  The stability of a quantized vortex state in Bose-Einstein condensation is
examined within Bogoliubov theory for alkali atom gases confined in a harmonic
potential under forced rotation. By solving the non-linear Bogoliubov equations
coupled with the Gross-Pitavskii equation, the elementary excitations and the
total energy of the systems are calculated as a function of rotation velocity.
There are two distinct criteria of vortex stability; The position of the
excitation energy levels relative to the condensate energy level yields the
local stability criterion, and the total energy relative to that of the
non-vortex state yields the global stability criterion. The vortex stability
phase diagram in the rotation velocity vs the particle density of the system is
obtained, allowing one to locate the appropriate region to observe the singly
quantized vortex.
