Thesis (Ph. D.)--Ohio State University, 2004. / Title from first page of PDF file. Document formatted into pages; contains x, 135 p.; also includes graphics. Includes bibliographical references (p. 131-135).

Thesis (Ph.D.)--Hong Kong University of Science and Technology, 2005. / Includes bibliographical references. Also available in electronic version.

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In this thesis we develop Bragg scattering as a tool for probing and manipulating ultra-cold atoms. Our approach is based on a mean-field treatment of degenerate quantum gases. Bose-Einstein condensates are described by the Gross-Pitaevskii equation and degenerate Fermi gases are described by the Bogoliubov-de-Gennes equations. Our work is presented in three inter-related topics. In Part I we investigate Bose-Einstein condensation in a time-averaged orbiting potential trap by deriving solitary-wave dynamical eigenstates of the system. We invoke the quadratic average approximation in which the dynamic effects of the time-dependent potential can be described simply, even when accounting for atomic collisions. By deriving the transformation to the translating frame, dynamical eigenstates of the system are defined and those states are solitary-wave solutions in the laboratory frame, with a particular circular centre-of-mass motion independent of the strength of the collisional interactions. Our treatment in the translating frame is more general than previous treatments that use the rotating frame to define system eigenstates, as the use of the rotating frame restricts eigenstates to those that are cylindrically symmetric about their centre of mass. In Part II we describe Bragg spectroscopy of a condensate with solitary-wave motion. Our approach is based on a momentum space two-bin approximation, derived by Blakie et al. [Journal of Physics B 33:3961, 2000] to describe Bragg scattering of a stationary condensate. To provide an analytic treatment of Bragg scattering of a solitary-wave condensate we use the translating frame, in which the time dependence of the system is described entirely by a time-dependent optical potential. We derive a simplified treatment of the two-bin approximation that provides a physical interpretation of the Bragg spectrum of a solitary-wave condensate. Our methods are applied to Bragg spectroscopy of a condensate in a time-averaged orbiting potential trap, which accelerates as a solitary wave as derived in Part I. The time-averaged orbiting potential trap system is ideal for testing our approximate analytic methods because the micromotion velocity is large compared to the condensate momentum width. In Part III we present a theoretical treatment of Bragg scattering of an ultra-cold Fermi gas. We give the first non-perturbative numerical calculations of the dynamic behaviour of a degenerate Fermi gas subjected to an optical Bragg grating. We observe first order Bragg scattering, familiar from Bragg scattering of stationary Bose-Einstein condensates, and at lower Bragg frequencies we predict scattering of Cooper pairs into a correlated spherical shell of atoms. Correlated-pair scattering is associated with formation of a grating in the pair potential. We give an analytic treatment of Bragg scattering of a homogeneous Fermi gas, and develop a model that reproduces the key features of the correlated-pair Bragg scattering. We discuss the effect of either a trapping potential or finite temperature on the correlated-pair Bragg scattering.

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Thesis (Ph. D.)--Oregon State University, 2010. / Printout. Includes bibliographical references (leaves 103-104). Also available on the World Wide Web.

An orbital dependent local spin density-functional (LSD) scheme with a generated exchange, the LSD GX scheme, has been developed based on the correct normalization conditions of an electron gas. This scheme contains no adjustable parameters; the B$ sb1$, B$ sb2$ and $ alpha sp lim$ are constant for all atoms once the shape of the Fermi hole is chosen. These parameters are rigorously calculated using an unspecified Fermi hole correlation factor and they give an exchange density which reduces exactly to the homogeneous free electron gas one at the high electron density limit. / The LSD GX exchange density is corrected for self-interaction (SI) by splitting the total Fermi hole correlation factor into pure-exchange and self-interaction holes. / These new LSD and SI corrected schemes are compared to each other. They also compare very well theoretically and numerically (total energies and eigenvalues) with other local schemes current in the literature. / New equations for the IP and electronegativities of the atoms in these local schemes are derived which give good results.

Thesis (Ph. D.)--Oregon State University, 2008. / Printout. Includes bibliographical references (leaves 162-163). Also available on the World Wide Web.

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