Cascaded Optomechanical Sensing for Small Signals

TL;DR

This work tackles the problem of detecting extremely weak forces with high sensitivity by proposing a cascaded network of optomechanical sensors connected via a unidirectional optical bus. The main idea is to coherently average the phase information imprinted on each mechanical element, achieving Heisenberg-like scaling in the ideal lossless limit without entanglement, while remaining robust to decoherence in practice. The authors develop a detailed theoretical framework across stroboscopic and continuous-wave regimes, derive SNR bounds via Gaussian-state QFI, and show how losses introduce an optimal number of sensors, $N_{ m opt}$. They also outline three application domains—dark matter detection, gravitational waves, and gravitational fields of ultra-relativistic matter at the LHC—demonstrating the scheme’s potential to enable precision sensing in fundamental physics. The work provides a practical, resource-efficient path to precision force sensing by leveraging coherent light-matter interactions and outlines clear directions for future experimental and theoretical exploration.

Abstract

We propose a sensing scheme for detecting weak forces that achieves Heisenberg-limited sensitivity without relying on entanglement or other non-classical resources. Our scheme utilizes coherent averaging across a chain of N optomechanical cavities, unidirectionally coupled via a laser beam. As the beam passes through the cavities, it accumulates phase shifts induced by a common external force acting on the mechanical elements. Remarkably, this fully classical approach achieves the sensitivity scaling typically associated with quantum-enhanced protocols, providing a robust and experimentally feasible route to precision sensing. Potential applications range from high-sensitivity gravitational field measurements at the Large Hadron Collider to probing dark matter interactions and detecting gravitational waves. This work opens a new pathway for leveraging coherent light-matter interactions for force sensing.

Figures (3)

• Figure 1: Sketch of the cascaded system with $N$ optomechanical cavities. An input optical pulse enters the first cavity and, using suitable optical elements (quarter-wave plates (QWPs) and polarizing beam splitters (PBSs)), is directed through all subsequent cavities before reaching the detector. During its propagation, the pulse interacts with each mechanical resonator, acquiring a phase shift that cumulatively encodes the contributions from all $N$ systems.
• Figure 2: Plot of the ratio of the upper bounds for the coherent and incoherent signal to noise ratios $\text{SNR}_{\rm CR}(N)$ and $\text{SNR}_{\rm CR, incoh}(N)$. In the ideal case of no losses (blue dots) the ratio increases indefinitely proportionally to $\sqrt{N}$. As losses are introduced (yellow dots $\eta=0.9$, green dots $\eta=0.8$, red dots $\eta=0.7$) there is an interplay between the coherent accumulation of the signal and decoherence which leads to an optimal number of systems $N_{\rm opt}$ above which the advantage is lost, and the SNR decreases. Higher values of losses correspond to lower SNR-ratios and smaller $N_{opt}$.
• Figure 3: Plots of the optimal number of sensors $N_{\rm opt}$ and the maximal SNR ratio $\text{SNR}_{\rm CR}(N_{\rm opt})/\text{SNR}_{\rm CR, incoh}(N_{\rm opt})$ as a function of the loss from the light field between the sensors $1-\eta$ from $\eta=0.999$ to $\eta=0.8$.