Quantum Dynamics and Fluctuations in Nonlinear Nanomechanical Systems

纳米力学系统具有重要的基础意义，并且在各种应用中发挥着越来越重要的作用，包括生物传感、质谱分析、原子尺度上的力检测和稳定频率源的实现。这种系统的独特和有利的特点是，它们足够大，可以在单个系统中研究振动，同时，它们足够小，可以提供特殊的检测灵敏度，从而实现它们的新应用。由于纳米力学系统的体积小，量子涨落在其动力学中起着至关重要的作用，即使在低温下也不可避免。同样基本的是，与系统大小相比，振动的幅度相对较大；因此，它们会变得非常非线性。虽然在过去的几年中已经取得了实质性的进展，但关于纳米机械系统的波动及其各种后果的主要问题仍然存在。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不了解限制了纳米机械系统在应用中的性能。这项研究的动机是该领域尚未开发的丰富性。它的双重目标是研究纳米级振动系统的底层物理，并利用这些系统在一个独特的良好控制和高灵敏度的环境中探索非平衡现象。理论物理学和实验物理学的主要研究人员的综合专业知识应促进这些研究取得重大和迅速的进展。为理论物理和实验物理研究生和本科生的跨学科培养提供一个良好的平台。提出的研究重点是：(1)发展新的理论和实验手段，并利用这些手段研究特征频率波动的谱和统计。这将揭示这些波动背后的物理机制。（ii）探索周期驱动非线性量子耗散模式的Floquet动力学。这里，特别令人感兴趣的是量子相干体系中离散时间平移对称性的自发破缺。同样令人感兴趣的是具有周期的新型量子相干和耗散状态，这是驱动周期的倍数，以及这些状态之间的转换，以及（iii）探索由量子和经典波动介导的耦合周期性调制非线性模式的相互作用诱导的对称破缺。这种对称性破缺应该敏感地依赖于纳米力学模式的连通性——研究人员可以精确地设计——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定态中发生的微观电流。该奖项反映了美国国家科学基金会的法定使命，并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，被认为值得支持。

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.