Landau-like quantized levels of neutral atom induced by a dark-soliton shaped electric field

Motivated by the fascinating progresses in the cold atom experiments and theories, especially the artificial gauge field induced spin-orbit coupling of neutral atoms, we present a novel dispersion of neutral atoms carrying a non-vanishing magnetic moment in a special gauge field, an external electric field of dark-soliton shaped profile. By means of WKB approximation, we obtain discrete quantized landau-like energy levels, which is instructive for the quantum Hall effect of neutral particles. The observability of the results is also discussed.