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A sensitive model captures the reactivity cliffs but overfit to yield outliers. On the other hand, a robust model disregards the yield outliers but underfits the reactivity cliffs.

 

Squeezed light has long been used to enhance the precision of a single optomechanical sensor. An emerging set of proposals seeks to use arrays of optomechanical sensors to detect weak distributed forces, for applications ranging from gravity-based subterranean imaging to dark matter searches; however, a detailed investigation into the quantum-enhancement of this approach remains outstanding. Here, we propose an array of entanglement-enhanced optomechanical sensors to improve the broadband sensitivity of distributed force sensing. By coherently operating the optomechanical sensor array and distributing squeezing to entangle the optical fields, the array of sensors has a scaling advantage over independent sensors (i.e.,$$\sqrt{M}\to M$$$\sqrt{M}\to M$, whereMis the number of sensors) due to coherence as well as joint noise suppression due to multi-partite entanglement. As an illustration, we consider entanglement-enhancement of an optomechanical accelerometer array to search for dark matter, and elucidate the challenge of realizing a quantum advantage in this context.

 

Optomechanical systems have been exploited in ultrasensitive measurements of force, acceleration and magnetic fields. The fundamental limits for optomechanical sensing have been extensively studied and now well understood—the intrinsic uncertainties of the bosonic optical and mechanical modes, together with backaction noise arising from interactions between the two, dictate the standard quantum limit. Advanced techniques based on non-classical probes, in situ ponderomotive squeezed light and backaction-evading measurements have been developed to overcome the standard quantum limit for individual optomechanical sensors. An alternative, conceptually simpler approach to enhance optomechanical sensing rests on joint measurements taken by multiple sensors. In this configuration, a pathway to overcome the fundamental limits in joint measurements has not been explored. Here we demonstrate that joint force measurements taken with entangled probes on multiple optomechanical sensors can improve the bandwidth in the thermal-noise-dominant regime or the sensitivity in the shot-noise-dominant regime. Moreover, we quantify the overall performance of entangled probes with the sensitivity–bandwidth product and observe a 25% increase compared with that of classical probes. The demonstrated entanglement-enhanced optomechanical sensors would enable new capabilities for inertial navigation, acoustic imaging and searches for new physics. 

Inorganic salts usually demonstrate simple phasal behaviors in dilute aqueous solution mainly involving soluble (homogeneous) and insoluble (macrophase separation) scenarios. Herein, we report the discovery of complex phase behavior involving multiple phase transitions of clear solution – macrophase separation – gelation – solution – macrophase separation in the dilute aqueous solutions of a structurally well-defined molecular cluster [Mo₇O₂₄]⁶⁻macroanions with the continuous addition of Fe³⁺. No chemical reaction was involved. The transitions are closely related to the strong electrostatic interaction between [Mo₇O₂₄]⁶⁻and their Fe³⁺counterions, the counterion-mediated attraction and the consequent charge inversion, leading to the formation of linear/branched supramolecular structures, as confirmed by experimental results and molecular dynamics simulations. The rich phase behavior demonstrated by the inorganic cluster [Mo₇O₂₄]⁶⁻expands our understanding of nanoscale ions in solution.