Seminar Laboratorije za primenu racunara u nauci
U sredu 10. septembra 2008. godine u 13:00 sati,
u citaonici biblioteke Instituta za fiziku, Pregrevica br. 118, Zemun
Priv-Doz. Dr. Axel Pelster
University of Duisburg-Essen, Germany
Bosons in Optical Lattices
Systems of ultracold bosonic gases in optical lattices have recently become a popular research topic as they represent model systems for quantum phase transitions in solid-state physics with a yet unprecendented level of control. For a small laser strength the bosons can tunnel from site to site and explore the whole lattice. This leads to a superfluid state which is characterized by long-range correlations, a continuous excitation spectrum, and a finite compressiblity. In the opposite situation of a large laser strength the bosons can no longer tunnel to the neighboring sites, so the occupation number of the sites is fixed. This so-called Mott phase has no long-range correlation, shows a gap in the excitation spectrum and is nearly incompressible. It is of particular interest to determine how the location of the transition from the superfluid to the Mott phase depends on the respective system parameters. Usually, one assumes that the temperature in the experiments is so low that thermal effects are completely negligible. In that case the phase boundary has been calculated analytically within both a mean-field theory and a strong-coupling approach or numerically by Monte-Carlo simulations. Only recently, one has initiated some theoretical work to include thermal effects in a systematic way. However, until today, the temperature of the bosons in an optical lattice is not known. Therefore, more experimental and theoretical studies are needed which aim at designing a thermometer for these systems.
This motivates the investigation of the present contribution how the temperature affects the one-particle Green’s function of such a lattice system. It is a central quantity of interest as it allows to extract various temperature-dependent system properties. We start with determining perturbatively the Green’s function for the underlying Bose-Hubbard model within the Mott phase. To this end we work out a hopping expansion up to second order at finite temperatures. The resulting Green’s function is useful for qualitatively reconstructing time-of-flight absorption pictures which are taken after switching off the one-particle potential. Additionally, the Green’s function also allows to locate the boundary between the superfluid and the Mott phase as its divergence indicates the emergence of a phase transition. It turns out that the first-order calculation reproduces the finite-temperature mean-field results, whereas the second-order goes beyond and takes into account corrections due to quantum fluctuations.