Spectroscopy and spin dynamics for strongly interacting few spinor bosons in one-dimensional traps

We consider a one-dimensional trapped gas of strongly interacting few spin-1 atoms which can be described by an effective spin chain Hamiltonian. Away from the SU(3) integrable point, where the energy spectrum is highly degenerate, the rules of ordering and crossing of the energy levels and the symmetry of the eigenstates in the regime of large but finite repulsion have been elucidated. We study the spin-mixing dynamics which is shown to be very sensitive to the ratio between the two channel interactions g0/g2 and the effective spin chain transfers the quantum states more perfectly than the Heisenberg bilinear-biquadratic spin chain.