Measurement, Detection, and Parameter Estimation of Single Photon Correlations

The continuous time-tagging of photon arrival times for high count rate sources isnecessary for applications such as optical communications, quantum key encryption, and astronomical measurements. Detection of Hanbury-Brown and Twiss (HBT) single photon correlations from thermal sources, such as stars, requires a combination of high dynamic range, long integration times, and low systematics in the photon detection and time tagging system. The continuous nature of the measurements and the need for highly accurate timing resolution requires a customized time-to-digital converter (TDC). A custom built, two-channel, field programmable gate array (FPGA)-based TDC capable of continuously time tagging single photons with sub clock cycle timing resolution was characterized. Auto-correlation and cross-correlation measurements were used to constrain spurious systematic effects in the pulse count data as a function of system variables. These variables included, but were not limited to, incident photon count rate, incoming signal attenuation, and measurements of fixed signals. Additionally, a generalized likelihood ratio test using maximum likelihood estimators (MLEs) was derived as a means to detect and estimate correlated photon signal parameters. The derived GLRT was capable of detecting correlated photon signals in a laboratory setting with a high degree of statistical confidence. A proof is presented in which the MLE for the amplitude of the correlated photon signal is shown to be the minimum variance unbiased estimator (MVUE). The fully characterized TDC was used in preliminary measurements of astronomical sources using ground based telescopes. Finally, preliminary theoretical groundwork is established for the deep space optical communications system of the proposed Breakthrough Starshot project, in which low-mass craft will travel to the Alpha Centauri system to collect scientific data from Proxima B. This theoretical groundwork utilizes recent and upcoming space based optical communication systems as starting points for the Starshot communication system.