Hamiltonian Chaos with a Cold Atom in an Optical Lattice
From MaRDI portal
Publication:3094383
DOI10.1007/978-3-642-12718-2_4zbMATH Open1223.81114arXiv1205.6087OpenAlexW3027997083MaRDI QIDQ3094383
Author name not available (Why is that?)
Publication date: 24 October 2011
Published in: (Search for Journal in Brave)
Abstract: We consider a basic model of the lossless interaction between a moving two-level atom and a standing-wave single-mode laser field. Classical treatment of the translational atomic motion provides the semiclassical Hamilton-Schrodinger equations which are a 5D nonlinear dynamical system with two integrals of motion. The atomic dynamics can be regular or chaotic in dependence on values of the control parameters, the atom-field detuning and recoil frequency. We develop a semiclassical theory of the chaotic atomic transport in terms of a random walk of the atomic electric dipole moment . Based on a jump-like behavior of this variable for atoms crossing nodes of the standing wave, we construct a stochastic map that specifies the center-of-mass motion. We find the relations between the detuning, recoil frequency and the atomic energy, under which atoms may move in a optical lattice in a chaotic way. We obtain the analytical conditions under which deterministic atomic transport has fractal properties and explain a hierarchical structure of the dynamical fractals. Quantum treatment of the atomic motion in a standing wave is studied in the dressed state picture where the atom moves in two optical potentials simultaneously. If the values of the detuning and a characteristic atomic frequency are of the same order, than there is a probability of nonadiabatic transitions of the atom upon crossing nodes of the standing wave. At the same condition exactly, we observe sudden jumps in the atomic dipole moment when the atom crosses the nodes. Those jumps are accompanied by splitting of atomic wave packets at the nodes. Such a proliferation of wave packets at the nodes of a standing wave is a manifestation of classical atomic chaotic transport. At large values of the detuning, the quantum evolution is shown to be adiabatic in accordance with a regular character of the classical atomic motion.
Full work available at URL: https://arxiv.org/abs/1205.6087
No records found.
This page was built for publication: Hamiltonian Chaos with a Cold Atom in an Optical Lattice
Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q3094383)
