Band Structure in Bose-Einstein Condensates in Periodic Lattices

Mason Porter, Georgia Institute of Technology, School of Mathematics

Since their experimental discovery in 1995, Bose-Einstein condensates (BECs) have generated considerable excitement in the physics community both because their study allows one to explore new regimes of fundamental physics and because of their eventual engineering applications.

The macroscopic behavior of BECs at 0 Kelvin is modeled by a nonlinear Schrodinger equation (NLS) in the presence of an external potential. When this potential is spatially periodic, the BEC spectrum exhibits a band structure (spatial resonance structure). I will begin this talk with an introduction to Bose-Einstein condensation. I will then discuss the use of Hamiltonian perturbation theory and supporting numerical simulations to study coherent structures in BECs and their concomitant band structure in detail. This perturbative approach relies on the elliptic function structure of solutions in the absence of an external potential. I will also briefly discuss recent generalizations of this theory to multiple-component BECs, which are described by coupled Nonlinear Schrodinger equations. My work on single-species condensates is joint with Predrag Cvitanovic and that multiple-species condensates is joint with Boris Malomed and Panos Kevrekidis.