Abstract
We consider analytically and numerically chaotic walking of cold atoms in a tilted optical lattice created by two counter-propagating running waves with an additional external field in the semiclassical and Hamiltonian approximations. The effect consists in random-like changing the direction of atomic motion in a rigid lattice under the influence of a constant force due to a specific behavior of the atomic dipole-moment component that changes abruptly in a random-like manner while atoms cross standing-wave nodes. Chaotic walking generates a fractal-like scattering of atoms that manifests itself in a self-similar structure of the scattering function in the atom–field detuning in the position and momentum spaces. We show that the probability distribution function of the scattering time decays in a non-exponential way with a power-law tail.
Highlights
The mechanical action of light upon neutral atoms placed in a laser standing wave is at the heart of laser cooling, trapping, and Bose-Einstein condensation [1]
What is the ultimate reason of chaotic walking? For an optical lattice without an external force, it has been found in Ref. [10] that instability is caused by the specific behavior of the Bloch-vector component of a moving atom, u, whose shallow oscillations between the standing-wave nodes are interrupted by sudden jumps with different amplitudes while atom crosses each node of the wave
Different types of fractal-like structures may arise in chaotic Hamiltonian systems. It is known from many studies in celestial mechanics [21], fluid dynamics [22, 23], atomic physics [7, 10, 12, 25], cavity quantum electrodynamics [8, 9], underwater acoustics [24] and other disciplines [26] that under certain conditions the motion inside an interaction region may have features that are typical for dynamical chaos, the particle’s trajectories are not chaotic in a rigorous sense because chaos is defined as an irregular motion over infinite time
Summary
The mechanical action of light upon neutral atoms placed in a laser standing wave is at the heart of laser cooling, trapping, and Bose-Einstein condensation [1]. A single atom in a standing-wave laser field may be semiclassically treated as a nonlinear dynamical system with coupled internal (electronic) and external (mechanical) degrees of freedom [4,5,6].
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