Tuesday, 19 June, 2012
Group seminar LMU: Dynamics of strongly interacting lattice bosons: an extended quasi-particle theory approach
Tuesday, 19.06.2012 10:00 a.m. (s.t.) in H107, Fakultät für Physik, LMU
Ulf Bissbort, Universität Frankfurt
We develop a systematic quasi-particle theory for interacting bosons in optical lattices, which does not rely on a large condensate fraction and is valid for arbitrary interaction strengths. It is based upon the definition of fluctuation operators, which become bosonic when the system is close to equilibrium. In terms of these, the Bose-Hubbard Hamiltonian can be rewritten in terms of different order above the Gutzwiller ground state. The various collective modes, such as the renormalized sound and amplitude modes in the condensate, or the particle and hole mode in the Mott insulator emerge naturally from this unified formalism and the time-dependent Gutzwiller approach is recovered when considering coherent states of quasi-particles only. We obtain the explicit transformation relations between arbitrary operators given in the Wannier or Bloch basis and the various quasi-particle creation and annihilation operators. The coupling of various processes to the different modes of a strongly interacting bosonic system can thus be explicitly calculated and the formalism furthermore sets the stage for a linear response analysis of various dynamical processes. The decay processes of the various quasi-particle modes induced by the higher order terms neglected in the quasi-particle Hamiltonian can be identified and determined.