Controllable exact self-similar evolution of the Bose-Einstein condensate

We show analytically that the profile of the Bose-Einstein condensate can evolve exact self-similarly when the time-dependent interatomic interaction and harmonic potential satisfy a certain condition for one-, two- and three-dimensional geometries, respectively. Based on the exact scaling laws for the amplitude and width of the condensate profile, we propose experimentally feasible ways to improve the accuracy in measuring the stationary-state profile of the condensate when its spatial size is so small that the direct measurement is not available, and to squeeze the condensate to high local particle density to check the validity of the Gross-Pitaevskii equation via the controllable exact self-similar evolution of the condensate profile.