Abstract
State-of-the-art platforms for quantum simulations, using photons, trapped ions, ultracold atoms, or
superconducting qubits, share the common feature that they are very complex and involve many
degrees of freedom. Quite unsurprisingly, pioneering studies with such quantum simulation platforms
were therefore focused on obtaining a better understanding of the generic properties of complex
quantum many-body systems and their relation with the notions of integrability or chaos. I will
address these quantum signatures of chaos in the specific context of ultracold bosonic atoms confined
within optical lattices, theoretically described by Bose-Hubbard systems which feature a well-defined
classical counterpart. I will specifically focus on deviations from the quantum-classical
correspondence in this context, owing to many-body quantum interference effects. Those deviations
can be rather subtle, if induced by the presence of discrete symmetries or time-reversal invariance, or
rather important, as exemplified by scars, i.e., eigenstates that are strongly localized in phase space
and thereby defy thermalisation despite global chaos. Being aware of these generic phenomena will
be of key importance for the conception and handling of efficient quantum simulators.
