Chaotic motion of atom in the coherent field of a standing light wave

Prants, S. V.; Kon’kov, L. E.

doi:10.1134/1.1368710

Cited by 30 publications

(41 citation statements)

References 11 publications

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“…The detuning δ, as it was shown in [39,40], is the crucial parameter in transition to chaos in the atom-field system with the center-of-mass motion. It is obvious from the set (8), which is equivalent to the basic one (3), that at exact resonance, δ = 0, the motion is regular.…”

Section: Sectionsmentioning

confidence: 86%

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Chaos and flights in the atom-photon interaction in cavity QED

2002

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We study dynamics of the atom-photon interaction in cavity quantum electrodynamics (QED), considering a cold two-level atom in a single-mode high-finesse standing-wave cavity as a nonlinearHamiltonian system with three coupled degrees of freedom: translational, internal atomic, and the field. The system proves to have different types of motion including Lévy flights and chaotic walkings of an atom in a cavity. It is shown that the translational motion, related to the atom recoils, is governed by an equation of a parametric nonlinear pendulum with a frequency modulated by the Rabi oscillations. This type of dynamics is chaotic with some width of the stochastic layer that is estimated analytically. The width is fairly small for realistic values of the control parameters, the normalized detuning δ and atomic recoil frequency α. It is demonstrated how the atom-photon dynamics with a given value of α depends on the values of δ and initial conditions. Two types of Lévy flights, one corresponding to the ballistic motion of the atom and another one corresponding to small oscillations in a potential well, are found. These flights influence statistical properties of the atom-photon interaction such as distribution of Poincaré recurrences and moments of the atom position x. The simulation shows different regimes of motion, from slightly abnormal diffusion with < x 2 >∼ τ 1.13 at δ = 1.2 to a superdiffusion with < x 2 >∼ τ 2.2 at δ = 1.92 that corresponds to a superballistic motion of the atom with an acceleration. The obtained results can be used to find new ways to manipulate atoms, to cool and trap them by adjusting the detuning δ.

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Section: Sectionsmentioning

confidence: 86%

“…Generally speaking, the atom-photon interaction in a high-finesse cavity is, mainly, the interaction between internal (electronic) and external (motional) atomic degrees of freedom and the cavity field. A corresponding one-dimensional model, including the interaction of all those degrees of freedom, has been introduced in papers [39,40] …”

Section: Introductionmentioning

confidence: 99%

Chaos and flights in the atom-photon interaction in cavity QED

2002

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“…The detuning ∆ will be varied in a wide range, and the Bloch variables are restricted by the length of the Bloch vector (7). It should be noted that we use in this paper the normalization to the laser Rabi frequency Ω, not to the vacuum (or single-photon) Rabi frequency as it has been done in our previous papers [14,15,16,17]. So the ranges of the normalized control parameters, taken in this paper, differ from those in the cited papers.…”

Section: Hamilton-schrödinger Equations Of Motionmentioning

confidence: 99%

“…It has been predicted in Refs. [14,15] that, besides the well-known transport properties of atoms in optical lattices, there should exist a deterministic chaotic transport with a complicated alternation of atomic oscillations in wells of the optical potential and atomic flights over many potential wells when the atom may change the direction of motion many times. This phenomenon looks like a random walk but it should be stressed that it may occur without any random fluctuations of the lattice parameters and any noise like spontaneous emission.…”

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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“…In the simplest case of a two-level atom interacting with a single mode of an one-dimensional standing wave in a cavity, there are, at least, three strongly coupled subsystems: internal and external atomic degrees of freedom and field degrees of freedom. Recently, it has been shown theoretically and numerically that Hamiltonian dynamics of a single atom in a standing light wave demonstrates a variety of new dynamical effects such as correlations between Rabi oscillations and atomic translational motion [6,7], the Doppler-Rabi resonance [7,8], Hamiltonian chaos [9,10], Lévy flights [7,11,12], and atomic dynamical fractals [7,12,13]. The semiclassical and quantum theory of these effects has been developed in the cited papers.…”

Section: Introductionmentioning

confidence: 99%

Synchronization of internal and external degrees of freedom of atoms in a standing laser wave

Argonov

Prants

2005

Phys. Rev. A

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We consider dissipative dynamics of atoms in a strong standing laser wave and find a nonlinear dynamical effect of synchronization between center-of-mass motion and internal Rabi oscillations. The synchronization manifests itself in the phase space as limit cycles which may have different periods and riddled basins of attraction. The effect can be detected in the fluorescence spectra of atoms as equidistant sideband frequencies with the space between adjacent peaks to be inversely proportional to the value of the period of the respective limit cycle. With increasing the intensity of the laser field, we observe numerically cascades of bifurcations that eventually end up in settling a strange chaotic attractor. A broadband noise is shown to destroy a fine structure of the bifurcation scenario, but prominent features of period-1 and period-3 limit cycles survive under a weak noise. The character of the atomic motion is analyzed with the help of the friction force whose zeroes are attractor or repellor points in the velocity space. We find ranges of the laser parameters where the atomic motion resembles a random but deterministic walking of atoms erratically jumping between different wells of the optical potential. Such a random walking is shown to be fractal in the sense that the measured characteristic of the motion, time of exit of atoms from a given space of the standing wave, is a complicated function that has a self-similar structure with singularities on a Cantor set of values of one of the control parameters.

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Chaotic motion of atom in the coherent field of a standing light wave

Cited by 30 publications

References 11 publications

Chaos and flights in the atom-photon interaction in cavity QED

Chaos and flights in the atom-photon interaction in cavity QED

Theory of chaotic atomic transport in an optical lattice

Synchronization of internal and external degrees of freedom of atoms in a standing laser wave

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