We estimate the changes in the condensate ground state energy induced by one or more "sizable" impurities. By "sizable", we mean an impurity whose size is within a few orders of magnitude of the trap size and not necessarily atomic in scale. A sizable impurity will "drill" a hole in the condensate wave function and alter the condensate energy. The question is whether this microscopic change can be detected macroscopically because of the Bose-Einstein condensation effect. We discuss the effect of impurity expulsion, condensate interactions, and the induced interaction between two impurities.
When a sizable, hard-sphere-like impurity is placed in a trapped Bose-Einstein condensate, it will create a hole in the condensate wave function. Since it costs more energy to drill a hole at the wave function's maximum (near the trap center) than at its minimum (near the trap edge), the impurity will be expelled from the condensate. This suggests that C-60 molecules freely falling through a condensate of atomic hydrogen may be deflected by a radial acceleration comparable to g. The scattered fullerenes would then form a characteristic banded density pattern outside of the trap. The detection of these deflected molecules can be used to identify the onset of Bose-Einstein condensation.
We theoretically investigate the dynamics of a matter-wave soliton created in a harmonic potential, which is attractive in the transverse direction but expulsive in the longitudinal direction. This Bose-Einstein-condensate (BEC) bright soliton made of
7Li atoms has been observed in a recent experiment [Khaykovich et al., Science 296, 1290 (2002)]. We show that the nonpolynomial Schr\"odinger equation, an effective one-dimensional equation we derived from the three-dimensional Gross-Pitaevskii equation, is able to reproduce the main experimental features of this BEC soliton in an expulsive potential.