Vortex in the yrast band of condensates of pseudo-spin-1/2 bosonic atoms

Abstract

The possible excitation of angular degrees of freedom of pseudo-spin-1/2 $N\ensuremath{-}boson$ systems has been considered. For this purpose, the analytical forms of the fractional parentage coefficients have been introduced to deal with the symmetry problems involved. A set of equations for the Yrast band has been derived, and related numerical calculation has been performed. The yrast band is found to contain $N∕2$ subbands specified by the total spin $S$ ranging from $N∕2$ to 0 or 1/2, the one with a larger $S$ is lower. The states in a subband are further specified by the total orbital angular momentum $L$. Each state is a fragmented state (except the lowest one), where a part of particles have been excited and may form vortex. Specifically, the structure of the yrast band appears to obey the Hund's first and second rules.