Entanglement swapping and heralding are at the heart of many protocols for distributed quantum information. For photons, this typically involves Bell state measurements based on two-photon interference effects. In this context, hybrid systems that combine high rate, ultra-stable and pure quantum sources with long-lived quantum memories are particularly interesting. Here, we develop a theoretical description of pulsed two-photon interference of photons from dissimilar sources to predict the outcomes of second-order cross-correlation measurements. These are directly related to, and hence used to quantify, photon indistinguishability. We study their dependence on critical system parameters such as quantum state lifetime and frequency detuning, and quantify the impact of emission time jitter, pure dephasing and spectral wandering. Our results show that for fixed lifetime of emitter one, for each frequency detuning there is an optimal lifetime of emitter two that leads to highest photon indistinguishability. Expectations for different hybrid combinations involving III-V quantum dots, color centers in diamond, 2D materials and atoms are quantitatively compared for real-world system parameters. Our work both provides a theoretical basis for the treatment of dissimilar emitters and enables assessment of which imperfections can be tolerated in hybrid photonic quantum networks.
Christian Dangel, Jonas Schmitt, Anthony J. Bennett, Kai Müller, Jonathan J. Finley