Ricardo Carretero received a two-year National Science Foundation Grant, New Directions in Atomic Bose-Einstein Condensates.

The recent experimental realization of Bose-Einstein Condensates (BECs)—leading to the 2001 Nobel Prize in Physics— has ignited an intense interest from the Mathematics and Physics communities. BECs area fascinating, fertile platform for the study of nonlinear waves such as solitons and vortices with profound implications in areas such as superconductivity, superfluidity (topics of the 2003 Nobel Prize in Physics) and quantum computing.  The main theme of this grant is to study newly emerging directions pertaining to the existence, stability, bifurcations, dynamics and interactions of coherent structures (solitons, vortices, and vortex rings) in BECs.  The plan involves a coordination of mathematical modeling, analytical and asymptotic methods, and computational techniques synergistically interwoven with the collaborations of two experimental groups of Profs. P. Engels (Washington State) and D.S. Hall (Amherst College).

figure 1a color pattern figure 1B color pattern fugure 1c color pattern

 figure with twirling cone pattern

Figure 1: Prototypical example of the a) amplitude and b) phase profiles of a trapped vortex at the center of a parabolic trap. c) (x,y,t) dynamics for an off-center precessing vortex from the full GPE (1) (blue points) and the reduced ODE model (2) (thin black line). d) Animation of the evolution of the density for a precessing vortex.