Adversarial autoencoder ensemble for fast and probabilistic reconstructions of few-shot photon correlation functions for solid-state quantum emitters

Second-order photon correlation measurements [${g}^{(2)}(\ensuremath{\tau})$ functions] are widely used to classify single-photon emission purity in quantum emitters or to measure the multiexciton quantum yield of emitters that can simultaneously host multiple excitations -- such as quantum dots -- by evaluating the value of ${g}^{(2)}(\ensuremath{\tau}=0)$. Accumulating enough photons to accurately calculate this value is time consuming and could be accelerated by fitting of few-shot photon correlations. Here, we develop an uncertainty-aware, deep adversarial autoencoder ensemble (AAE) that reconstructs noise-free ${g}^{(2)}(\ensuremath{\tau})$ functions from noise-dominated, few-shot inputs. The model is trained with simulated ${g}^{(2)}(\ensuremath{\tau})$ functions that are facilely generated by Poisson sampling time bins. The AAE reconstructions are performed orders-of-magnitude faster, with reconstruction errors and estimates of ${g}^{(2)}(\ensuremath{\tau}=0)$ that are lower in variance and similar in accuracy compared to Maximum likelihood estimation and Levenberg-Marquardt least-squares fitting approaches, for simulated and experimentally measured few-shot ${g}^{(2)}(\ensuremath{\tau})$ functions (\ensuremath{\sim}100 two-photon events) of InP/ZnS/ZnSe and CdS/CdSe/CdS quantum dots. The deep-ensemble model comprises eight individual autoencoders, allowing for probabilistic reconstructions of noise-free ${g}^{(2)}(\ensuremath{\tau})$ functions, and we show that the predicted variance scales inversely with number of shots, with comparable uncertainties to computationally intensive Markov chain Monte Carlo sampling. This work demonstrates the advantage of machine learning models to perform uncertainty-aware, fast, and accurate reconstructions of simple Poisson-distributed photon correlation functions, allowing for on-the-fly reconstructions and accelerated materials characterization of solid-state quantum emitters.