Role of asymmetry in the geometric phase of a coupled atom-heteronuclear molecule system.

We investigate the role of asymmetry in the geometric phase of an ultracold bosonic atom-heteronuclear molecule system where the asymmetry denotes the particle-number imbalance between two atomic species. Based on the mean-field approach, we derive the analytical expression of the geometric phase and confirm it by our numerical simulations. It is found that the geometric phase strongly depends both on the atom-number imbalance and the nonlinear particle interaction. We show that the geometric phase can be dramatically enhanced by increasing the imbalance or the repulsive interaction strength. For the symmetric case, a discontinuous behavior for the first-order derivative of the ground-state geometric phase at a critical point is seen which gives a distinct signal of a phase transition from mixed atom-molecule phase to pure molecule phase. The virtual magnetic field interpretation for the geometric phase is also given. [ABSTRACT FROM AUTHOR]