Fractals and chaotic scattering of atoms in the field of a standing light wave

Argonov, V. Yu.; Prants, S. V.

doi:10.1134/1.1581937

Cited by 38 publications

(7 citation statements)

References 16 publications

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“…New opportunities are opened if one works near the optical resonance where the dynamics of internal atomic states should be taken into account [33][34][35][36]. Different nonlinear dynamical effects have been analytically and numerically found with atoms interacting with a 1D SWF in the semiclassical approximation where atomic translational motion is treated classically: chaotic Rabi oscillations of atomic population [33,[37][38][39][40], Poincaré sections with many features typical for chaotic Hamiltonian systems with a mixed phase space [36,41], chaotic atomic transport and dynamical fractals [42][43][44], Lévy flights and anomalous diffusion [35,41,45]. Hamiltonian evolution is a fully coherent process described in the semiclassical approximation by the Hamilton-Schrödinger equations.…”

Section: Cold Atoms In Optical Latticesmentioning

confidence: 99%

“…The fast (u, v, z) and slow (x, p) variables are now can be separated, and we can integrate exactly the reduced equations of motion. An exact solution for the translational motion has been found in terms of elliptic functions in [33,42] ) is described by equation (7) but with a frequency modulation. It has been shown in [33,42,46] that chaotic atomic transport may occur at comparatively small values of the detunings.…”

Section: Hamiltonian Dynamicsmentioning

confidence: 99%

“…An exact solution for the translational motion has been found in terms of elliptic functions in [33,42] ) is described by equation (7) but with a frequency modulation. It has been shown in [33,42,46] that chaotic atomic transport may occur at comparatively small values of the detunings. The Bloch variable u for atoms moving far from the SWF nodes performs shallow oscillations.…”

Section: Hamiltonian Dynamicsmentioning

confidence: 99%

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Quantum–classical correspondence in chaotic dynamics of laser-driven atoms

Prants

2017

Phys. Scr.

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This paper is a review article on some aspects of quantum–classical correspondence in chaotic dynamics of cold atoms interacting with a standing-wave laser field forming an optical lattice. The problem is treated from both (semi)classical and quantum points of view. In both approaches, the interaction of an atomic electic dipole with the laser field is treated quantum mechanically. Translational motion is described, at first, classically (atoms are considered to be point-like objects) and then quantum mechanically as a propagation of matter waves. Semiclassical equations of motion are shown to be chaotic in the sense of classical dynamical chaos. Point-like atoms in an absolutely deterministic and rigid optical lattice can move in a random-like manner demonstrating a chaotic walking with typical features of classical chaos. This behavior is explained by random-like ‘jumps’ of one of the atomic internal variable when atoms cross nodes of the standing wave and occurs in a specific range of the atom-field detuning. When treating atoms as matter waves, we show that they can make nonadiabatic transitions when crossing the standing-wave nodes. The point is that atomic wave packets split at each node in the same range of the atom-field detuning where the classical chaos occurs. The key point is that the squared amplitude of those semiclassical ‘jumps’ equal to the quantum Landau–Zener parameter which defines the probability of nonadiabatic transitions at the nodes. Nonadiabatic atomic wave packets are much more complicated compared to adiabatic ones and may be called chaotic in this sense. A few possible experiments to observe some manifestations of classical and quantum chaos with cold atoms in horizontal and vertical optical lattices are proposed and discussed.

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Section: Cold Atoms In Optical Latticesmentioning

confidence: 99%

Section: Hamiltonian Dynamicsmentioning

confidence: 99%

Section: Hamiltonian Dynamicsmentioning

confidence: 99%

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Quantum–classical correspondence in chaotic dynamics of laser-driven atoms

Prants

2017

Phys. Scr.

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“…The motion in the phase space takes place on a three-dimensional manifold and may be chaotic in some ranges of the control parameters, the values of the maximal Rabi and atomic recoil frequencies. A number of nonlinear dynamical effects have been analytically and numerically demonstrated with this system: chaotic Rabi oscillations [33,34], Hamiltonian chaotic atomic transport and dynamical fractals [35][36][37], Lévy flights and anomalous diffusion [34,38]. These effects are caused by local instability of the center-of-mass motion in a laser field.…”

Section: Introductionmentioning

confidence: 99%

A group-theoretical approach to study atomic motion in a laser field

Prants¹

2011

J. Phys. A: Math. Theor.

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Group-theoretical approach is applied to study behavior of lossless twolevel atoms in a standing-wave laser field. Due to the recoil effect, the internal and external atomic degrees of freedom become coupled. The internal dynamics is described quantum mechanically in terms of the SU (2) group parameters. The evolution operator is found in an explicit way after solving a single ODE for one of the group parameters. The translational motion in a standing wave is governed by the classical Hamilton equations which are coupled to the SU (2) group equations. It is shown that the full set of equations may be chaotic in some ranges of the control parameters and initial conditions. It means physically that there are regimes of motion with chaotic center-ofmass motion and irregular internal dynamics. It is established that the chaotic regime is specified by the character of oscillations of the group parameter characterizing the mean interaction energy between the atom and the laser field. It is shown that the effect of chaotic walking can be observed in a real experiment with cold atoms crossing a standing-wave laser field.

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“…It has been shown in Refs. [11][12][13] that, when neglecting spontaneous emission (SE), there should exist a deterministic chaotic transport of atoms with exponential sensitivity to small variations in initial conditions and/or lattice parameters. In our recent work [14] we developed a semiclassical theory of this phenomenon resembling a random walking but without any random forces and noise.…”

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confidence: 99%

Nonlinear control of chaotic walking of atoms in an optical lattice

Argonov¹,

Prants²

2007

Europhys. Lett.

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PACS 42.50.Vk -Mechanical effects of light on atoms, molecules, electrons and ions PACS 05.40.Fb -Random walks and Levy flights PACS 05.45.-a -Nonlinear dynamics and nonlinear dynamical systemsAbstract. -Centre-of-mass atomic motion in an optical lattice is shown to be near the resonance a chaotic walking due to the interplay between coherent internal atomic dynamics and spontaneous emission. Statistical properties of chaotic atomic motion can be controlled by the single parameter, the detuning between the atomic transition frequency and the laser frequency. We derive a Fokker-Planck equation in the energetic space to describe the atomic transport near the resonance and demonstrate numerically how to manipulate the atomic motion varying the detuning.

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Fractals and chaotic scattering of atoms in the field of a standing light wave

Cited by 38 publications

References 16 publications

Quantum–classical correspondence in chaotic dynamics of laser-driven atoms

Quantum–classical correspondence in chaotic dynamics of laser-driven atoms

A group-theoretical approach to study atomic motion in a laser field

Nonlinear control of chaotic walking of atoms in an optical lattice

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