Deep learning in quantum optics and spectroscopy
Single molecule spectroscopy is an important tool for characterizing materials properties beyond what can be achieve in ensemble experiments. For quantum photonic applications, studying a single emitter at a time is indeed necessary to evaluate the fidelity of quantum light they generate. Unsurprisingly, the amount of photons and signal generated from a single quantum emitter is usually very small, and characterizing single emitters can be time-consuming - which is especially true for weakly emissive species or low collection efficiency configurations. Denoising or signal reconstruction approaches, such as the Levenberg–Marquardt algorithm or Maximum Likelihood Estimation, can accelerate experimental throughput. However, such conventional approaches rely on assigning a model to fit to the data, which imparts bias onto the predicted result, and model selection can be difficult for noisy data. Deep learning or machine learning (ML) approaches can remove the need for model selection, by instead incorporating multiple different possible models into the training data. ML approaches have also been shown to achieve higher accuracies with fewer measurements (in our case, photons collected) compared to conventional fitting, accelerating experimental throughput.
In this area of research, I develop new neural network models that are tailored for applications in quantum optics and single molecule spectroscopy experiments. My work thus far has made use of Adversarial Autoencoder Ensemble (AAE) models that take few-shot inputs (e.g. photon correlation functions with 100 - 1000 coincidences) and generate low-variance, high-accuracy outputs. More details are given below.
Fig 1. (a) Schemiatc of our deep Adversarial Autoencoder Ensemble (AAE) model. (b) (left) Few-shot photon correlation data input, the ensemble model output μ, and the uncertainty (two std. deviations) ± 2σ. (right) Reconstruction of the same input using Hamiltonian Monte Carlo. Ref: A. H. Proppe,† K. L. K. Lee† et al., Phys. Rev. B., 2022
Accelerating the acquistion of photon correlation functions: faster, higher accuracy, and lower variance deep learning reconstructions. The second-order photon intensity correlation function is used characterize photon statistics and determine whether or not the emissive species is a single emitter. For systems that can host multiple excitations like semiconductor quantum dots, photon correlation functions can instead measure the multiexciton quantum yield. The biexction quantum yield (BXQY) of quantum dots is an important property for their usage in high-flux applications like light-emitting diodes or lasers that can benefit from high BXQY. Photon correlation functions are also used ubiquitously throughout quantum optics to classify the photon indistinguishability and entanglement fidelity, as well in quantum spectroscopy and imaging.
Given their widespread usage, it is of interest to accelerate the acquistion of these correlation functions through signal reconstruction. A single quantum dot in a confocal microscope may emit as little as 1 - 5 kHz of photons, which can require minutes to hours to accumulate enough photon coincidences to attain a sufficient signal-to-noise ratio.
To tackle this problem, we developed an uncertainty-aware neural network model, which we called a deep Adversarial Autoencoder Ensemble (AAE). This model reconstructs noise-free photon correlation functions from noise-dominated, few-shot inputs. The model is trained with simulated correlation functions that are facilely generated by Poisson sampling time bins.
The AAE reconstructions are performed orders of magnitude faster, and Fig. 1b and c show that the reconstruction errors and estimates of BXQY are lower in variance and similar in accuracy compared to Maximum Likelihood Estimation (MLE) and Levenberg–Marquardt (LM) least-squares fitting approaches (MLEP = maximum likelihood estimation with a Poisson likelihood). This result held true for both simulated and experimentally measured few-shot photon correlation functions (~100 two-photon events) of InP/ZnS/ZnSe and CdS/CdSe/CdS quantum dots. We also showed that the predicted variance scales inversely with number of shots, with comparable uncertainties to computationally intensive Markov Chain Monte Carlo sampling. This work demonstrated 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.
Deep learned photon correlations to access time-resolved lineshapes of single quantum emitters. Solid-state single-photon emitters (SPEs) are quantum light sources that combine atom-like optical properties with solid-state integration and fabrication capabilities. SPEs are hindered by spectral diffusion, where the emitter’s surrounding environment induces random energy fluctuations. Timescales of spectral diffusion span nanoseconds to minutes, and requires probing single emitters to remove ensemble averaging. Photon correlation Fourier spectroscopy (PCFS) can be used to measure time-resolved single emitter lineshapes, but is hindered by poor signal-to-noise in the measured correlation functions at early times due to low photon counts.
Fig. 2. (a) Noise-dominated input, ground truth, and ensemble-average reconstruction μ ± one standard deviation (σ) for (top) simulated and (bottom) experimental data. (b) PCFS interferograms from photon corrleation functions without (top) and with (bottom) ML-reconstruction. (c) Fourier transformation of the interferograms gives the spectral correlations of the emission lineshape. With our ML model, we can now resolve single emitter lineshapes at timescales as fast as 10 nanoseconds. This work has been accepted for publication in Physical Review Letters.
We develop a new framework to simulate PCFS correlation functions directly from diffusing spectra that match well with experimental data for single colloidal quantum dots. We use these simulated datasets to train a fully convolutional deep ensemble autoencoder machine learning model that outputs accurate, noiseless, and probabilistic reconstructions of the noisy correlations. Using this model, we obtain reconstructed time-resolved single dot lineshapes at timescales as low as 10 ns, which are otherwise completely obscured by noise (Fig. 2). This enables PCFS to extract optical coherence times on the same timescales as Hong-Ou-Mandel two-photon interference, but with the advantage of providing spectral information in addition to estimates of photon indistinguishability. Our machine learning approach is broadly applicable to different photon correlation spectroscopy techniques and SPE systems, offering an enhanced tool for probing single emitter lineshapes on previously inaccessible timescales.