Carlos presents his talk “Nucleation of dark solitons and vortices in dipolar Bose-Einstein condensates” at the Eighth IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory (http://waves.uga.edu/index.shtml), Athens, Georgia, March 25-28, 2013. Carlos is a Ph.D. student under the guidance of Prof. Carretero. The work Carlos presented in the conference is based on his M.S. research in Applied Mathematics with concentration in Dynamical Systems (http://nlds.sdsu.edu/masters/)
“Bose-Einstein condensation is a state of matter of boson particles at ultra cold temperatures. The Gross-Pitaevskii (GP) equation, a variant of the nonlinear Schroedinger equation that includes the external trapping, can effectively describe the mean field dynamical properties of Bose-Einstein condensates (BECs). Experimental progress has been made to create BECs with particles with a strong dipolar moment such as in chromium. The dipole-dipole interaction adds a nonlocal term to the GP equation in the form of a convolution.
On the other hand, previous work has focused on vortex nucleation in non-dipolar condensates by dragging impurities at supercritical speeds in the condensate. In the case of the one-dimensional GP equation with no external potential nor dipolar effects, a critical velocity can be found analytically above which dark (grey) solitons are emitted from the moving impurity. However, the case pertaining the supercritical velocity for vortex nucleation in dipolar condensates has not been considered so far. In this talk, we present analytical and numerical results for the nucleation of dark solitons in one-dimensional condensates with dipolar terms. Numerical results will also be presented for two-dimensional dipolar condensates.
Interestingly, since the dipole-dipole interaction is anisotropic in two dimensions, the critical speed is found to depend on the orientation of the trajectory of the moving impurity with respect to the dipolar axis.”