Spin-textures of medium-body boson systems with trapped spin-f cold atoms

Abstract

The spin-textures of bound medium-body systems with spin-mathfrak {f} atoms (mathfrak {f}ge 3) have been studied. The Hamiltonian is assumed to be dominated by the two-body interaction favoring parallel spins. The system with particle number N=8 and mathfrak {f}=3 is first chosen, and the Hamiltonian is exactly diagonalized by using Fock-states as basis-states, thereby all the eigenenergies and eigenstates are obtained and a detailed analysis is made. Then the cases with N=13 and mathfrak {f}=4 are further studied. Since the total spin S is conserved, the eigenstates having the same S form an S-group. Let the lowest (highest) energy state of an S-group be called a bottom-state (top-state). We found that all the bottom-states are bipartite product states with constituent states describing fully polarized subsystems containing N_1 and N_2 (le N_1) particles, respectively. For two bottom-states different in N_2, the one with a larger N_2 is higher. For two having the same N_2, the one with a smaller S is higher. Whereas all the top-states are found to be essentially a product state of the pairs, in each pair the two spins are coupled to lambda if the strength of the lambda-channel is more repulsive than the others. For the states belonging to an S-group, the higher one would contain more pieces. As the energy goes up, larger pieces (those containing more than two particles) will disappear.