explained, in the dynamics of kicked cold atoms in the presence of gravity, when the kicking period is close to a half-integer multiple of the Talbot time. We generalize the theory to the case when the kicking period is sufficiently close to any rational multiple of the Talbot time, and thus predict new rich families of experimentally observable quantum accelerator modes.

arXiv:0805.2040•Physical Review Letters•Jun 13, 2008•11 citations

Exact Nonlinear Dynamics in Spinor Bose-Einstein Condensates

Jun’ichi Ieda, Miki Wadati

Bose–Einstein Condensation (BEC) of atomic gases has attracted a renewed theoretical and experimental interest in quantum many-body systems at extremely low temperatures (Pethick & Smith; 2002). This excitement stems from two favorable features: (1) by applying magnetic fields and lasers, most of the system parameters, such as the shape, dimensionality, internal states of the condensates, and even the strength of the interatomic interactions, are controllable; (2) due to the diluteness, the mean-field theory explains experiments quite well. In particular, the Gross–Pitaevskii (GP) equation demonstrates its validity as a basic equation for the condensate dynamics. The GP equation is the counterpart of the nonlinear Schrodinger (NLS) equation in nonlinear optics. Thus, a study based on nonlinear analysis is possible and important. In nonlinear physics, a soliton is remarkable object not only for the fact that exact solutions can be obtained but also for its usefulness as a communications tool due to its robustness. In general, solitons are formed under the balance between nonlinearity and dispersion. For atomic condensates, the former is attributed to the interatomic interactions, while the latter comes from the kinetic energy. Either dark or bright solitons are allowable depending on the positive or negative sign of the interatomic coupling constants g, respectively, and indeed have been observed in a quasione-dimensional (q1D) optically constructed waveguide (Strecker et al.; 2002) (Khaykovich et al.; 2002). Such matter-wave solitons are expected in atom optics for applications in atom laser, atom interferometry, and coherent atom transport (Meystre; 2002). In this chapter, we extend the analysis of the matter-wave solitons to a multicomponent case by considering the so-called spinor condensate (Stenger et al.; 1998) whose spin degrees of freedom are liberated under optical traps. Based on theoretical and experimental results, we introduce a new integrable model which describes the dynamical properties of the matter-wave soliton of spinor condensates (Ieda et al.; 2004a). We employ the inverse scattering method to solve this model exactly. As a result, we predict the occurrence of undiscovered physical phenomena such as macroscopic spin precession and spin switching. The chapter is organized as follows. In Sec. 2, the mean field theory of condensate is briefly reviewed. Section 3 introduces an effective interatomic coupling in a q1D condensate. Using these results, we consider a spinor condensate in q1D regime in Sec. 4. Then, in Sec. 5, we

InTech eBooks•Jan 1, 2010•1 citation

Impact of Three-Body Interactions and Nonlinear Dispersion on the Dynamics of Bose-Einstein Condensates with Time-Dependent Scattering Length in a Harmonic Potential

Emmanuel Kengne, Ahmed Lakhssassi

A one-dimensional (1D) Gross-Pitaevskii (GP) equation which governs the dynamics of Bose-Einstein condensates (BECs) with time-dependent scattering length in a harmonic potential is considered. Through a modified phase imprint transformation into the macroscopic order parameter, we suitably generate a derivative cubic-quintic Gross-Pitaevskii (DCQ-GP) equation that describes the dynamics of condensates in the harmonic potential for both twoand three-body interatomic interactions in the presence of nonlinear dispersion. Employing a modified lens-type transformation, we reduce the DCQ-GP equation into a derivative cubic-quintic Ginzburg-Landau (DCQ-GL) equation that allows us to investigate the modulational instability (MI) of the system and study, through the analytical exact solutions of the considered 1D GP equation, the effects of the three-body interactions and nonlinear dispersion on the dynamics of the BECs. We observe that for BECs with repulsive two-body interatomic interactions, the attractive three-body interactions and the nonlinear dispersion have opposite effects on the condensate: (i) The attractive three-body interactions enhance the instability, while the nonlinear dispersion softens the instability of the system; (ii) the attractive three-body interactions contributes to the ejections of atoms from the condensates while the nonlinear dispersion contributes to the accumulation of atoms in the condensates; (iii) the attractive three-body interactions contributes to the broadening of the matter wave solitons, while the nonlinear dispersion contributes to the compression of the matter wave solitons.

Chinese Journal of Physics•Feb 1, 2015•4 citations
We consider the influence of the inclusion of interatomic interactions on the \ensuremathδ\ensuremath{\delta}\ensuremathδ-kicked accelerator model. Our analysis concerns in particular quantum accelerator modes, namely quantum ballistic transport near quantal resonances. The atomic interaction is modeled by a Gross-Pitaevskii cubic nonlinearity, and we address both attractive (focusing) and repulsive (defocusing) cases. The most remarkable effect is enhancement or damping of the accelerator modes, depending on the sign of the nonlinear parameter. We provide arguments showing that the effect persists beyond mean-field description, and lies within the experimentally accessible parameter range.
This thesis is devoted to the study of some theoretical aspects of the problem of Quantum Accelerator Modes (QAMs), which has received considerable interest in recent years both by experimentalists and theorists in the fields of Quantum Chaos, Quantum Optics and cold-ultracold atomic physics.\nQAMs, recently observed in cold atom optics, are formed by exposing cold alkali atoms to periodic kicks in the direction of the gravitational field. The kicks are generated by a pulsed standing wave of light. A QAM is characterized by a momentum transfer, which increases linearly with the number of pulses, to a substantial fraction of the atoms. QAMs arise for values of the pulse period close to a integer multiple of half of a characteristic time TB (the Talbot time), typical of the kind of atoms used.\nA detailed theoretical explanation of this quantum effect is presented. The system can be modelled by a variant of the well-known quantum Kicked Rotator, in which the effects of a static force, produced by the earth gravitational field, are taken into account. A pseudo-classical theory has been formulated, in which the role of Planck constant is played by the detuning of the kicking period from the resonant value: in the asymptotic limit for a vanishing detuning, QAMs are described by the stable periodic orbit of a “formally” classical map on the 2-torus. An analysis of parametric dependence of the map is performed perturbatively; the parameter regions where the motion is stable and periodic exhibit Arnol’d tongues-like structures. The ordering of Arnol’d tongues and hence the classification of experimentally observed accelerator modes is provided by a number-theoretic construction known as the Farey Tree.\nQuantum decay of the modes from classical stable islands immersed in a chaotic sea is analysed and its relations to the famous Wannier-Stark problem are investigated. Theoretical estimates for the lifetimes of the metastable states as a function of the effective Planck constant are obtained.\nQAM dynamics in a Bose-Einstein condensate is then considered. Modifications on transport phenomena, imposed by nonlinearities of Gross-Pitaevskii type, which describe the atomic interactions in a mean-field approach, are examined by computer-assisted analysis.\nFinally, the problem of QAMs in the vicinity of a generic quantum resonance, namely for kicking period sufficiently close to any rational multiple of the Talbot time, is studied.\nThe theoretical framework is nontrivially generalized in terms of spinor dynamics: an ansatz of the Born-Oppenheimer type allows to decouple the dynamics of spinor and orbital degrees of freedom and a description of the orbital motion by means of “formally” classical equations is achieved. New rich families of experimental observable QAMs are predicted.
We present a thorough analysis of the nonlinear tunneling of Bose-Einstein condensates in static and accelerating two-dimensional lattices within the framework of the mean-field approximation. We deal with nonseparable lattices, considering different initial atomic distributions in highly symmetric states. For an analytical description of the condensate before instabilities develop, we derive several few-mode models, analyzing essentially both nonlinear and quasilinear regimes of tunneling. By direct numerical simulations, we show that two-mode models provide an accurate description of tunneling when either initially two states are populated or tunneling occurs between two stable states. Otherwise, a two-mode model may give only useful qualitative hints for understanding tunneling, but does not reproduce many features of the phenomenon. This reflects the crucial role of instabilities developed due to two-body interactions resulting in a non-negligible population of the higher bands. This effect becomes even more pronounced in the case of accelerating lattices. In the latter case we show that the direction of the acceleration is a relevant physical parameter which affects the tunneling by changing the atomic rates at different symmetric states and by changing the numbers of bands involved in the atomic transfer.
Bose–Einstein Condensation (BEC) of atomic gases has attracted a renewed theoretical and experimental interest in quantum many-body systems at extremely low temperatures (Pethick & Smith; 2002). This excitement stems from two favorable features: (1) by applying magnetic fields and lasers, most of the system parameters, such as the shape, dimensionality, internal states of the condensates, and even the strength of the interatomic interactions, are controllable; (2) due to the diluteness, the mean-field theory explains experiments quite well. In particular, the Gross–Pitaevskii (GP) equation demonstrates its validity as a basic equation for the condensate dynamics. The GP equation is the counterpart of the nonlinear Schrodinger (NLS) equation in nonlinear optics. Thus, a study based on nonlinear analysis is possible and important. In nonlinear physics, a soliton is remarkable object not only for the fact that exact solutions can be obtained but also for its usefulness as a communications tool due to its robustness. In general, solitons are formed under the balance between nonlinearity and dispersion. For atomic condensates, the former is attributed to the interatomic interactions, while the latter comes from the kinetic energy. Either dark or bright solitons are allowable depending on the positive or negative sign of the interatomic coupling constants g, respectively, and indeed have been observed in a quasione-dimensional (q1D) optically constructed waveguide (Strecker et al.; 2002) (Khaykovich et al.; 2002). Such matter-wave solitons are expected in atom optics for applications in atom laser, atom interferometry, and coherent atom transport (Meystre; 2002). In this chapter, we extend the analysis of the matter-wave solitons to a multicomponent case by considering the so-called spinor condensate (Stenger et al.; 1998) whose spin degrees of freedom are liberated under optical traps. Based on theoretical and experimental results, we introduce a new integrable model which describes the dynamical properties of the matter-wave soliton of spinor condensates (Ieda et al.; 2004a). We employ the inverse scattering method to solve this model exactly. As a result, we predict the occurrence of undiscovered physical phenomena such as macroscopic spin precession and spin switching. The chapter is organized as follows. In Sec. 2, the mean field theory of condensate is briefly reviewed. Section 3 introduces an effective interatomic coupling in a q1D condensate. Using these results, we consider a spinor condensate in q1D regime in Sec. 4. Then, in Sec. 5, we
A one-dimensional (1D) Gross-Pitaevskii (GP) equation which governs the dynamics of Bose-Einstein condensates (BECs) with time-dependent scattering length in a harmonic potential is considered. Through a modified phase imprint transformation into the macroscopic order parameter, we suitably generate a derivative cubic-quintic Gross-Pitaevskii (DCQ-GP) equation that describes the dynamics of condensates in the harmonic potential for both twoand three-body interatomic interactions in the presence of nonlinear dispersion. Employing a modified lens-type transformation, we reduce the DCQ-GP equation into a derivative cubic-quintic Ginzburg-Landau (DCQ-GL) equation that allows us to investigate the modulational instability (MI) of the system and study, through the analytical exact solutions of the considered 1D GP equation, the effects of the three-body interactions and nonlinear dispersion on the dynamics of the BECs. We observe that for BECs with repulsive two-body interatomic interactions, the attractive three-body interactions and the nonlinear dispersion have opposite effects on the condensate: (i) The attractive three-body interactions enhance the instability, while the nonlinear dispersion softens the instability of the system; (ii) the attractive three-body interactions contributes to the ejections of atoms from the condensates while the nonlinear dispersion contributes to the accumulation of atoms in the condensates; (iii) the attractive three-body interactions contributes to the broadening of the matter wave solitons, while the nonlinear dispersion contributes to the compression of the matter wave solitons.