Using the signal and idler photons produced by parametric downconversion, 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.Published in: Phys. Rev. Lett. 101, 180405 (2008) Geometric phase, or Berry's phase, is the phase acquired by a system when it is transported around a closed circuit in an abstract space [1]. The manifestation of this phase in polarization optics is also known as Pancharatnam phase, which is the phase acquired by a photon field when its polarization is taken through a closed circuit on the Poincaré sphere [2][3][4]. Pancharatnam phase has been observed both at high light levels [5][6][7] and at a single photon level [8]. Effects of Pancharatnam phase in two-photon interference, using the signal and idler photons produced by parametric downconversion (PDC), have also been studied in many different situations [9-13].Bell's inequality [14] was derived in order to show that any local hidden variable interpretation [15] of quantum mechanics is incompatible with the statistical predictions of quantum mechanics. Clauser, Horne, Shimony and Holt (CHSH) generalized Bell's inequality so that it could be applied to realizable experiments [16]. Since then, using the signal and idler photons produced by PDC, violations of the generalized forms of Bell's inequality have been observed for various degrees of freedom including polarization [17,18], phase and momentum [19], and energy and time [20][21][22]. In recent years, using hyperentangled states, even simultaneous violations of Bell inequalities for more than one degrees of freedom have been reported [23][24][25][26]. In addition to proving the impossibility of local hidden variable interpretations of quantum mechanics, a violation of Bell's inequality, based on a certain degree of freedom, verifies entanglement and guarantees that it can be exploited through that particular degree of freedom.Bell inequality for energy and time was suggested by J. D. Franson using an experimental scheme commonly known as the Franson interferometer [20]. Franson's scheme for violating a Bell inequality requires changing the phases of the signal and idler photons in one of the interfering alternatives. In all the experimental realizations of Franson's scheme so far, the phases of the signal and idler photons have been changed by adjusting their dynamic phases, i.e., by adjusting their optical path lengths [21,22]. Therefore, all these previous violations can be said to be the dynamic phase-based violations of Bell inequality for energy and time.In this paper, we show that the Bell inequality for energy and time can also be violated using geometric phases of the signa...