Generalized Gross-Pitaevskii equation adapted to the U(5) superset of SO(5) superset of SO(3) symmetry for spin-2 condensates

摘要

A generalized Gross-Pitaevskii equation adapted to the U(5) superset of SO(5) superset of SO(3) symmetry has been derived and solved for the spin-2 condensates. The spin-textile and the degeneracy of the ground state (g.s.) together with the factors affecting the stability of the g.s., such as the gap and the level density in the neighborhood of the g.s., have been studied. Based on a rigorous treatment of the spin-degrees of freedom, the spin-textiles can be understood in an N-body language. In addition to the ferro, polar, and cyclic phases, the g.s. might in a mixture of them when vertical bar M vertical bar is not equal to 0 and 2N (M is the total magnetization). The great difference in the stability and degeneracy of the g.s. caused by varying phi (which marks the features of the interaction) and M is notable. Since the root-mean-square radius R-rms is an observable, efforts have been made to derive a set of formulas to relate R-rms and N,omega (frequency of the trap), and phi. These formulas provide a way to check the theories with experimental data.