Critical Properties of Bose-Einstein Condensates

• Applicant: Professor Dr. Hagen Kleinert
• Subject Area: Optics, Quantum Optics and Physics of Atoms, Molecules and Plasmas
• Term: from 2003 to 2007
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 5407417

The goal of the project is to understand the critical properties of homogeneous Bose-Einstein condensates above and, especially, below the critical point by applying field-theoretic methods of many-body physics. In both regimes we shall analyze the effect of an arbitrarily weak repulsive two-particle interaction on the critical temperature and the specific heat. Furthermore, below the transition, we want to investigate the influence of phase fluctuations upon the superfluid properties of homogeneous Bose-Einstein condensates. The same field-theoretic methods will then be applied to Bose-Einstein condensates trapped in optical lattices. There the periodicity leads to a quasi-free behavior due to Bloch´s theorem. In the lattice systems one can increase the effective repulsive interaction between the bosons which leads to a state with uncorrelated phases behaving like a Mott insulator. In the neighborhood of any of these transitions, perturbation expansions of physical quantities suffer from ubiquitous infrared divergencies so that the effective expansion parameter becomes infinite. We master this problem with the help of variational perturbation theory, a method developed recently in our group to determine the strong-coupling limit of divergent weak-coupling expansions.

• DFG Programme: Priority Programmes
• Subproject of: SPP 1116: Interactions in ultracold and molecular gases
• Participating Person: Privatdozent Dr. Axel Pelster