TRIAL SOLUTION AND CRITICAL FREQUENCY TO THE SINGLY QUANTIZED VORTEX IN BIG BOSE–EINSTEIN CONDENSATES

A novel solution to the singly quantized vortex is presented for big Bose–Einstein condensates in axis-symmetric harmonic traps, which is valid in the regime of strong coupling parameters. This solution manifests the vortex as a topological soliton and describes correctly its global structure for the whole region of large condensates including the vortex-core, except for the thin boundary region. An improved expression for thermodynamical critical rotation frequency for vortex formation is derived based on our solution, conforming to the known frequency formula given by Lundh et al. in the Thomas–Fermi limit.