Quantum dissipation in carbon-nanotube optomechanics

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Quantum mechanics constitutes the basic paradigm that underlies our current understanding of physical reality. Though formulated almost a century ago and since then thoroughly tested to an exquisite precision, the interpretation of its basic principles continues to excite controversy to this very date. For example, a puzzling consequence of them is that an object can be in a "quantum superposition" state in which it seems to be simultaneously in two distinct locations. Though such features have been borne out in detail in the microscopic realm, they certainly defy our everyday notions of physical reality which raises the question of how the classical "macroscopic" world around us emerges from this quantum weirdness. Over the last decades it has transpired that this quantum-to-classical transition of a macroscopic object, known as its "decoherence", is effected by its unavoidable interaction with its surroundings.In turn, recent years have witnessed a miniaturisation of mechanical cantilevers used for sensing applications. This has culminated in mechanical beams having atomic-sized cross-sections, made from a single sheet of carbon atoms rolled into a seamless cylinder to form a narrow tube known as a carbon nanotube. These behave essentially like sensitive springs and researchers are currently developing a variety of transducers to convert their oscillatory motion into an electrical or optical signal. Such transducers can then be used to manipulate these "nanosprings", which given their small dimensions and high quality are also ideal candidates for studying the aforementioned intriguing aspects of quantum mechanics. For example researchers are trying to realise with them quantum superpositions of macroscopically distinguishable oscillation amplitudes. A configuration which often involves a similar superposition of the transducer itself. An important prerequisite for this goal is to understand what determines the intrinsic decoherence in these systems, i.e., what are the fundamental limits for the survival of their quantum superpositions.To this effect, we will predict the intrinsic decoherence expected in a nanotube optical transducer. The latter is based on bound pairs of oppositely charged carriers within the nanotube known as excitons. These can be generated with light and their presence can distort the tube via electrical forces so that an indirect coupling is generated between the scattered light and the oscillations of the nanotube. In particular, we will elucidate the decoherence that arises from the fact that regarding the nanotube as a single ideal spring is an oversimplification. A more accurate description is to think of it as an elastic string containing innumerable harmonics, whose vibrations will all influence and disrupt the workings of the "exciton transducer" while we try to use it to bring the fundamental resonance into a quantum superposition. Within a quantum setting, vibrational energy is quantised and the elemental quanta of these harmonics are known as phonons, so that our focus will be the phonon-induced decoherence of nanotube excitons. In a first phase, we will consider this phenomenon in situations where one can ignore the finite length of the nanotube, and we will study how the phonons influence the properties of the scattered light. A second phase will focus on situations where the fact that the nanotube is suspended over a finite length and coupled to an underlying chip, plays a role. In particular, the nanotube's oscillations can be damped by being converted into elastic waves that are radiated into the chip that supports it, and this adds a further twist to the problem of how the exciton transducer decoheres.Finally, beyond furthering our understanding of the basic fabric of reality, the resulting insights will impact on the usage of these systems as sensors at the single particle scale, and on a variety of quantum technologies that rely on exploiting quantum superpositions.