Rotating Bose gas dynamically entering the lowest Landau level

Motivated by recent experiments, we model the dynamics of a condensed Bose gas in a rotating anisotropic trap, where the equations of motion are analogous to those of charged particles in a magnetic field. As the rotation rate is ramped from zero to the trapping frequency, the condensate stretches along one direction and is squeezed along another, becoming long and thin. When the trap anisotropy is slowly switched off on a particular timescale, the condensate is left in the lowest Landau level. We use a time dependent variational approach to quantify these dynamics and give intuitive arguments about the structure of the condensate wavefunction. This preparation of a lowest Landau level condensate can be an important first step in realizing bosonic analogs of quantum Hall states.