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 Schrdinger equation (NLS) in the presence of an external potential. When this potential is spatially periodic (e.g., due to an optical lattice, which may be created using counter-propagating laser beams), the spectrum of the BEC exhibits a band structure (spatial resonance structure). In this talk, I will discuss the I use of Hamiltonian perturbation theory and supporting numerical simulations to study coherent structures in BECs and their concomitant band structure in detail. Time-permitting, I will discuss recent extensions to coupled BECs that are a work in progress.
To prepare the audience for what is about to befall them, I will spend the first portion of the talk discussing the importance and properties of BECs. (That is, I am specifically not assuming any prior knowledge of BECs.)
My research on individual BECs is joint with Predrag Cvitanovic'. The work on coupled BECs is joint with Boris Malomed and Panos Kevrekidis.