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arXiv:physics/0512159 · The European Physical Journal D

A nonadiabatic semi-classical method for dynamics of atoms in optical lattices

S. Jonsell, Claude M. Dion, Mats Nylén, S.J.H. Petra, Peder Sjölund, Anders Kastberg

Published Apr 10, 2006• 9 citations
arXivHTMLPDF
DOI
10.1140/epjd/e2006-00082-6

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Abstract 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.
This thesis gives an account of work done on semi-classical and quantum Monte Carlo simulations in far-detuned optical lattices. Firstly, the basic principles of laser cooling of atoms are presented including a short introduction to optical lattices in the near and far-detuned regime. A detailed analysis is made of the band-structure of optical lattices, using the Bloch formalism, and of the bound-state population distribution appropriate for a thermal sample of trapped atoms. Secondly, a general overview is given of the quantum Monte Carlo method for simulating the dynamics of atom-light interactions. This is followed by a detailed study of the concept of Raman cooling, which is a useful tool to prepare atoms in the ground motional state of the lattice and an important first step to achieving quantum state control with ultra-cold atoms. A simplified model of Raman cooling is introduced and simulated using the quantum Monte Carlo wave-function approach. Then the implementation of simulations of resolved-sideband Raman cooling based on this model is discussed as is how the results were used to optimize the experimental work done by our group. The results of these simulations show for the first time that the quantum Zeno effect has a crucial impact on the efficiency of Raman cooling experiments. Also the experimental measurements of the temperature of Raman sideband cooled atoms for a range of parameters are compared with theoretical results and shows a good qualitative agreement. Thirdly, the results of semi-classical numerical simulations of parametric excitation in optical lattices are presented. It is shown that the modulation of the potential can result in selective parametric excitation of trapped atoms. The theoretical results show good qualitative agreement with experiment. The thesis is concluded with a description of possible avenues for future studies on quantum state control in optical lattices.