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Title: Towards quantum superpositions of a mirror
Author: Marshall, William
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 2004
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In principle Quantum Mechanics allows the creation of macroscopic mass superposition states - so called "Schrödinger Cat States". This has not been confirmed experimentally largely due to the difficulty of isolating such states from environmental decoherence. It is of interest to create massive superpositions both in order to test Quantum Mechanics and to shed light on the elusive 'measurement problem'. This thesis presents the theoretical analysis of, and the initial experimental steps towards, an ambitious proposal to test the superposition principle of Quantum Mechanics at the 10-12 kg-scale, approximately nine orders of magnitude more massive than any superposition observed to date. The experimental principle is that a small mirror mounted on a micro-mechanical oscillator (cantilever) forms one end of a high-finesse cavity in one arm of a Michelson interferometer and is coupled to a single photon by radiation pressure. The photon, in a superposition of each arm, and the cantilever evolve into a superposition involving two distinct locations of the cantilever. By observing the interference of the photon only, one can study the creation and decoherence of the combined state. Firstly, a detailed analysis of the experimental requirements is given based on (1) the need for sufficient momentum transfer from the photon to displace the micro-mirror/cantilever to a distinguishable degree, (2) the need to isolate the cantilever to avoid significant environmental decoherence, and (3) the need to have sufficient interferometric stability to perform the measurement. An iterative analysis was performed to optimise these to a set that is feasible with current technology. This demands: (1) cavity mirrors with a reflectivity of R ≥ 0.9999998 at visible wavelength, (2) a system temperature of ≤ 3mK, (3) a cantilever mechanical quality Q ≥ 105 , (4) a vacuum with gas particle density of 1012/m3, (5) a relative position stability of the cavity mirrors of ≤ 10-13 m/min, and (6) optical mirror switching to 50% for ≤ lμs. Whilst extremely demanding, all of these goals appear to be within reach of current technology. Secondly, initial experimental results are described: (1) the fabrication of a 10μm radius dielectric mirror designed for peak reflectivity R > 0.99997 and the attaching of this to an AFM-type cantilever of mechanical quality Q > 4 x 104 ; (2) the alignment of a cavity of length 2.5cm involving this micro-mirror/cantilever at one end and the demonstration of a finesse of F > 1000 using two independent measurement techniques. The diffraction losses for the cavity are calculated numerically to be < 10-6 . Other mechanisms limiting the finesse are investigated and the dominant one is determined to be accoustic noise which can be alleviated by placing the cavity into a vacuum. In addition, results demonstrating ultra-fast optical switching of high reflectivity mirrors are shown.
Supervisor: Bouwmeester, Dirk Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Quantum theory ; Schrödinger equation