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

Abstract

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.

New developments in classical chaotic scattering

“…A cold atom in an optical lattice can be trapped in the potential wells and it can move over many wavelengths in dependence on whether its energy is below or above the potential barrier. Some of these problems have been studied in [82][83][84][85][86][87][88].…”

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

“…The dissipative force does not exist in the Hamiltonian system (5). Its action depends on the atomic momentum and the sign of detuning [16,59]. The dissipative force may cause acceleration, deceleration and velocity grouping of atoms [16].…”

Scaling Laws in the Transient Dynamics of Firefly-like Oscillators

“…However, the scope of synchronous behaviours runs far beyond neural dynamics [3,4]. Synchronisation exhibits itself in physical [5], chemical [6], biological [7] and electronic [8] systems. Furthermore, phenomena involving synchronisation in complex networks [9,10], chaotic systems [11] or time-delayed systems [12], have been intensively studied in recent years.…”