Theory of Quantum Electromechanical Systems

技术总结：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产生的理解。在纳米尺度和更大的结构的力学特性中证明量子力学所描述的行为的探索，对于理解宏观经典世界是如何从量子世界中近似出现的，以及对于推进超灵敏测量技术的最新进展具有重要意义。目前正在进行的实验工作采用光机械或固态机电方案来实现这些目标。在前一种方案中，利用光学腔模式的量子相干特性将典型的大于微尺度的机械柔顺镜驱动到非经典状态，并测量该状态。在后一种方案中，可控量子相干超导器件通过电容耦合或电感耦合将纳米到微尺度的机械谐振器驱动到非经典状态，并测量该状态。本研究项目由三个相互关联的推力组成，这些推力与超导器件方案特别相关，通常称为？量子机电系统？第一个推力将研究放大器动力学中的非线性对于接近位移检测的量子极限的意义，以及使用探测器反作用将机械谐振器冷却到量子基态的相关问题。第二部分研究了在稀释冰箱和低温条件下，隧穿两能级系统缺陷对纳米到微尺度机械谐振器阻尼和退相干率的影响。第三部分将分析产生和检测纳米到微尺度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。该方案涉及将超导量子比特嵌入微波腔中，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一名理论物理研究生提供培训。项目二和项目三是为两名即将升学的大三本科生准备的，他们对量子力学有初步的了解。通过在他们大三和大四期间的项目工作，他们将带着对开放系统量子动力学的相对先进的理解毕业。非技术总结：该奖项支持理论研究和教育，旨在促进我们对经典力学所支配的熟悉世界如何从量子力学看似违反直觉的定律中出现的理解，量子力学描述了原子尺度和更小长度尺度上的现象。在与实验密切相关的情况下，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。这种谐振器装置的操作就像是在由经典力学和量子力学控制的世界之间的一个界面上。对这类系统的研究促进了基础知识的发展，也解决了一些非常实际的问题，包括：测量的基本限制是什么？能制造的最灵敏的测量装置是什么？随着我们的科学和技术向每一个更小的尺度发展，随着电子和机械设备的发展，这类问题变得更加紧迫，这些设备可能只有几个原子在一个或多个维度上，某种程度上有一个方面在量子力学的世界中表现得很明显，而其他方面在经典力学的世界中表现得很明显。本研究将为理论物理的研究生，以及对量子力学有初级认识的本科生提供宝贵的教育经验。通过在大三和大四期间的项目工作，本科生将在毕业时对分水岭动力学有一个相对深入的了解。在经典力学和量子力学之间。

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.