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Developing a quantum light source that carries more than one bit per photon is pivotal for expanding quantum information applications. Characterizing a high-dimensional multiple-degree-of-freedom source at the single-photon level is challenging due to the large parameter space as well as limited emission rates and detection efficiencies. Here, we characterize photon pairs generated in optical fiber in the transverse-mode and frequency degrees of freedom by applying stimulated emission in both degrees of freedom while detecting in one of them at a time. This method may be useful in the quantum state estimation and optimization of various photon-pair source platforms in which complicated correlations across multiple degrees of freedom may be present. 

The purpose of this tutorial paper is to present a broad overview of photon-pair generation through the spontaneous four wave mixing (SFWM) process in optical fibers. Progress in optical fiber technology means that today we have at our disposal a wide variety of types of fiber, which, together with the fact that SFWM uses two pump fields, implies a truly remarkable versatility in the resulting possible photon-pair properties. We discuss how the interplay of frequency, transverse mode, and polarization degrees of freedom—the first linked to the latter two through fiber dispersion—leads to interesting entanglement properties both in individual degrees of freedom and also permitting hybrid and hyper entanglement in combinations of degrees of freedom. This tutorial covers methods for photon-pair factorability, frequency tunability, and SFWM bandwidth control, the effect of frequency non-degenerate and counterpropagating pumps, as well as methods for characterizing photon pairs generated in optical fibers.