Quantum Dynamics and Fluctuations in Nonlinear Nanomechanical Systems

纳米机械系统具有重要的基本意义，并且在各种应用中也发挥着越来越重要的作用-包括生物传感，质谱，原子尺度的力检测以及稳定频率源的实现。这种系统的独特和有利的特征在于，它们足够大，使得可以在单个系统中研究振动，同时，它们足够小，以提供能够实现其新颖应用的异常检测灵敏度。由于纳米机械系统的小，量子涨落在其动力学中起着根本性的重要作用，即使在低温下也不可避免。同样重要的是，与系统尺寸相比，振动具有相对较大的振幅;因此，它们可能变得强烈非线性。虽然在过去的几年里已经取得了实质性的进展，主要问题仍然是关于纳米机械系统的波动及其各种后果。解决这些问题需要新的表征工具和新的理论技术。目前，对波动和能量耗散的理解不足限制了纳米机械系统在应用中的性能。这项研究的动机是这一领域尚未开发的丰富资源。它具有双重目的，即研究纳米振动系统的基本物理学，并利用这些系统在一个独特的良好控制和高度敏感的环境中探索非平衡现象。主要研究人员在理论和实验物理学方面的综合专业知识应有助于这些研究取得重大而迅速的进展。该项目还将为研究生和本科生的理论和实验物理跨学科培训提供一个极好的平台。拟议研究的主要重点是：（i）发展新的理论和实验手段，并利用这些手段研究本征频率涨落的谱和统计。这将揭示这些波动背后的物理机制。(ii)研究非线性量子耗散模的Floquet动力学。在这里，特别感兴趣的是在量子相干制度的离散时间平移对称性的自发破缺。还感兴趣的是新类型的量子相干和耗散状态的周期，这是一个多个周期的驱动，以及这些状态之间的过渡，和（iii）探索相互作用引起的耦合，spirally-modulated非线性模式介导的量子和经典的波动破缺。这种对称性破缺应该敏感地依赖于纳米力学模式的连接性--研究人员可以精确地设计这种连接性--并且应该包括诸如时域中的挫折和量子相变等现象，以及在远离热平衡的量子系统的定态中微观电流的发生。该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的知识价值和更广泛的影响审查标准进行评估。

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.