Macroscopic quantum behaviour : superconductivity and cold atomic gases

The study of physics at the atomic scale led to the development of quantum mechanics in the early twentieth century. Since then, quantum mechanics has developed into one of the most successfully tested of all physical theories. Central to quantum mechanics is the concept of coherence. Keeping quantal coherence over large time scales or macroscopic length scales has proven to be a difficult, but fruitful endeavour both theoretically and experimentally. Two manifestations of this so-called macroscopic quantum coherence will be investigated in this thesis; the century-old field of superconductivity and the decade-old field of cold atomic gases. Yttrium barium copper oxide is a layered superconductor whose transition temperature can be changed by controlling the amount of oxygen found between the copper oxide planes. Motivated by recent experiments where the penetration depth along the direction perpendicular to the copper oxygen planes was measured on extremely underdoped samples, a theoretical model is constructed which phenomenologically explains the observed electrodynamic properties. The field of atomic physics underwent a revolution in 1994 when dilute atomic gases were cooled to nanokelvin temperatures, which resulted in the much sought after Bose-Einstein condensate. In the past decade, ultra-cold atomic experiments have been used to study fundamental quantum mechanics and more recently, with the application of optical lattices, many-body physics. The second project contained in this thesis investigates a method to engineer the emergence of Dirac Ferinions in an ultra-cold Fermionic gas with the application of an optical lattice. The Hamiltonian governing the low energy properties of this system is well known, and is shown to undergo a quantum phase transition where the low energy Fermionic quasiparticles acquire a mass, due to the appearance of "antiferromagnetic" ordering.Science, Faculty ofPhysics and Astronomy, Department ofGraduat