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

The problem of explaining the critical angular velocity Ω_c 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 Ω_c 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 Ω_c 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.