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Abstract

In this work, we study complex many-body systems consisting of ultracold bosonic atoms in optical lattices.Motivated by the state-of-the-art of experiments realizing higher bands physics with ultracold atoms, we use a one-dimensional bichromatic optical lattice, whose properties permit to engineer a very well isolated two-band system. The underlying single- and manyparticle physics is investigated based on a two-band Bose-Hubbard Hamiltonian. An external Stark force is introduced to drive the inter-band dynamics. In a first, andmain part of thiswork, we numerically characterize ourmany-bodyWannier-Stark systemthrough its spectral and dynamical properties, in terms of important system parameters. We present a detailed study of the diffusion in Hilbert space. Relaxation and controlled non-adiabatic dynamics are studied by driving the system across the spectral resonances, mainly by using quantum sweeps. In a second part, we implement an effective Hamiltonian in order to characterize the spectral properties of a leaky one-dimensional optical lattice with controlled dissipation. We show that the stability of long-lived localizedmany-body states, i.e. discrete solitonic states, can be described with good accuracy by the decay rates statistics of the accessible complex energy spectrum of the effective (non-hermitian)Hamiltonian.