Parametric Bose-Hubbard Hamiltonians: Quantum Dissipation, Irreversibility, and Pumping

Abstract

In this thesis, we study interacting bosons on lattices consisting of a few sites. The main focus is on their response to external driving fields, their transport and decay properties. We address fundamental questions of quantum classical correspondence and investigate the implications of interactions in the transport properties of (ultra-)cold atom devices. Quantum mechanically, we describe bosons on lattices using a parametric Bose-Hubbard Hamiltonian while the corresponding classical limit is described by the discrete nonlinear Schrödinger equation.In the first part of this thesis we focus on the chaotic regime of the Bose-Hubbard Hamiltonian. We investigate the parametric change of eigenstates as the coupling strength between neighboring sites is varied, using perturbative and semiclassical methods. We then turn to the quantum evolution of driven interacting bosonic systems and study the resulting quantum dynamics and the irreversibility (fidelity) of the quantum motion.In the second part we initiate the study of quantum pumping/stirring in Bose-Einstein condensates with the aim to identify optimal pumping cycles and propose such a device in order to probe the interatomic interactions. Finally, in the last part we focus on the interplay of intrinsic dynamics with coupling to the continuum and investigate the structure of the resonance widths of a Bose-Hubbard dimer which is coupled to the continuum at one of the sites using an effective non-Hermitian Hamiltonian formalism.