Synchronization of Nanomechanical Oscillators

California Institute Of Technology, Pasadena CA

Investigators

Abstract

TECHNICAL SUMMARY This award supports a theoretical project to study the phenomenon of synchronization in collections of disparate oscillators, with a special focus on the application to arrays of nanomechanical oscillators. Synchronization is the formation of collective states of coherent motion of oscillators with diverse intrinsic frequencies, through the interaction between the elements and their nonlinear behavior. It represents a particularly interesting and practically important collective behavior of a driven, non-equilibrium system. A focus of the research will be the synchronization of large arrays of coupled nonlinear mechanical devices at the scale of tens to a hundred nanometers with quantitatively understood and controllable coupling and nonlinearity. These nanomechanical systems possess a unique combination of properties, including small size, high frequencies, and easily accessible and controllable nonlinearities, which make them extremely well-suited for realizing an experimental system of large coupled oscillator arrays, to test preexisting theory and to provoke further extensions. This project is a renewed theoretical study of synchronization exploiting ideas and methods from statistical mechanics, dynamical systems theory, and pattern formation theory, motivated by the prospect of experimental realization in nanomechanical systems. The project will have two main thrusts. The first is a quantitative analysis of the systems of a few nanomechanical oscillators that will likely be the first target of experiment. This effort will help the design of experimental systems, suggest protocols for experimental measurements, and will test the results as they become available against the theoretical models. The second thrust will be a study of the basic theory of large arrays of oscillators, extending the understanding particularly in directions relevant to future experimental work on large arrays of nanomechanical oscillators. A variety of systems will be investigated, including ones with short range, power-law long range, and all-to-all coupling, using techniques such as real space renormalization group methods, expansions analogous to spin-wave methods in magnets, and numerical simulations. The role of spatial dimension, the importance of topological defects, and effects of noise driven fluctuations, will also be investigated. The proposed study of synchronization in nanomechanical oscillators has important technological applications, will have a broad impact on diverse areas of basic science, and provides unique educational opportunities, particularly for training graduate students. NON-TECHNICAL SUMMARY This award supports a theoretical project to study the phenomenon of synchronization in collections of disparate oscillators, with a special focus on the application to arrays of nanomechanical oscillators. This research project involves the study of systems of oscillators, each with different intrinsic frequencies. Oscillators of particular interest are many tiny vibrating beams some ten thousand to a hundred thousand times smaller than the diameter of a human hair, the nanometer scale. Synchronization occurs when the oscillators reach a state where their motion is in lock-step. This is a consequence of the interactions among the oscillators or vibrating beams. Synchronization occurs in many different contexts in nature and in artificially fabricated systems. Large arrays of coupled mechanical devices at the scale of ten to a hundred nanometers lie on the forefront of lithographic fabrication technology, provide a unique laboratory to test theory, and have many potential technological applications such as exquisitely precise clocks, and sensitive detectors even down to the single molecule level. The collective behavior of disparate oscillators is also important in wide areas of basic science, including the dynamics of neurons in the brain and muscle cells in the heart, and the coherent grouping of lasers to make high power sources. A deeper understanding of the general phenomenon of synchronization gained from the careful study of nanomechanical systems will impact these and other areas of research. This award provides unique educational opportunities, particularly for training graduate students. It represents fundamental research and contributes to the intellectual foundation of future device and nanoscale device technologies.