Validating an algebraic approach to characterizing resonator networks.

Resonator networks are ubiquitous in natural and engineered systems, such as solid-state materials, electrical circuits, quantum processors, and even neural tissue. To understand and manipulate these networks it is essential to characterize their building blocks, which include the mechanical analogs of mass, elasticity, damping, and coupling of each resonator element. While these mechanical parameters are typically obtained from response spectra using least-squares fitting, this approach requires a priori knowledge of all parameters and is susceptible to large error due to convergence to local minima. Here we validate an alternative algebraic means to characterize resonator networks with no or minimal a priori knowledge. Our approach recasts the equations of motion of the network into a linear homogeneous algebraic equation and solves the equation with a set of discrete measured network response vectors. For validation, we employ our approach on noisy simulated data from a single resonator and a coupled resonator pair, and we characterize the accuracy of the recovered parameters using high-dimension factorial simulations. Generally, we find that the error is inversely proportional to the signal-to-noise ratio, that measurements at two frequencies are sufficient to recover all parameters, and that sampling near the resonant peaks is optimal. Our simple, powerful tool will enable future efforts to ascertain network properties and control resonator networks in diverse physical domains.

Coupled Nanomechanical Graphene Resonators: A Promising Platform for Scalable NEMS Networks.

Arrays of coupled nanoelectromechanical resonators are a promising foundation for implementing large-scale network applications, such as mechanical-based information processing and computing, but their practical realization remains an outstanding challenge. In this work, we demonstrate a scalable platform of suspended graphene resonators, such that neighboring resonators are persistently coupled mechanically. We provide evidence of strong coupling between neighboring resonators using two different tuning methods. Additionally, we provide evidence of inter-resonator coupling of higher-order modes, demonstrating the rich dynamics that can be accessed with this platform. Our results establish this platform as a viable option for realizing large-scale programmable networks, enabling applications such as phononic circuits, tunable waveguides, and reconfigurable metamaterials.

Deterministic Quantum Emitter Formation in Hexagonal Boron Nitride via Controlled Edge Creation.

Quantum emitters (QEs) in 2D hexagonal boron nitride (hBN) are extremely bright and are stable at high temperature and under harsh chemical conditions. Because they reside within an atomically thin 2D material, these QEs have a unique potential to couple strongly to hybrid optoelectromechanical and quantum devices. However, this potential for coupling has been underexplored because of challenges in nanofabrication and patterning of hBN QEs. Motivated by recent studies showing that QEs in hBN tend to form at edges, we use a focused ion beam (FIB) to mill an array of patterned holes into hBN. Using optical confocal microscopy, we find arrays of bright, localized photoluminescence that match the geometry of the patterned holes. Furthermore, second-order photon correlation measurements on these bright spots reveal that they contain single and multiple QEs. By optimizing the FIB parameters, we create patterned single QEs with a yield of 31%, a value close to Poissonian limit. Using atomic force microscopy to study the morphology near emission sites, we find that single QE yield is highest with smoothly milled holes on unwrinkled hBN. This technique dramatically broadens the utility and convenience of hBN QEs and achieves a vital step toward the facile integration of the QEs into large-scale photonic, plasmonic, nanomechanical, or optoelectronic devices.

Electron spin resonance of nitrogen-vacancy centers in optically trapped nanodiamonds.

Using an optical tweezers apparatus, we demonstrate three-dimensional control of nanodiamonds in solution with simultaneous readout of ground-state electron-spin resonance (ESR) transitions in an ensemble of diamond nitrogen-vacancy color centers. Despite the motion and random orientation of nitrogen-vacancy centers suspended in the optical trap, we observe distinct peaks in the measured ESR spectra qualitatively similar to the same measurement in bulk. Accounting for the random dynamics, we model the ESR spectra observed in an externally applied magnetic field to enable dc magnetometry in solution. We estimate the dc magnetic field sensitivity based on variations in ESR line shapes to be approximately 50 µT/√Hz. This technique may provide a pathway for spin-based magnetic, electric, and thermal sensing in fluidic environments and biophysical systems inaccessible to existing scanning probe techniques.

Aggregation behavior and chromonic liquid crystal properties of an anionic monoazo dye.

X-ray scattering and various optical techniques are utilized to study the aggregation process and chromonic liquid crystal phase of the anionic monoazo dye Sunset Yellow FCF. The x-ray results demonstrate that aggregation involves pi-pi stacking of the molecules into columns, with the columns undergoing a phase transition to an orientationally ordered chromonic liquid crystal phase at high dye concentration. Optical absorption measurements on dilute solutions reveal that the aggregation takes place at all concentrations, with the average aggregation number increasing with concentration. A simple theory based on the law of mass action and an isodesmic aggregation process is in excellent agreement with the experimental data and yields a value for the "bond" energy between molecules in an aggregate. Measurements of the birefringence and order parameter are also performed as a function of temperature in the chromonic liquid crystal phase. The agreement between these results and a more complicated theory of aggregation is quite reasonable. Overall, these results both confirm that the aggregation process for some dyes is isodesmic and provide a second example of a well-characterized chromonic system.