QMATH Seminar: Generalized geometric Bogoliubov theory for the Bose-Hubbard model

Speaker: Lucas Hackl, the Max Planck Harvard Research Center for Quantum Optics 

Title: Generalized geometric Bogoliubov theory for the Bose-Hubbard model

Abstract: The paradigmatic Bose-Hubbard model describes interacting bosons which can be experimentally realized with ultracold atoms in optical lattices. In this talk, I will focus on the superfluid phase and introduce geometric methods to find approximate ground states and quasi particle excitations. For the variational class of all Gaussian states, we can systematically extend Bogoliubov theory and compute quasi particle excitations, life times and spectral functions. To our surprise, we find a bound state below the continuum. Depending on the interaction strength, the dispersion relation of the bound state (Goldstone mode) enters the continuum for large momentum. I will conclude with discussing observable effects and the physical relevance of our findings.