Quantum Dynamics and Fluctuations in Nonlinear Nanomechanical Systems

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Nanomechanical systems are of significant fundamental interest and are also playing an increasingly important role in various applications - including biosensing, mass spectrometry, force detection at the atomic scale, and realization of stable frequency sources. The unique and advantageous feature of such systems is that they are sufficiently large that the vibrations can be studied in an individual system while, at the same time, they are sufficiently small as to provide that exceptional detection sensitivity enabling their novel applications. Because of the smallness of nanomechanical systems, a fundamentally important role in their dynamics is played by quantum fluctuations, which are unavoidable even for low temperatures. Also fundamental is that vibrations have a relatively large amplitude compared to the system size; as a consequence, they can become strongly nonlinear. Although substantial progress has been made over the last few years, major questions remain concerning the fluctuations of nanomechanical systems and their various consequences. Addressing these questions requires new characterization tools and new theoretical techniques. Poorly understood fluctuations and energy dissipation currently limit the performance of nanomechanical systems in applications. The proposed research is motivated by the largely untapped richness of this field. It has the dual aims of studying the underlying physics of nanoscale vibrational systems and using these systems to explore nonequilibrium phenomena in a uniquely well-controlled and highly-sensitive setting. The combined expertise of the principal investigators in theoretical and experimental physics should facilitate significant and rapid progress in these studies. The project should also provide an excellent platform for cross-disciplinary training of graduate and undergraduate students in theoretical and experimental physics.The major emphases of the proposed research are: (i) To develop new theoretical and experimental means and to study, using these means, both the spectra and the statistics of eigenfrequency fluctuations. This should reveal the physical mechanisms underlying these fluctuations. (ii) To explore Floquet dynamics of periodically-driven nonlinear quantum dissipative modes. Here, of particular interest is the spontaneous breaking of the discrete time-translation symmetry in the quantum-coherent regime. Also of interest are new types of quantum-coherent and dissipative states with a period, which is a multiple of the period of the driving, as well as the transitions between these states, and (iii) To explore interaction-induced symmetry-breaking for coupled, periodically-modulated nonlinear modes that is mediated by quantum and classical fluctuations. This symmetry breaking should sensitively depend on the connectivity of the nanomechanical modes - which the investigators can precisely engineer - and should encompass phenomena such as frustration and quantum phase transitions in the time domain, as well as the occurrence of microscopic currents in the stationary state of quantum systems far from thermal equilibrium.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.