Explanation of critical angular velocities of the vortex formation in a stirred Bose-Einstein condensate

The problem of explaining the critical angular velocity Ωc when the formation of a vortex in the stirred Bose-Einstein condensate becomes energetically possible is considered in the framework of the variational approach. The origin of smallness of the calculated Ωc in comparison with the measured values, which takes place for a pure quantum state with the unit angular momentum per condensed particle, is uncovered. The agreement with the measured Ωc is achieved upon admitting a small admixture of the zero angular-momentum state in the wave function of the one-vortex quantum state prepared after stirring. A portion of this admixture amounts to 1–13% of the total condensed atoms. A possible test of this hypothesis is proposed.