Berry Phase in Atom-Molecule Conversion Systems and Fractional Monopole

We investigate the geometric phase or Berry phase of adiabatic quantum evolution in an atom-molecule conversion system, and find that the Berry phase in such system consists of two parts: the usual Berry connection term and a novel term from the nonlinearity brought forth by the atom-molecule conversion. The geometric phase can be viewed as the flux of the magnetic field of a monopole through the surface enclosed by a closed path in parameter space. The charge of the monopole, however, is found to be one third of the elementary charge of the usual quantized monopole.