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

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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.