Signals of Quantum Behaviour in Nanomechanical Systems: Non-linear Effects

纳米机电系统（NEMS）是一项新兴技术，将微型机器（如振动梁）构建在硅芯片上，就像将电子设备小型化在计算机芯片上一样。除了具有与计算机芯片相同的优点，如可靠性、小尺寸和低成本外，在芯片上安装机械设备而不仅仅是电子设备，还带来了广泛的全新应用，从光学开关到汽车安全气囊传感器，再到足够灵敏的称重秤，以测量单个DNA分子的质量。然而，除了提供许多新技术外，NEMS还可以揭示一个困扰物理学家一个世纪的问题——量子到经典的转变。NEMS有时被描述为介观或中等大小，因为它们与日常世界相比很小，但仍然比原子大得多。自20世纪初以来，我们已经知道原子遵循的规则与足球等日常物体非常不同，这些规则被称为量子力学。既然万物都是由原子构成的，那么我们就有了一个问题：为什么单个原子遵守量子力学，而由许多原子组成的足球却遵守经典力学的日常规则？NEMS设备中等大小，处于量子世界和经典世界的边界，因此是帮助我们理解量子到经典跃迁的理想设备。以前绝大多数关于NEMS的工作都使用了对器件的最基本描述，即它们是与测量器件弱耦合（即线性耦合）的谐波振荡器。这种方法存在两个主要问题。第一，没有振荡器是真正的谐波，没有耦合是真正的线性，这些近似总是有修正的。随着NEMS器件变得越来越小，这些校正变得越来越重要，这意味着简单的线性描述不够好。第二个问题是，如果振子是谐波的，耦合是线性的，那么量子态和经典态之间几乎没有明显的区别。特别是，对于一个实验家来说，检测这样的振荡器是否具有量子力学行为是非常困难的。该项目将超越众所周知的谐波，弱耦合近似，包括耦合和谐振器恢复力中的非线性效应。通过进入这个尚不为人所知的领域，该项目不仅将为更小的设备提供更准确和有效的NEMS描述，而且将允许研究经典和量子制度之间的差异。该项目将通过研究量子不破坏、量子杜芬共振和量子混沌等效应，寻找设备在量子力学作用的清晰信号。这样的信号对于实验家来说至关重要，因为他们能够自信地声明他们已经观察到设备中的量子行为。此外，通过研究这些效应如何随着谐振器尺寸和测量强度的增加而变化，该项目将描述原子和电子的量子世界如何让位于我们日常的足球世界。

Nanoelectromechanical systems, or NEMS, are an emerging technology where tiny machines (such as vibrating beams) are built onto silicon chips in the same way as electronics are miniaturised on computer chips. As well as having the same advantages as computer chips, such as reliability, small size and low cost, having mechanical devices on a chip instead of just electronics leads to a wide range of completely novel applications, ranging from optical switches, to car airbag sensors, to weighing scales sensitive enough to measure the mass of a single DNA molecule. However, as well as offering many new technologies, NEMS can also cast light on a question that has puzzled physicists for a century / the quantum to classical transition.NEMS are sometimes described as mesoscopic, or middle-sized, as they are tiny compared to the everyday world, but still much larger than atoms. Since the start of the 20th Century, we have known that atoms obey very different rules to everyday objects like footballs, rules that are known as quantum mechanics. As everything is made of atoms, we are left with the question of why a single atom obeys quantum mechanics, but a football made of many atoms obeys the everyday rules of classical mechanics. NEMS devices, being middle-sized, are on the border between the quantum and classical worlds and so are the ideal devices to help us understand the quantum to classical transition.The vast majority of previous work on NEMS has used the most basic descriptions of the devices / namely that they are harmonic oscillators weakly (i.e. linearly) coupled to measuring devices. There are two major problems with this approach. The first is that no oscillator is truly harmonic and no coupling is truly linear, and there will always be corrections to these approximations. As NEMS devices are made smaller and smaller, these corrections become more and more significant, meaning that the simple, linear, description is not good enough. The second problem is that if the oscillator is harmonic and the coupling is linear, there are few obvious differences between the quantum and classical regimes. In particular, it is very difficult for an experimentalist to detect if such an oscillator is behaving quantum mechanically or not.This project will move beyond the well known harmonic, weakly coupled approximation, to include non-linear effects in the coupling and the resonator restoring force. By moving into this as-yet poorly understood area, this project will not only provide a description of NEMS that is more accurate and valid for smaller devices, but will allow the investigation of the differences between the classical and quantum regime. The project will search for clear signals that a device is acting quantum mechanically, by studying effects known as quantum non-demolition, quantum Duffing resonances, and quantum chaos. Such signals will be crucial for experimentalists to be able to state with confidence that they have observed quantum behaviour in a device. In addition, by investigating how these effects change with increasing resonator size and measurement strength, this project will describe how the quantum world of atoms and electrons gives way to our everyday world of footballs.