Optimal single-mode squeezing for beam displacement sensing

2025-09-14

AI Summary

In lateral displacement sensing, quantum-limited performance degrades due to diffraction loss and multimode effects. Method: This paper proposes a single-mode squeezed-state detection scheme that jointly optimizes spatial mode profile, squeezing degree, and coherent amplitude. By approximating the infinite-mode optical field as a three-mode linear interaction model and integrating quantum estimation theory with Gaussian state analysis, we systematically derive the optimal detection strategy under photon loss. Results: Theoretical analysis reveals that, in the high-energy limit, the two-mode homodyne receiver becomes asymptotically optimal. Our designed scheme—employing single-mode squeezed light combined with two-mode homodyne detection—significantly outperforms classical coherent-state probes. It achieves sub-shot-noise precision in small-displacement measurements, approaching the quantum Cramér–Rao bound. This work establishes a practical pathway toward quantum-enhanced lateral displacement sensing while mitigating multimode-induced decoherence and loss penalties.

Technology Category

• Search and Optimization: Learning to Search
• Intelligent Robots: State Estimation
• Machine Learning: Quantum Machine Learning

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work

Abstract

Estimation of an optical beam's transverse displacement is a canonical imaging problem fundamental to numerous optical imaging and sensing tasks. Quantum enhancements to the measurement precision in this problem have been studied extensively. However, previous studies have neither accounted for diffraction loss in full generality, nor have they addressed how to jointly optimize the spatial mode and the balance between squeezing and coherent amplitude. Here we show that, in the small-displacement limit, the seemingly intractable infinite-spatial-mode problem can be reduced to a compact three-mode interaction framework. We quantify the improvement afforded by an optimized single-spatial-mode Gaussian-state probe over the optimal classical laser probe, and show that a two-spatial-mode homodyne receiver is asymptotically optimal for the former in the limit of high probe energy. Our findings reveal a strategy for identifying quantum-optimal probes in the presence of generic multimode linear probe-target interaction and photon loss.

Problem

• Optimizing quantum-enhanced optical beam displacement sensing precision
• Addressing diffraction loss and joint spatial mode optimization
• Developing quantum-optimal probes with multimode linear interactions

Innovation

• Three-mode interaction framework for beam displacement
• Optimized single-spatial-mode Gaussian-state probe
• Two-spatial-mode homodyne receiver asymptotically optimal