Abstract
In this paper we predict a topological quantum interference effect in an extended Dicke model with controllable long-range atom-atom interactions by means of coherent-state path integral. Due to the intrinsic competition between the atom-atom interactions and atom-field coupling, an interesting topological interference of the instanton and anti-instanton tunneling paths could occur. As a consequence, this model only with a few odd-number atoms has a twofold absolute degenerate ground-state subspace with a large energy gap, which becomes larger with the increasing of the system size. Therefore, the collective decoherence arising from noise in the external control parameters could be effectively suppressed in terms of adiabatic process between this absolute degenerate ground-state subspace associated with a finite energy gap.