Nonequilibrium phenomena in the sine-Gordon model: From Josephson junctions and high-Tc superconductors to ultracold atoms

This thesis explores the out-of-equilibrium dynamics and collective behavior of increasingly complex sine-Gordon-type models. The sine-Gordon (SG) model is ubiquitous in solid-state systems, from extended Josephson junctions and high-temperature (high-Tc) superconductors to ultracold atoms and quantum computers being studied in Google and IBM experiments. This model is very rich because it is integrable and it supports collective soliton excitations that play a prominent role in its dynamics. Hence, the SG model constitutes an excellent framework to investigate the properties of integrable systems and their nearly-integrable counterparts, as well as the relations between mathematical models and experiments. Inspired by the theoretical and experimental relevance of the SG model, we explored several aspects of its nonequilibrium and collective behavior, often in connection with open challenges of theoretical and experimental interest. We tackled the detection of breather solitons in extended Josephson junctions—a long-standing problem in superconducting electronics—leveraging thermal noise as a resource to enhance breathers' stability and facilitate their experimental probing. Our results offer new insights into the emergence and dynamics of breathers in the presence of dissipative, stochastic, and external perturbations, and allowed us to conceive different breather probing approaches, all within reach of current technology. Our further research extends to layered high-Tc superconductors, where we developed a theory for a recent groundbreaking experiment on optically pumped YBa2Cu3O6+x. This experiment found superconducting-like signatures, during pumping with a THz pulse, far above the superconducting transition temperature, in the so-called pseudogap phase. Our theoretical findings not only quantitatively explain the experimental data, but shed new light on the pseudogap phase and reveal a new instability in SG-type models, with implications for both fundamental physics and quantum technology. Lastly, we formulated a framework for applying advanced spectroscopy techniques to the study of the quantum SG model and its soliton excitations, providing detailed information on its out-of-equilibrium dynamics and collective modes. This work bridges theoretical advancements with experimental realizations, such as those based on ultracold atoms and superconducting qubits, contributing significantly to the understanding of many-body integrable theories.