Chaotic dynamics of a single two-level atom in the field of a plane standing electromagnetic wave

Gubernov, Vladimir

doi:10.1103/physreva.66.013408

Cited by 2 publications

(2 citation statements)

References 21 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%

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%

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

Prants

2017

Phys. Scr.

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“…The deterministic chaotic transport is a result of chaotic atomic dynamics in the standing-wave field that means an exponential sensitivity of the internal and translational atomic variables to small variations in the lattice parameters and/or initial conditions. The chaotic transport and its manifestations like atomic dynamical fractals may occur both in classical [16,17,18,19] and quantized light fields [20,21]. Spontaneous emission events interrupt the coherent atomic dynamics in random instants of time and may give rise anomalous statistical properties of atomic transport [22].…”

Section: Introductionmentioning

confidence: 99%

Theory of chaotic atomic transport in an optical lattice

Argonov

Prants

2007

Phys. Rev. A

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A semiclassical theory of chaotic atomic transport in a one-dimensional nondissipative optical lattice is developed. Using the basic equations of motion for the Bloch and translational atomic variables, we derive a stochastic map for the synchronized component of the atomic dipole moment that determines the center-of-mass motion. We find the analytical relations between the atomic and lattice parameters under which atoms typically alternate between flying through the lattice and being trapped in the wells of the optical potential. We use the stochastic map to derive formulas for the probability density functions (PDFs) for the flight and trapping events. Statistical properties of chaotic atomic transport strongly depend on the relations between the atomic and lattice parameters. We show that there is a good quantitative agreement between the analytical PDFs and those computed with the stochastic map and the basic equations of motion for different ranges of the parameters. Typical flight and trapping PDFs are shown to be broad distributions with power law "heads" with the slope −1.5 and exponential "tails". The lengths of the power law and exponential parts of the PDFs depend on the values of the parameters and can be varied continuously. We find analytical conditions, under which deterministic atomic transport has fractal properties, and explain a hierarchical structure of the dynamical fractals.

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Chaotic dynamics of a single two-level atom in the field of a plane standing electromagnetic wave

Cited by 2 publications

References 21 publications

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

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

Theory of chaotic atomic transport in an optical lattice

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