Ground Band and a Generalized GP-equation for Spinor Bose-Einstein Condensates

Abstract

For the spinor Bose-Einstein condensates both the total spin $S$ and its Z-component $S_Z$ should be conserved. However, in existing theories, only the conservation of $S_z$ has been taken into account. To remedy, this paper is the first attempt to take the conservation of both and $S_Z$ into account. For this purpose, a total spin-state with the good quantum numbers $S$ and $S_Z$ is introduced in the trial wave function, thereby a generalized Gross-Pitaevskii equation has been derived. With this new equation, the ground bands of the ${}^{23}$Na and Rb condensates have been studied, where the levels distinct in $S$ split. It was found that the level density is extremely dense in the bottom of the ground band of ${}^{23}$Na, i.e., in the vicinity of the ground state. On the contrary, for ${}^{87}$Rb, the levels are extremely dense in the top of the ground band,

7 page, 5 figures

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• Fragmented Many-Body states of definite angular momentum and stability of attractive 3D Condensates
• Generalized Gross-Pitaevskii equation adapted to the $U(5)\supset SO(5)\supset SO(3)$ symmetry for spin-2 condensates
• Sensitivity of spin structures of small spin-1 condensates against a magnetic field studied beyond the mean field theory
• Hyperfine state entanglement of spinor BEC and scattering atom
• Characteristic frequency of the magnetic radiation of spinor condensates
• Two-body and three-body substructures served as building blocks in small spin-3 condensates
• Symmetry breaking and entropy production during the evolution of spinor Bose-Einstein condensate driven by coherent atom beam
• Spin-textures of the Bose-Einstein condensates with three kinds of spin-1 atoms