Two-Way Exchange of Quantum Information and Thermodynamic Work with a Nanomechanical Platform

该项目的目的是在涉及能量相干性时，发展对量子系统交换功的理论理解，并将这一理论转化为新的实验平台的具体协议，这些预测可以在该实验平台上进行测试。总的基本目标是回答热力学过程是否以及何时可以从相干性中受益。我们将重点关注的实验平台是一个新的纳米力学实验，它是由牛津大学的阿瑞斯小组建造的。该平台由悬浮在两根金属柱之间的半导体碳纳米管组成，其传导电子同时充当纳米管的源极和漏极，并作为具有明确温度的储热器。栅极电极调节电子进出纳米管的势垒，并且已被证明可以将电流控制到单个电子的水平。该小组目前正在研究如何将相干态编码到电子的自旋谷自由度中。在交变场的驱动下，电子管的机械振荡被证明是与状态强耦合的。电子对纳米管运动所做的功预计可以通过其对谐振LC电路电容的影响来检测。在这个项目中，学生将建立理论模型和预测来量化执行某些量子信息处理任务所需的热力学功，例如兰道尔擦除和从相干中提取功。这将涉及评估关键问题，如“工作到哪里去了”和“应该使用什么熵”来评估量子体制中的信息变化和能量交换。学生还将澄清处理两个或多个非交换量子态是否与处理交换量子态时具有相同的工作平衡。该学生将与牛津大学的实验组密切合作，讨论进展和测量结果，以及我们研究结果的哲学含义。预计这些与量子态/相干相关的工作的首次实验测试可以为量子信息处理的热力学成本带来全新的视角，这是我们希望探索的。埃克塞特理论博士生定期访问牛津的实验组，以及访问格勒诺布尔/马德里的其他团队成员，将成为博士项目的一部分。

The aim of this project is to develop the theoretical understanding of work exchanged by a quantum system when energetic coherence are involved, and translate this theory into concrete protocols for new experimental platforms on which these predictions can be tested. The overall fundamental goal is to answer if and when thermodynamic processes could benefit from making use of coherences. The particular experimental platform that we will focus on is a new nanomechanics experiment that is being built by the Ares group at the University of Oxford. The platform consists of a semiconducting carbon nanotube suspended between two metal pillars, whose conduction electrons act simultaneously as source and drain for the nanotube, and as thermal reservoirs with well-defined temperature. Gate electrodes tune the potential barrier for electrons tunneling into and out of the nanotube, and have been shown to control current to the level of single electrons. The group is currently investigating how to encode coherent states into the electrons' spin-valley degree of freedom. Mechanical oscillations of the tube when driven by an alternating field have been shown to be strongly coupled to the state. Work done by the electron on the nanotube's motion is anticipated to be detectable via its effect on the capacitance of a resonant LC circuit.During this project, the student will build theoretical models and predictions to quantify the thermodynamic work needed to perform certain quantum information processing tasks, such as Landauer erasure and work extraction from coherences. This will involve assessing key issues such as "where did the work go" and "what entropy should one use" to assess information changes and energetic exchanges in the quantum regime. The student will also clarify if processing of two or more non-commuting quantum states has the same work balance as when processing the commuting quantum states. The student will work closely with the experimental group in Oxford to discuss progress and measurement results, as well as the philosophical implications of our findings. It is expected that these first experimental tests of work associated with quantum states/coherences can bring up entirely new perspectives on the thermodynamic cost of quantum information processing, which we hope to explore. Regular visits of the Exeter theory PhD student to the experimental group in Oxford, as well as visits to the other team members in Grenoble/Madrid, will be part of the PhD project.