Graded-index optical fiber transverse-spatial-mode entanglement

We present a study of spontaneously arisen spatially entangled photon pairs via intermodal four-wave mixing in a graded-index multimode optical fiber. Unique dispersive features of the fiber allow spectral indistinguishability of two different phase-matched processes, producing entangled pairs of spatial qubits. The bases are realized as superpositions of orthogonal transverse fiber modes having opposite parities. In particular, we take into consideration the spectral properties of the processes by examining their joint spectral amplitudes. It is shown that illuminating graded-index optical fiber with different pump wavelengths has an impact upon efficiency parameters accordingly the degree of spatial entanglement and gives rise to photon pairs with various spectral purities. Photons with higher spectral purity enable desired single-photon based interactions to take place, whereas photons with lower spectral purity exhibit hybrid entanglement in frequency and transverse mode. We also discuss Wigner function formalism and parity-displacement-based realization to characterize spatial properties of the states, as well as to verify quantum entanglement through a violation of Clauser-Horne-Shimony-Holt inequality.