Entangled two-photon states in the helical Mathieu-Gauss modes basis

In this work, we provide a complete theoretical and experimental study of a two-photon quantum state entangled in the orbital angular momentum (OAM) degree of freedom of the helical Mathieu-Gauss (HMG) modes. The state is generated by a type II spontaneous parametric down conversion (SPDC) process. Our analysis shows that the generated state is composed by the superposition of two symmetric Bell states with tunable contributions determined by the eccentricity parameter of the HMG modes. The predicted entangled state is confirmed experimentally by measuring the HMG modal joint probability of the SPDC two-photon state and the violation of Bell-type inequalities.