Investigation of first and second order correlation functions of ultra-cold atomic gases
|dc.identifier.citation||Toth, E. (2016). Investigation of first and second order correlation functions of ultra-cold atomic gases (Thesis, Doctor of Philosophy). University of Otago. Retrieved from http://hdl.handle.net/10523/6287||en|
|dc.description.abstract||In the first part of the thesis we develop a theoretical description of the correlations between ultra-cold bosons after free expansion from confinement in an optical lattice. We describe the single particle evolution of the system during expansion and establish criteria for a far-field regime. We develop expressions for first and second order two-point correlations based on a variety of commonly used approximations to the many-body state of the system including: Bogoliubov theory, mean-field decoupling, and particle-hole perturbative expantion about the perfect Mott-insulator state. Using these approaches we examine the effects of quantum depletion and pairing on system correlations. We justify a Gaussian approximation from which we develop a general three-dimensional theoretical formalism for an inhomogeneous lattice system by comparison with the directly calculated correlation functions. In the second part of the thesis we show how the conventional wisdom that increasing tem- perature means decreasing quantum coherence in system can be faulty. We explore a practical example that can be explored in optical lattice experiments. Using finite temperature perturbation theory and exact calculations we show that the short-range coherence of the Mott-insulating phase of bosons in an optical lattice can increase substantially with increasing temperature. We demonstrate that this phenomenon originates from thermally produced defects that can tunnel with ease. Since the near zero temperature coherence properties have been measured with high precision we expect these results to be verifiable in current experiments. In the last part of the thesis we turn our attention to one dimensional Bose gases. We fo- cus on the moderate temperature weakly interacting regime namely the high temperature quasicondensate and quantum decoherent regimes, which we investigate using the stochas- tic projected Gross-Pitaevskii equation (SPGPE) formalism. Here we compare the SPGPE results against the Bethe ansatz and a mean-field formalism adapted to the quasicondensate regime. This theory covers a regime not addressed by other formalism.|
|dc.publisher||University of Otago|
|dc.rights||All items in OUR Archive are provided for private study and research purposes and are protected by copyright with all rights reserved unless otherwise indicated.|
|dc.subject||particle-hole perturbative expantion|
|dc.subject||quantum decoherent regimes|
|dc.title||Investigation of first and second order correlation functions of ultra-cold atomic gases|
|thesis.degree.name||Doctor of Philosophy|
|thesis.degree.grantor||University of Otago|
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