Exploring Energy-Time Entanglement Using Geometric Phase

Using the signal and idler photons produced by parametric down-conversion, we report an experimental observation of a violation of the Bell inequality for energy and time based purely on the geometric phases of the signal and idler photons. We thus show that energy-time entanglement between the signal and idler photons can be explored by means of their geometric phases. These results may have important practical implications for quantum information science by providing an additional means by which entanglement can be manipulated.