Harnessing the Spatial Degree of Freedom for Quantum Photonic Sensors

Abstract

Quantum information and estimation theory provide a systematic framework for analyzing fundamental performance limits in optical sensing tasks and have proven helpful in the design of novel sensor systems. In this dissertation, we analyze a canonical imaging task, that of estimating the transverse displacement of an optical beam, while optimally using the rich spatial-mode degree of freedom, the quantum state(s) in which those modes are excited, and the design of novel receivers that may employ optical pre-processing of the target-return information-bearing light. We theoretically analyze this task using a free-space propagation channel with soft-Gaussian apertures at both the transmitter and the receiver sides, to allow for an analytical treatment of diffraction loss. Using a quantum Fisher information (QFI) analysis, we find the optimal spatial mode—to excite in either a coherent state (laser-light) or a displaced squeezed state—for a probe with a transmitted-energy constraint, when paired with their respective optimal receiver choices. We also report several alternatives of structured optimal receiver designs, i.e., those whose classical Fisher information (CFI) equals the QFI of the optimal classical or quantum probes. Furthermore, using a CFI analysis, we find the optimal spatial mode to excite a coherent state in, when the receiver employs a pixelated camera. We report preliminary experimental results for the above, wherein our setup is capable of exciting an arbitrary spatial mode in a coherent state with a phase-only spatial light modulator (SLM). Finally, we present the margins of improvement in precision attainable for beam-deflection sensing with the various aforementioned optimized classical and quantum strategies, including a conjecture on the optimal Gaussian spatially-entangled probe. We conclude this dissertation with thoughts on various future directions on theoretical and experimental investigations of quantum enhanced optomechanical sensing and beyond.