Characterising Photon Pair Sources Beyond Joint-Spectra

Pure, heralded, single photons provide a resource for quantum computation, communication and sensing, however, spectral correlations and losses degrade interference visibility. It is customary to characterise the Joint-spectral-amplitude (JSA) of photon pair sources, Schmidt decompose to assess the purity of heralded photons, and use this to predict the behaviour of subsequent experiments. Whilst in the lossless case this is complete, in general, the JSA contains insufficient information to fully characterize the transformation, and even precludes definition. Unfortunately, loss is a significant source of error in applications[1], particularly, in cavity based systems where backscattering is present[2] and thresholds necessary for future tasks stretch the applicability of lossless approximations.

We review source characterisation methods emphasizing how bi-photon states arise from underlying Gaussian transformations. We consider the general form of transformations including loss, explicate how these Gaussian transformations may be decomposed, which constraints are necessary for said decompositions[3] and see that full characterisation requires twice as many parameters (than a JSA) to be determined. We present a model for micro-ring resonator sources with back-scattering demonstrating these features. Finally, we derive the output statistics for some commonly used characterisation methods, and propose fair black-box source characterisation techniques.

[1]Bonneau, D., Mendoza, G. J., O’Brien, J. L., & Thompson, M. G. (2015). Effect of loss on multiplexed single-photon sources. New Journal of Physics, 17(4), 1–15. https://doi.org/10.1088/1367-2630/17/4/043057
[2]Li, A., Van Vaerenbergh, T., De Heyn, P., Bienstman, P., & Bogaerts, W. (2016). Backscattering in silicon microring resonators: A quantitative analysis. Laser and Photonics Reviews, 10(3), 420–431. https://doi.org/10.1002/lpor.201500207
[3]McCutcheon, W. (2018). Structure in Multimode Squeezing: A Generalised Bloch-Messiah Reduction. Retrieved from http://arxiv.org/abs/1809.02544