Browsing by Subject "Cold gases--Optical properties."
Now showing 1 - 2 of 2
Results Per Page
Sort Options
Item Open Access Ground-state properties of ultra-cold atomic gases(Bilkent University, 2008) Sevinçli, SevilayAfter the observation of Bose-Einstein condensation, the developments in the experimental control and measurement methods provided the realization of basic models of many-body physics using dilute, ultra-cold gases. This thesis presents a theoretical study on a number of topics on ultra-cold atomic gas systems. First, a simple model of trapped, degenerate ultra-cold plasma is presented. Using the variational approach, the dependence of the cloud size on electron density is studied, electron and ion densities are also calculated by means of modified Thomas-Fermi model. Next, the behavior of a single particle hopping on a three dimensional cubic optical lattice in the presence of a Mott insulator of bosons is investigated. Localization problem of a single fermion is studied and effects of lattice anisotropy, and higher impurity bands are also calculated. Then, a two-dimensional condensate with long-range, attractive gravity-like interaction is studied. Ground-state properties, dynamics, and vortex states are analyzed by using a variational approach for this system. Finally, the thermodynamics of the harmonically trapped ideal gas obeying generalized exclusion statistics is investigated.Item Open Access Quantum gases in rotating optical lattices(Bilkent University, 2010) Umucalılar, Rifat OnurThe thesis is structured into two main parts so as to cover bosons and fermions in rotating optical lattices separately. In the first part, after a brief introduction to ultracold atoms in optical lattices, we review the single-particle physics for the lowest (s) band of a periodic potential under an artificial magnetic field created by rotation. Next, we discuss rotational effects on the first excited (p) band of the lattice, extending the methods available for the lowest band. We conclude the first part with a discussion of many-body physics in rotating lattice systems using a mean-field approach and investigate how the transition boundary between superfluid and Mott insulator phases is affected by the single-particle spectrum. In this context, we also examine a possible coexistent phase of Mott insulator and bosonic fractional quantum Hall states, appearing for certain system parameters near the Mott insulator lobes in the phase diagram. The second part starts with the proposal of a realization and detection scheme for the so-called topological Hofstadter insulator, which basically reveals the single-particle spectrum discussed before. The scheme depends on a measurement of the density profile for noninteracting fermions in a rotating optical lattice with a superimposed harmonic trapping potential. This method also allows one to measure the quantized Hall conductance, a feature which appears when the Fermi energy lies in an energy gap of the lattice potential. Finally, we explore the Bardeen-Cooper-Schrieffer type of pairing of fermionic atoms in optical lattices under an artificial magnetic field by paying special attention to single-particle degeneracies and present our results for the vortex lattice structure of the paired fermionic superfluid phase.