Pancharatnam phase in non-separable states of light

Abstract: We generate the non-separable state of polarization and orbital angular momentum (OAM) using a laser beam. The generated state undergoes a cyclic polarization evolution which introduces a Pancharatnam geometric phase to the polarization state and in turn a relative phase in the non-separable state. We experimentally study the violation of Bell - CHSH inequality for different Pancharatnam phases introduced by various cyclic polarization evolutions with linear and circular states as measurement bases. While measuring in linear bases, the Bell-CHSH parameter oscillates with Pancharatnam phase. One can overcome this dependence by introducing a relative phase in one of the projecting state. However for measurement in circular bases, the Pancharatnam phase does not affect the Bell-CHSH violation.