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Networks of nonlinear oscillators can exhibit complex collective behaviour ranging from synchronised states to chaos. Here, we simulate the dynamics of three coupled Duffing oscillators whose multiple equilibrium states can be used for information processing and storage. Our analysis reveals that even for this small network, there is the emergence of an error correcting phase where the system autonomously corrects errors from random impulses. The system has several surprising and attractive features, including dynamic isolation of resonators exposed to extreme impulses and the ability to correct simultaneous errors. The existence of an error correcting phase opens the prospect of fault-tolerant information storage, with particular applications in nanomechanical computing.

Integrated acoustic circuits leverage guided acoustic waves for applications ranging from radio-frequency filters to quantum state transfer, biochemical sensing and nanomechanical computing. In many applications it is desirable to have a method for unidirectional acoustic wave emission. In this work we demonstrate directional emission in an integrated single-mode, on-chip membrane waveguide, demonstrating over 99.9% directional suppression and reconfigurable directionality. This avoids both loss and unwanted crosstalk, allowing the creation of more complex and compact phononic circuits.

The rise of globalisation has led to a sharp increase in international trade, with high volumes of containers, goods and items moving across the world. Unfortunately, these trade pathways also facilitate the movement of unwanted pests, weeds, diseases, and pathogens. Each item could contain biosecurity risk material, but it is impractical to inspect every item. Instead, inspection efforts typically focus on high risk items. However, low risk does not imply no risk. It is crucial to monitor the low risk pathways to ensure that they are and remain low risk. To do so, many approaches would seek to estimate the risk to some precision, but the lower the risk, the more samples needed to estimate the risk. On a low-risk pathway that can be afforded more limited inspection resources, it makes more sense to assign fewer samples to the lower risk activities. We approach the problem by introducing two thresholds. Our method focuses on letting us know whether the risk is below certain thresholds, rather than estimating the risk precisely. This method also allows us to detect a significant change in risk. Our approach typically requires less sampling than previous methods, while still providing evidence to regulators to help them efficiently and effectively allocate inspection effort., Comment: 12 + 2 pages, 8 figures, 2 tables

We propose the Optomechanical Dark-matter INstrument (ODIN), based on a new method for the direct detection of low-mass dark matter. We consider dark matter interacting with superfluid helium in an optomechanical cavity. Using an effective field theory, we calculate the rate at which dark matter scatters off phonons in a highly populated, driven acoustic mode of the cavity. This scattering process deposits a phonon into a second acoustic mode in its ground state. The deposited phonon ($\mu$eV range) is then converted to a photon (eV range) via an optomechanical interaction with a pump laser. This photon can be efficiently detected, providing a means to sensitively probe keV scale dark matter. We provide realistic estimates of the backgrounds and discuss the technical challenges associated with such an experiment. We calculate projected limits on dark matter-nucleon interactions for dark matter masses ranging from 0.5 to 300 keV and estimate that a future device could probe cross-sections as low as $\mathcal{O}(10^{-32})$ cm$^2$., Comment: 7 pages, 4 figures + appendices; v2: journal version

National governments use border information to efficiently manage the biosecurity risk presented by travel and commerce. In the Australian border biosecurity system, data about cargo consignments are collected from records of directions: that is, the records of actions taken by the biosecurity regulator. This data collection is complicated by the way directions for a given entry are recorded. An entry is a collection of import lines where each line is a single type of item or commodity. Analysis is simple when the data are recorded in line mode: the directions are recorded individually for each line. The challenge comes when data are recorded in container mode, because the same direction is recorded against each line in the entry. In other words, if at least one line in an entry has a non-compliant inspection result, then all lines in that entry are recorded as non-compliant. Therefore, container mode data creates a challenge for estimating the probability that certain items are non-compliant, because matching the records of non-compliance to the line information is impossible. We develop a statistical model to use container mode data to help inform biosecurity risk of items. We use asymptotic analysis to estimate the value of container mode data compared to line mode data, do a simulation study to verify that we can accurately estimate parameters in a large dataset, and we apply our methods to a real dataset, for which important information about the risk of non-compliance is recovered using the new model.

When confined within an optical cavity, light can exert strong radiation pressure forces. Combined with dynamical backaction, this enables important processes such as laser cooling, and applications ranging from precision sensors to quantum memories and interfaces. However, the magnitude of radiation pressure forces is constrained by the energy mismatch between photons and phonons. Here, we overcome this barrier using entropic forces arising from the absorption of light. We show that entropic forces can exceed the radiation pressure force by eight orders of magnitude, and demonstrate this using a superfluid helium third-sound resonator. We develop a framework to engineer the dynamical backaction from entropic forces, applying it to achieve phonon lasing with a threshold three orders of magnitude lower than previous work. Our results present a pathway to exploit entropic forces in quantum devices, and to study nonlinear fluid phenomena such as turbulence and solitons., Comment: Main text is 10 pages, 5 figures. Supplements is 21 pages, 11 figures

Nanomechanical computers promise robust, low energy information processing. However, to date, electronics have generally been required to interconnect gates, while no scalable, purely nanomechanical approach to computing has been achieved. Here, we demonstrate a nanomechanical logic gate in a scalable architecture. Our gate uses the bistability of a nonlinear mechanical resonator to define logical states. These states are efficiently coupled into and out of the gate via nanomechanical waveguides, which provide the mechanical equivalent of electrical wires. Crucially, the input and output states share the same spatiotemporal characteristics, so that the output of one gate can serve as the input for the next. Our architecture is CMOS compatible, while realistic miniaturisation could allow both gigahertz frequencies and an energy cost that approaches the fundamental Landauer limit. Together this presents a pathway towards large-scale nanomechanical computers, as well as neuromorphic networks able to simulate computationally hard problems and interacting many-body systems., Comment: Manuscript 11 pages 5 figures, includes supplementary information 11 pages 6 figures

This work introduces a comprehensive approach to assess the sensitivity of model outputs to changes in parameter values, constrained by the combination of prior beliefs and data. This novel approach identifies stiff parameter combinations strongly affecting the quality of the model-data fit while simultaneously revealing which of these key parameter combinations are informed primarily by the data or are also substantively influenced by the priors. We focus on the very common context in complex systems where the amount and quality of data are low compared to the number of model parameters to be collectively estimated, and showcase the benefits of this technique for applications in biochemistry, ecology, and cardiac electrophysiology. We also show how stiff parameter combinations, once identified, uncover controlling mechanisms underlying the system being modeled and inform which of the model parameters need to be prioritized in future experiments for improved parameter inference from collective model-data fitting.

Nanomechanical circuits for transverse acoustic waves promise to enable new approaches to computing, precision biochemical sensing and many other applications. However, progress is hampered by the lack of precise control of the coupling between nanomechanical elements. Here, we demonstrate virtual-phonon coupling between transverse mechanical elements, exploiting tunnelling through a zero-mode acoustic barrier. This allows the construction of large-scale nanomechanical circuits on a silicon chip, for which we develop a new scalable fabrication technique. As example applications, we build mode-selective acoustic mirrors with controllable reflectivity and demonstrate acoustic spatial mode filtering. Our work paves the way towards applications such as fully nanomechanical computer processors and distributed nanomechanical sensors, and to explore the rich landscape of nonlinear nanomechanical dynamics., Comment: 9 pages, 6 figures

Scientific knowledge and advances are a cornerstone of modern society. They improve our understanding of the world we live in and help us navigate global challenges including emerging infectious diseases, climate change and the biodiversity crisis. For any scientist, whether they work primarily in fundamental knowledge generation or in the applied sciences, it is important to understand how science fits into a decision-making framework. Decision science is a field that aims to pinpoint evidence-based management strategies. It provides a framework for scientists to directly impact decisions or to understand how their work will fit into a decision process. Decision science is more than undertaking targeted and relevant scientific research or providing tools to assist policy makers; it is an approach to problem formulation, bringing together mathematical modelling, stakeholder values and logistical constraints to support decision making. In this paper we describe decision science, its use in different contexts, and highlight current gaps in methodology and application. The COVID-19 pandemic has thrust mathematical models into the public spotlight, but it is one of innumerable examples in which modelling informs decision making. Other examples include models of storm systems (eg. cyclones, hurricanes) and climate change. Although the decision timescale in these examples differs enormously (from hours to decades), the underlying decision science approach is common across all problems. Bridging communication gaps between different groups is one of the greatest challenges for scientists. However, by better understanding and engaging with the decision-making processes, scientists will have greater impact and make stronger contributions to important societal problems.

The ability to tune the wavelength of light emission on a silicon chip is important for scalable photonic networks, distributed photonic sensor networks and next generation computer architectures. Here we demonstrate light emission in a chip-scale optomechanical device, with wide tunablity provided by a combination of radiation pressure and photothermal effects. To achieve this, we develop an optically active double-disk optomechanical system through implantation of erbium ions. We observe frequency tuning of photoluminescence in the telecommunications band with a wavelength range of 520 pm, green upconversion lasing with a threshold of $340\pm 70 \; \mu$W, and optomechanical self-pulsing caused by the interplay of radiation pressure and thermal effects. These results provide a path towards widely-tunable micron-scale lasers for photonic networks., Comment: Main text 7 pages, 5 figures; Appendix 4 pages, 4 figures

Brillouin systems operating in the quantum regime have recently been identified as a valuable tool for quantum information technologies and fundamental science. However, reaching the quantum regime is extraordinarily challenging, owing to the stringent requirements of combining low thermal occupation with low optical and mechanical dissipation, and large coherent phonon-photon interactions. Here, we propose an on-chip liquid based Brillouin system that is predicted to exhibit ultra-high coherent phonon-photon coupling with exceptionally low acoustic dissipation. The system is comprised of a silicon-based "slot" waveguide filled with superfluid helium. This type of waveguide supports optical and acoustical traveling waves, strongly confining both fields into a subwavelength-scale mode volume. It serves as the foundation of an on-chip traveling wave Brillouin resonator with a single photon optomechanical coupling rate exceeding $240$kHz. Such devices may enable applications ranging from ultra-sensitive superfluid-based gyroscopes, to non-reciprocal optical circuits. Furthermore, this platform opens up new possibilities to explore quantum fluid dynamics in a strongly interacting condensate., Comment: 11 pages, 4 figures, 1 table

We show that highly confined superfluid films are extremely nonlinear mechanical resonators, offering the prospect to realize a mechanical qubit. Specifically, we consider third-sound surface waves, with nonlinearities introduced by the van der Waals interaction with the substrate. Confining these waves to a disk, we derive analytic expressions for the cubic and quartic nonlinearities and determine the resonance frequency shifts they introduce. We predict single-phonon shifts that are three orders of magnitude larger than in current state-of-the-art nonlinear resonators. Combined with the exquisitely low intrinsic dissipation of superfluid helium and the strongly suppressed acoustic radiation loss in phononic crystal cavities, we predict that this could allow blockade interactions between phonons as well as two-level-system-like behavior. Our work provides a new pathway towards extreme mechanical nonlinearities, and towards quantum devices that use mechanical resonators as qubits., Comment: 14 pages, 6 figures

Dual control denotes a class of control problems where the parameters governing the system are imperfectly known. The challenge is to find the optimal balance between probing, i.e. exciting the system to understand it more, and caution, i.e. selecting conservative controls based on current knowledge to achieve the control objective. Dynamic programming techniques can achieve this optimal trade-off. However, while dynamic programming performs well with discrete state and time, it is not well-suited to problems with continuous time-frames or continuous or unbounded state spaces. Another limitation is that multidimensional states often cause the dynamic programming approaches to be intractable. In this paper, we investigate whether continuous-time optimal control tools could help circumvent these caveats whilst still achieving the probing-caution balance. We introduce a stylized problem where the state is governed by one of two differential equations. It is initially unknown which differential equation governs the system, so we must simultaneously determine the true differential equation and control the system to the desired state. We show how this problem can be transformed to apply optimal control tools, and compare the performance of this approach to a dynamic programming approach. Our results suggest that the optimal control algorithm rivals dynamic programming on small problems, achieving the right balance between aggressive and smoothly varying controls. In contrast to dynamic programming, the optimal control approach remains tractable when several states are to be controlled simultaneously., Comment: 25 pages, 3 figures