Rotating trapped Bose-Einstein Condensates

I review free and trapped Bose-Einstein condensates (BECs) [1, 2,3,4, 5]. In an isotropic harmonic potential V (r) = 1/2M omega(2)r(2), the single-particle ground state introduces anew intrinsic scale of length [the ground-state size d = root h/(M omega)] and energy [the ground-state energy E-0 = 3/2h omega]. When the trap rotates [6, 7, 81, there is a critical angular velocity for the appearance of one or a few quantized vortices. For more rapid rotation [9, 10, 11, 12, 131 the condensate contains a vortex array. The resulting centrifugal forces expand the condensate radially and shrink it axially; thus the condensate becomes effectively two-dimensional. If the external rotation speed approaches the frequency of the radial harmonic confining potential, the condensate enters the "lowest-Landau-level" regime, and a simple description again becomes possible [14, 15]. Eventually, the system is predicted to make a quantum phase transition to a highly correlated state analogous to die fractional quantum Hall states of electrons in a strong magnetic field [16, 17, 18, 19, 20].