Composite particle and field theory in atomic quantum Hall effect

In this paper, we explore the composite particle description of the atomic quantum Hall (QH) effect. We further give the Chern-Simon-Gross-Pitaevskii (CSGP) effective theory for the atomic Hall liquid, which is the counterpart of Chern-Simon theory in electron Hall effect. What we obtained is equivalent to the Laughlin wavefunction approach. Our results show that in terms of composite particles, the atomic Hall effect is really the same as the electronic QH effect. The CSGP effective theory would shed new light on the atomic QH effect.