Ultra-cold bosons in one-dimensional single- and double-well potentials : a thesis submitted in partial fulfilment of the requirements for the degree of Masterate of Science at Massey University
dc.contributor.author | Gulliksen, Jake Steven | |
dc.date.accessioned | 2011-04-21T03:50:31Z | |
dc.date.available | 2011-04-21T03:50:31Z | |
dc.date.issued | 2010 | |
dc.description.abstract | A variationally optimised basis allows an accurate description of the quantum behaviour of ultra-cold atoms, even in the strongly correlated regime. A rescaling scheme corrects discrepancies caused by using a reduced Hilbert space. This approach also allows the modelling of experimentally realizable double-well potentials, which still reveals the maximally-entangled states seen in fixed basis models. Time dynamics of these double-well systems show macroscopic tunnelling between wells for bosons with a sufficient interaction strength. The many-body problem of interacting bosons in the highly-correlated regime is difficult. The number of basis states needed to describe this quantum system accurately quickly grows beyond computational reach. Rescaling the interaction strength proves a simple and effective method of calculating exact eigenvalues in a reduced Hilbert space. Bosonic systems in the double-well potential are investigated next. First, how different eigen-states depend on the interaction strength is examined. The variationally optimised method has advantages over a standard fixed basis method with the ability to model experimentally viable systems and explore more stronglycorrelated regimes. Secondly, tunnelling dynamics in the double well are studied, specifically for a system where all particles initially occupy a single well. Oscillations corresponding to collective tunnelling between wells are found in regimes where there are zero interactions or bosons lie in a maximally-entangled state. What governs the dynamics outside these two regimes is also considered. | en_US |
dc.identifier.uri | http://hdl.handle.net/10179/2299 | |
dc.language.iso | en | en_US |
dc.publisher | Massey University | en_US |
dc.rights | The Author | en_US |
dc.subject | Bosons | en_US |
dc.subject | One-dimensional single-well potentials | en_US |
dc.subject | One-dimensional double-well potentials | en_US |
dc.subject | Mathematical physics | en_US |
dc.title | Ultra-cold bosons in one-dimensional single- and double-well potentials : a thesis submitted in partial fulfilment of the requirements for the degree of Masterate of Science at Massey University | en_US |
dc.type | Thesis | en_US |
massey.contributor.author | Gulliksen, Jake Steven | |
thesis.degree.discipline | Mathematical physics | |
thesis.degree.grantor | Massey University | |
thesis.degree.level | Masters | |
thesis.degree.name | Master of Science (M.Sc.) |
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