The many-body problem is ubiquitous in the theoretical description of physical phenomena,
ranging from the behaviour of elementary particles to the physics of electrons in solids. Most …

We review recent developments regarding the quantum dynamics and many-body physics
with light, in superconducting circuits and Josephson analogues, by analogy with atomic …

Time evolution of spin-orbit-coupled cold atoms in an optical lattice is studied, with a two-
band energy spectrum having two avoided crossings. A force is applied such that the atoms …

A superconducting wire described by ap-wave pairing and a Kitaev Hamiltonian exhibits
Majorana fermions at its edges and is topologically protected by symmetry. We consider two …

The spontaneous symmetry breaking of a continuous symmetry in complex field theory at the
exceptional point (EP) of the parameter space is known to exhibit interesting phenomena …

In this thesis, I present experiments on making and probing strongly correlated gases of
ultracold atoms in an optical lattice with engineered potentials and dynamics. The quantum …

Recent experiments on ultracold atoms in optical lattices have synthesized a variety of
tunable bands with degenerate double-well structures in momentum space. Such …

We study the combined effects of electron–phonon coupling and dot-lead repulsion in the
transport properties of the Anderson–Holstein model. We employ a recently proposed …

In this thesis, we study theoretically different aspects of topological systems. These models
present resilient properties due to a non-trivial topology of their band structures, and in …

We present the phase diagram of the interacting Bose-Hubbard model defined on a two-leg
ladder geometry in the presence of a homogeneous flux. Our work is motivated by recent …