Adiabatic evolution in nonlinear systems with degeneracy

Abstract

We propose a general description of adiabatic evolution of degenerate quantum systems in both linear and nonlinear cases. We derive the effective evolution equations of the considered system. For nondegenerate cases, we obtain a generalized Berry's phase for nonlinear systems. For linear cases, the equations reduce to the Wilczek-Zee dynamics in degenerate quantum systems, where non-Abelian adiabatic connections appear. The method can be used to study the coherent atom-molecule transition in ultracold quantum gases with degeneracy and is consistent with quantized treatment.