Stability of a Vortex in a Rotating Trapped Bose-Einstein Condensate

The remarkable achievement of Bose-Einstein condensation in dilute trapped alkali-metal atomic gases [1-3] has stimulated the (now successful) search for quantized vortices that are usually associated with external rotation [4-8]. An essential feature of these condensates is the order parameter, characterized by a complex macroscopic wave function Psi({ěc r},t). Theoretical descriptions of vortices in trapped low-temperature condensates have relied on the time-dependent Gross-Pitaevskii (GP) equation [9-11], which omits dissipation. For a trap rotating at angular velocity Omega about hat z, it is a nonlinear Schrödinger equation ihbarfrac{partialPsi}{partial t}= (T+V_{tr}-Omega L_z+g\vertPsi\vert^2)Psi, (1)</TD></TR> </TABLE> where T=-hbar^2 nabla^2/2M is the kinetic-energy operator, V_{tr}=frac{1}{2}Msum_{j}omega_j^2x_j^2 is the harmonic trap potential, L_z = xp_y-yp_x is the z component of angular momentum, and gequiv 4pi hbar^2 a/M characterizes the strength of the short-range interparticle potential (here, a is the positive s-wave scattering length for repulsive two-body interactions; typically a is a few nm). Current experiments involve "dilute" systems, so that the zero-temperature condensate contains nearly all N particles, with int dV \vertPsi\vert^2 approx N. For a steady solution, Psi(ěc{r},t)=Psi(ěc{r})e^{-imu t/hbar}, where μ is the chemical potential.