Single-Shot Non-Gaussian Measurements for Optical Phase Estimation

Estimation of the properties of a physical system with minimal uncertainty is a central task in quantum metrology. Optical phase estimation is at the center of many metrological tasks where the value of a physical parameter is mapped to the phase of an electromagnetic field and single-shot measurements of this phase are necessary. While there are measurements able to estimate the phase of light in a single shot with small uncertainties, demonstrations of near-optimal single-shot measurements for an unknown phase of a coherent state remain elusive. Here, we propose and demonstrate strategies for single-shot measurements for ab initio phase estimation of coherent states that surpass the sensitivity limit of heterodyne measurement and approach the Cramer-Rao lower bound for coherent states. These single-shot estimation strategies are based on real-time optimization of coherent displacement operations, single photon counting with photon number resolution, and fast feedback. We show that our demonstration of these optimized estimation strategies surpasses the heterodyne limit for a wide range of optical powers without correcting for detection efficiency with a moderate number of adaptive measurement steps. This is, to our knowledge, the most sensitive single-shot measurement of an unknown phase encoded in optical coherent states.