Dark SU(2) states of the motion of a trapped ion

The preparation of SU(2) states as dark states of the motion of a trapped ion is considered. The difficulty in preparing these states is shown to arise from the degeneracy of eigenvalues of the Hamiltonian. This degeneracy is removed by making use of the nonlinearities appearing in the dynamics of an ion that is not well localized. The mechanism of approaching the dark state of interest is analyzed by using the quantum trajectory method.