Classical and Quantum Dynamics of 2D Optical Lattices

Date

2014

Authors

Horsley, Eric

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Abstract

Here we present the work and results of studies on a two-dimensional optical lattice. The initial work on the classical dynamics describes the onset of chaos using action-angle variables and techniques developed by Walker and Ford \cite{Walker}. Having documented the classical transition to chaos, using a technique called the discrete variable representation, we calculate the eigenvalues and eigenvectors of the two-dimensional optical lattice Hamiltonian operator. The surprising fidelity of these numerical results to the true values (which can be verified for a certain parameter value) will hopefully allow for the future study of level repulsion and the development of quantum phase space distributions (e.g. the Wigner and Husimi quasi-probability distributions).

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