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A gaseous Bose-Einstein condensate (BEC) offers an ideal testing ground for studying symmetry breaking, because a trapped BEC system is in a mesoscopic regime, and situations exist under which symmetry breaking may or may not occur. Investigating this problem can explain why mean-field theories have been so successful in elucidating gaseous BEC systems and when many-body effects play a significant role. We substantiate these ideas in four distinct situations: namely, soliton formation in attractive BECs, vortex nucleation in rotating BECs, spontaneous magnetization in spinor BECs, and spin texture formation in dipolar BECs. © 2006 American Institute of Physics [ABSTRACT FROM AUTHOR]

I review free and trapped Bose-Einstein condensates (BECs) [1, 2, 3, 4, 5]. In an isotropic harmonic potential V(r) = 1/2Mω2r2, the single-particle ground state introduces a new intrinsic scale of length [the ground-state size d = h/(Mω)] and energy [the ground-state energy E0 = 3/2hω]. When the trap rotates [6, 7, 8], there is a critical angular velocity for the appearance of one or a few quantized vortices. For more rapid rotation [9, 10, 11, 12, 13] 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 the fractional quantum Hall states of electrons in a strong magnetic field [16, 17, 18, 19, 20]. [ABSTRACT FROM AUTHOR]

We investigate numerically stable structures of vortex states in rotating two-component Bose-Einstein condensates (BECs) in a quadratic plus quartic potential. We discover various new vortex structures by changing the intracomponent coupling constants, the intercomponent coupling constant and the rotation frequency. © 2006 American Institute of Physics [ABSTRACT FROM AUTHOR]