The Quantum-Classical Correspondence for Nonlinear Resonator Systems

该奖项支持非线性谐振器的理论研究和教育，以及微观量子世界如何导致我们日常经验的宏观经典世界。非线性谐振系统可以表现出其派生量子和经典动力学行为之间的质的差异。这些相应的量子经典差异的性质和程度关键取决于谐振器耦合的环境和测量探头的强度和类型。与高质量因数机械或超导微波谐振器强耦合的低退相干电子器件的最新进展为研究这些非线性谐振器环境系统的量子-经典对应提供了理想的机会。这样的研究对于理解宏观的经典世界是如何从量子世界通过近似出现的，以及对于开发利用谐振器系统非线性的量子有限测量方案的非常实际的任务是相关的。PI研究包括两个非线性谐振器项目。在项目一中，PI将为近期和计划中的实验发展理论，研究宏观机械谐振器与嵌入在谐振器中的量子点接触的电子通过压电相互作用的动力学。在项目二中，PI将为正在进行的实验发展理论，研究一种新型低噪声超导微波谐振器方案的动力学，该方案具有嵌入式约瑟夫森结装置。这些项目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，使他们获得多体理论、介观量子物理、非线性动力学、量子光学和先进计算技术等领域的专业知识。该奖项支持理论研究和教育，以研究谐振器的操作，这些谐振器位于量子力学世界的边缘，不稳定地控制着我们每天所经历的电子、原子和分子的行为，以及经典力学的世界。机械谐振器的常见例子包括摆动的钟摆或被拨动时以特定频率振动的光束。为了接近量子世界，PI将研究的机械谐振器是比人类头发宽度小1万倍的微小光束。PI将研究更复杂的谐振器例子，涉及机械、电子和光学系统，这些谐振器是专门设计用来探测经典世界从量子力学世界中出现的。这项研究与实验密切相关，并建立在凝聚态物质和材料物理学的基本原理基础上，以测试和推进对世界的基本理解。这项研究的一个主题是促进我们对量子力学对物理量的精确测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.