Photon statistics modal reconstruction via detected and undetected light

The rapid growth of single-photon metrology [1] and (optical) quantum technologies [2-5] in the last years has made the development of simple, versatile and robust methods for characterizing complex optical states a task of the utmost relevance. <br/> <br/> Here we introduce and experimentally test a novel technique [6] for the reconstruction of multimode optical fields, based on the simultaneously exploiting both the generalized Glauber’s K^th-order correlation function g^((K)) and a recently-proposed anti-correlation function dubbed θ^((K)) [7], proven to be resilient to Poissonian noise. Our experimental results show how this method, although requiring less “a priori” information than other mode reconstruction techniques based only on g^((K))’s [8], steadily outperforms them. This is particularly advantageous for measurements in Hanbury-Brown & Twiss interferometric arrangements hosting non-photon-number-resolving detectors, since the insensitivity of θ^((K))’s to Poissonian fields forbids a reconstruction method relying only on these functions from delivering reliable results. <br/> <br/> Given its versatility and robustness, this new mode reconstruction technique is suited for a widespread use in real applications of optical quantum measurement, from quantum information to quantum metrology, especially for characterizing ensembles of single-photon emitters in the presence of background noise (caused by, e.g., residual excitation laser light, stray light or unwanted fluorescence). <br/> <br/> References <br/> A. Migdall, S. V. Polyakov, J. Fan, J. C. Bienfang, in Single-Photon Generation and Detection: Physics and Applications, Academic Press, Cambridge, MA, USA 2013. S. Pirandola et al., Adv. Opt. Photon. 12, 1012 (2020). M. Genovese, AVS Quantum Sci. 3, 044702 (2021). J. Wang, F. Sciarrino, A. Laing, M. G. Thompson, Nat. Photon. 14, 273 (2020). G. Petrini et al., Adv. Quantum Technol. 3, 2000066 (2020). L. T. Knoll et al., Adv. Quantum Technol. 6, 2300062 (2023). L. Lachman, L. Slodička, R. Filip, Sci. Rep. 6, 19760 (2016). E. Goldschmidt et al., Phys. Rev. A 88, 013822 (2013).