Control of the geometric phase in two open qubit-cavity systems linked by awaveguide

We explore the geometric phase in a system of two non-interacting qubits embedded in two separated open cavities linked via an optical fiber and leaking photons to the external environment. The dynamical behavior of the generated geometric phase is investigated under the physical parameter effects of the coupling constants of both the qubit-cavity and the fiber-cavity interactions, the resonance/off-resonance qubit-field interactions, and the cavity dissipations. It is found that these the physical parameters lead to generating, disappearing and controlling the number and the shape (instantaneous/rectangular) of the geometric phase oscillations.