  We investigate topological insulating states in both two and three dimensions
with the harmonic potential and strong spin-orbit couplings breaking the
inversion symmetry. Landau-level like quantizations appear with the full 2D and
3D rotational symmetry and time-reversal symmetry. Inside each band, states are
labeled by their angular momenta over which energy dispersions are strongly
suppressed by spin-orbit coupling to nearly flat. The radial quantization
generates energy gaps between neighboring bands at the order of the harmonic
frequency. Helical edge or surface states appear on open boundaries
characterized by the Z2 index. These Hamiltonians can be viewed from the
dimensional reduction of the high dimensional quantum Hall states in 3D and 4D
flat spaces. These states can be realized with ultra-cold fermions inside
harmonic traps with the synthetic gauge fields.
