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Max Prichard

Max Prichard




University of California, Santa Barbara


Peter Dotti

Faculty Sponsor(s): 

David Weld

Faculty Sponsor's Department(s): 


Project Title: 

Analytic Calculation of Wannier Functions and Bose-Hubbard Parameters

Project Description: 

Periodic potentials are of fundamental importance to many interesting experimental and
theoretical systems. Although the eigenstates of an ideal periodic potential are perfectly
delocalized, perhaps of greater interest are so-called Wannier functions, which represent
maximally localized electronic states in a crystal. In higher dimensions with complicated
potentials, such states are dicult to calculate analytically and are instead often found
via numerical optimization algorithms. However, these methods compromise the physical
reliability and intuition of the resulting outputs. We implement and generalize an analytic
method to calculate maximally localizedWannier functions that is designed for optical lattice
experiments. With this method, full Bose-Hubbard parameters can be calculated from the
input of a fairly general lattice beam conguration. This will be useful for the eventual
realization of such systems via optical lattice experiments.