The Quantum-Classical Correspondence for Nonlinear Resonator Systems

技术总结该奖项支持关于非线性谐振器的理论研究和教育，以及微观量子世界如何通向我们日常经验的宏观经典世界。非线性谐振器系统的量子行为与经典动力学行为之间存在着质的差异。这些相应的量子-经典差异的性质和程度都取决于谐振器耦合到的环境和测量探测器的强度和类型。近年来，与高品质因数机械或超导微波谐振器强耦合的低消相干电子器件的发展为研究这些非线性谐振器-环境系统的量子经典对应提供了一个理想的机会。这样的研究对于理解宏观经典世界是如何通过近似从量子世界出现的，以及对于开发利用共振器系统非线性的量子限制测量方案的非常实际的任务是相关的。PI研究由两个非线性共振器项目组成。在第一个项目中，PI将为最近和计划中的实验发展理论，这些实验研究宏观机械谐振器与通过嵌入在谐振器中的量子点接触隧穿电子的压电式相互作用的动力学。在第二个项目中，PI将为正在进行的实验开发理论，这些实验将研究一种新型的、低噪声的超导微波谐振器方案的动力学。该方案将为一名研究生和两名本科生提供理论物理工艺方面的培训，获得多体理论、介观量子物理、非线性动力学、量子光学和高级计算技术等领域的专业知识。该奖项支持理论研究和教育，以研究处于量子力学世界边界的谐振器的运行，量子力学世界控制着我们每天所经历的行为电子、原子和分子以及经典力学世界。机械谐振器的常见例子包括摆动的钟摆或拨动时以特征频率振动的梁。为了接近量子世界，PI将研究的机械谐振器是微小的光束，比人类头发的宽度小约1万倍。PI将研究更复杂的谐振器例子，涉及机械、电气和光学系统，这些系统是专门为探索量子力学世界中经典世界的出现而设计的。这项研究是在与实验密切相关的情况下进行的，并建立在凝聚态和材料物理学的基本原理基础上，以检验和促进对世界的基本理解。这项研究的一个主题是推进我们对量子力学对如何准确测量物理量的限制的基本理解。

TECHNICAL SUMMARYThis award supports theoretical research and education on nonlinear resonators and the how the microscopic quantum world leads to the macroscopic classical world of our everyday experience. Nonlinear resonator systems can exhibit qualitative differences between their derived quantum and classical dynamical behavior. Both the nature and extent of these corresponding quantum-classical differences depend crucially on the strength and type of environment and measurement probe to which the resonator couples. Recent advances in the development of low-decoherence electronic devices that are strongly coupled to high quality factor mechanical or superconducting microwave resonators present an ideal opportunity to investigate the quantum-classical correspondence for these nonlinear resonator-environment systems. Such an investigation is relevant for understanding how the macroscopic classical world emerges by approximation from the quantum world, as well as for the very practical task to develop quantum-limited measurement schemes that exploit the resonator system nonlinearities.The PI research consists of two nonlinear resonator projects. In project one, the PI will develop the theory for recent and planned experiments that investigate the dynamics of a macroscopic mechanical resonator interacting piezoelectrically with electrons tunneling through a quantum point contact that is embedded in the resonator. In project two, the PI will develop the theory for experiments underway that investigate the dynamics of a novel, low noise superconducting microwave resonator scheme with embedded Josephson junction device.The projects will provide training for one graduate student and two undergraduate students in the craft of theoretical physics, gaining expertise in such areas as many body theory, mesoscopic quantum physics, nonlinear dynamics, quantum optics, and advanced computing techniques.NONTECHNICAL SUMMARYThis award supports theoretical research and education to study the operation of resonators that lie precariously at the boundary of the world of quantum mechanics that governs the behavior electrons, atoms, and molecules, and the world of classical mechanics that we experience every day. Common examples of mechanical resonators include a pendulum that swings or a beam that vibrates at a characteristic frequency when plucked. To approach the quantum world, the mechanical resonators the PI will investigate are tiny beams some 10,000 times smaller than the width of a human hair. The PI will investigate more complex examples of resonators involving mechanical, electrical, and optical systems that are specially designed to probe the emergence of the classical world from the quantum mechanical world. The research is carried out in close connection to experiments and builds on fundamental principles of condensed matter and materials physics to test and to advance fundamental understanding of the world. One theme of the research is to advance our fundamental understanding of the limitations quantum mechanics places on how accurately physical quantities can be measured.