Vortex stabilization in dilute Bose-Einstein condensate under rotation

The stability of a quantized vortex state in Bose-Einstein condensation is examined within Bogoliubov theory for alkali atom gases confined in a harmo nic potential under forced rotation. By solving the non-linear Bogoliubov e quations coupled with the Gross-Pitavskii equation, the elementary excitati ons and the total energy of the systems are calculated as a function of rot ation velocity. There are two distinct criteria of vortex stability; The po sition of the excitation energy levels relative to the condensate energy le vel yields the local stability criterion, and the total energy relative to that of the non-vortex state yields the global stability criterion. The vor tex stability phase diagram in the rotation velocity vs the particle densit y of the system is obtained, allowing one to locate the appropriate region to observe the singly quantized vortex.