Theory of Quantum Electromechanical Systems

该奖项支持理论研究和教育，旨在促进对经典动力学如何从量子力学动力学中产生的理解。在纳米尺度和更大结构的力学性质中，探索量子力学所描述的行为对于理解宏观经典世界如何通过量子世界的近似出现以及推进超灵敏测量技术的发展具有根本意义。实验工作目前正在进行中，采用光学机械或固态机电方案来实现这些目标。在前一种方案中，光学腔模式的量子相干性质被用来驱动一个典型的大于微米尺度的机械顺应镜进入非经典状态，以及测量这种状态。在后者的计划中，一个可控的量子相干超导装置驱动纳米到微米尺度的机械谐振器进入非经典状态，通过电容或电感耦合，以及测量这种状态。量子机电系统第一个推力将调查在放大器动力学的非线性接近位移检测的量子极限的意义，以及使用检测器的反作用冷却到其量子基态的机械谐振器的相关问题。第二个突破将解决隧道两级系统缺陷对稀释冰箱和较低温度下纳米至微米级机械谐振器的阻尼和退相干率的贡献。第三个目标将分析产生和检测纳米到微米级机械谐振器的纠缠态和叠加态的方案，并测量它们的退相干率。该方案涉及嵌入微波腔中的超导量子比特，用于量子比特状态控制和读出。这个理论研究项目与实验密切相关。项目一中概述的活动将为理论物理研究生提供培训。项目二和项目三是为两个对量子力学有初步了解的大三学生准备的。通过在大三和大四期间的项目工作，他们将在毕业时对开放系统量子动力学有相对深入的理解。非技术性总结：该奖项支持理论研究和教育，旨在促进我们理解由经典力学支配的熟悉世界是如何从看似违反直觉的量子力学定律中产生的，这些定律描述了原子尺度和更小长度尺度上的现象。与实验密切相关，PI将研究由量子力学规则描述的设备驱动振荡的微小机械谐振器。这类谐振器装置的运作似乎是在由经典力学控制的世界和由量子力学控制的世界之间的一个界面上。对这类系统的研究推进了基础知识，也解决了一些非常实际的问题，包括：测量的基本极限是什么？可以制造的最灵敏的测量设备是什么？随着我们的科学和技术以电子和机械的设备的眼光向每一个更小的长度尺度施压，这类问题变得更加紧迫，在一个或多个维度上可能只有几个原子，并且在某种程度上有一个方面出现在量子力学的世界中，而其他方面则出现在经典力学的世界中。这项研究将为理论物理研究生，以及对量子力学有初步了解的大三本科生。通过在他们的大三和大四的项目工作，本科生毕业时将有一个相对先进的动力学的理解？分裂？经典力学和量子力学之间的联系

Technical Summary:This award supports theoretical research and education with an aim to advance understanding of how classical dynamics arises from quantum mechanical dynamics. The quest to demonstrate behavior described by quantum mechanics in the mechanical properties of nanoscale and larger structures is of fundamental significance for understanding how the macroscopic classical world emerges by approximation from the quantum world, as well as for advancing the state of the art in ultrasensitive measurement technology. Experimental efforts are currently underway that employ either optomechanical or solid state electromechanical schemes to realize these goals. In the former schemes, the quantum coherent nature of optical cavity modes are employed to drive a typically larger-than-micronscale mechanically compliant mirror into a nonclassical state, as well as to measure this state. In the latter schemes, a controllable quantum coherent superconducting device drives a nano-to-micronscale mechanical resonator into a nonclassical state via capacitive or inductive coupling, as well as measures this state.This research project consists of three interrelated thrusts that are particularly relevant to the superconducting device schemes, commonly called ?Quantum Electromechanical Systems.? The first thrust will investigate the significance of nonlinearities in amplifier dynamics for approaching the quantum limit of displacement detection, as well as for the related issue of using detector back-action to cool the mechanical resonator to its quantum ground state. The second thrust will address the contribution of tunneling two level system defects to the damping and decoherence rates of nano-to-micronscale mechanical resonators at dilution fridge and lower temperatures. The third thrust will analyze schemes to generate and detect entangled and superposition states of nano-to-micronscale mechanical resonators, as well as measure their decoherence rates. The schemes involve superconducting qubits embedded within microwave cavities that are employed for both qubit state control and readout. This theoretical research project is closely linked to experiments.The activity outlined in project one will provide training for a graduate student in theoretical physics. Projects two and three are intended for two rising junior undergraduates with an introductory-level understanding of quantum mechanics. Through working on the projects during their junior and senior years, they will graduate with a relatively advanced understanding of open system quantum dynamics.Non-Technical Summary:This award supports theoretical research and education with an aim to advance our understanding of how the familiar world governed by classical mechanics emerges from the seemingly counterintuitive laws of quantum mechanics that describe phenomena on the scale of atoms and across even smaller length scales. In close connection with experiment, the PI will study tiny mechanical resonators that are driven to oscillate by devices that are described by the rules of quantum mechanics. The operation of this sort resonator device lies at what seems like an interface between the world governed by classical mechanics and that governed by quantum mechanics. The study of these kinds of systems advances fundamental knowledge and also addresses some very practical questions, including: What are the fundamental limits of measurement? What is the most sensitive measurement device that can be made? Questions of this kind become more pressing as our science and technology press to every smaller length scales with the vision of devices, electronic and mechanical, that are perhaps only few atoms in one or more dimensions and somehow have one aspect that appears squarely in the world of quantum mechanics and others that appear to be squarely in the world of classical mechanics.This research will provide valuable educational experiences for a graduate student in theoretical physics, as well as for junior undergraduate students with an introductory-level understanding of quantum mechanics. Through working on the projects during their junior and senior years, the undergraduate students will graduate with a relatively advanced understanding of dynamics at the ?divide? between classical and quantum mechanics.