This volume provides a broad overview of the principal theoretical techniques applied to non-equilibrium and finite temperature quantum gases. Covering Bose-Einstein condensates, degenerate Fermi gases, and the more recently realised exciton-polariton condensates, it fills a gap by linking between different methods with origins in condensed matter physics, quantum field theory, quantum optics, atomic physics, and statistical mechanics.

This book explores the physics of atoms frozen to ultralow temperatures and trapped in periodic light structures. It introduces the reader to the spectacular progress achieved on the field of ultracold gases and describes present and future challenges in condensed matter physics, high energy physics, and quantum computation.

This thesis explores the physics of non-equilibrium quantum dynamics in homogeneous two-dimensional (2D) quantum gases. Ultracold quantum gases driven out of equilibrium have been prominent platforms for studying quantum many-body physics. However, probing non-equilibrium dynamics in conventionally trapped, inhomogeneous atomic quantum gases has been a challenging task because coexisting mass transport and spreading of quantum correlations often complicate experimental analyses. In this work, the author solves this technical hurdle by producing ultracold cesium atoms in a quasi-2D optical box potential. The exquisite optical trap allows one to remove density inhomogeneity in a degenerate quantum gas and control its dimensionality. The author also details the development of a high-resolution, in situ imaging technique to monitor the evolution of collective excitations and quantum transport down to atomic shot-noise, and at the length scale of elementary collective excitations. Meanwhile, tunable Feshbach resonances in ultracold cesium atoms permit precise and dynamical control of interactions with high temporal and even spatial resolutions. By employing these state-of-the-art techniques, the author performed interaction quenches to control the generation and evolution of quasiparticles in quantum gases, presenting the first direct measurement of quantum entanglement between interaction quench generated quasiparticle pairs in an atomic superfluid. Quenching to attractive interactions, this work shows stimulated emission of quasiparticles, leading to amplified density waves and fragmentation, forming 2D matter-wave Townes solitons that were previously considered impossible to form in equilibrium due to their instability. This thesis unveils a set of scale-invariant and universal quench dynamics and provides unprecedented tools to explore quantum entanglement transport in a homogenous quantum gas.

This book discusses non-equilibrium quantum many-body dynamics, recently explored in an analog quantum simulator of strongly correlated ultracold atoms. The first part presents a field-theoretical analysis of the experimental observability of the Higgs amplitude mode that emerges as a relativistic collective excitation near a quantum phase transition of superfluid Bose gases in an optical lattice potential. The author presents the dynamical susceptibilities to external driving of the microscopic parameters, taking into account a leading-order perturbative correction from quantum and thermal fluctuations and shows clear signatures of the Higgs mode in these observables. This is the first result that strongly supports the stability of the Higgs mode in three-dimensional optical lattices even in the presence of a spatially inhomogeneous confinement potential and paves the way for desktop observations of the Higgs mode. In the second part, the author applies the semi-classical truncated-Wigner approximation (TWA) to far-from-equilibrium quantum dynamics. Specifically, he considers the recent experiments on quantum-quench dynamics in a Bose-Hubbard quantum simulator. A direct comparison shows remarkable agreement between the numerical results from TWA and the experimental data. This result clearly indicates the potential of such a semi-classical approach in reliably simulating many-body systems using classical computers. The book also includes several chapters providing comprehensive reviews of the recent studies on cold-atomic quantum simulation and various theoretical methods, including the Schwinger-boson approach in strongly correlated systems and the phase-space semi-classical method for far-from-equilibrium quantum dynamics. These chapters are highly recommended to students and young researchers who are interested in semi-classical approaches in non-equilibrium quantum dynamics.

Cold atomic gases trapped and manipulated on atom chips allow the realization of seminal one-dimensional (1d) quantum many-body problems in an isolated and well controlled environment. In this context, this thesis presents an extensive experimental study of non-equilibrium dynamics in 1d Bose gases, with a focus on processes that go beyond simple dephasing dynamics. It reports on the observation of recurrences of coherence in the post-quench dynamics of a pair of 1d Bose gases and presents a detailed study of their decay. The latter represents the first observation of phonon-phonon scattering in these systems. Furthermore, the thesis investigates a novel cooling mechanism occurring in Bose gases subjected to a uniform loss of particles. Together, the results presented show a wide range of non-equilibrium phenomena occurring in 1d Bose gases and establish them as an ideal testbed for many-body physics beyond equilibrium.

This book provides authoritative tutorials on the most recent achievements in the field of quantum gases at the interface between atomic physics and quantum optics, condensed matter physics, nuclear and high-energy physics, non-linear physics, and quantum information.

This book studies the dynamics of fundamental collective excitations in quantum materials, focusing on the use of state-of-the-art ultrafast broadband optical spectroscopy. Collective behaviour in solids lies at the origin of several cooperative phenomena that can lead to profound transformations, instabilities and phase transitions. Revealing the dynamics of collective excitations is a topic of pivotal importance in contemporary condensed matter physics, as it provides information on the strength and spatial distribution of interactions and correlation. The experimental framework explored in this book relies on setting a material out-of-equilibrium by an ultrashort laser pulse and monitoring the photo-induced changes in its optical properties over a broad spectral region in the visible or deep-ultraviolet. Collective excitations (e.g. plasmons, excitons, phonons...) emerge either in the frequency domain as spectral features across the probed range, or in the time domain as coherent modes triggered by the pump pulse. Mapping the temporal evolution of these collective excitations provides access to the hierarchy of low-energy phenomena occurring in the solid during its path towards thermodynamic equilibrium. This methodology is used to investigate a number of strongly interacting and correlated materials with an increasing degree of internal complexity beyond conventional band theory.