Switching of Geometric Phase in Degenerate Systems

The geometric and open path phases of a four-state system subject to time varying cyclic potentials are computed from the Schr"{o}dinger equation. Fast oscillations are found in the non-adiabatic case. For parameter values such that the system possesses degenerate levels, the geometric phase becomes anomalous, undergoing a sign switch. A physical system to which the results apply is a molecular dimer with two interacting electrons. Additionally, the sudden switching of the geometric phase promises to be an efficient control in two-qubit quantum computing.