The 1995 observation of Bose-Einstein condensation in dilute atomic vapours spawned the field of ultracold, degenerate quantum gases. Unprecedented developments in experimental design and precision control have led to quantum gases becoming the preferred playground for designer quantum many-body systems.This self-contained 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. Thematically organised chapters on different methodologies, contributed by key researchers using a unified notation, provide the first integrated view of the relative merits of individual approaches, aided by pertinent introductory chapters and the guidance of editorial notes.Both graduate students and established researchers wishing to understand the state of the art will greatly benefit from this comprehensive and up-to-date review of non-equilibrium and finite temperature techniques in the exciting and expanding field of quantum gases and liquids./a

This thesis presents experiments performed to investigate the non-equilibrium dynamics of ultracold bosons. In depth understanding of the behaviour of quantum systems when taken out of equilibrium is of particular interest, especially for the production of quantum computers where thermal effects cause undesirable behaviours. We present our experiments on the thermalization of a87Rb Bose-Einstein condensate taken out of equilibrium by a partial Bragg pulse. We measure the rate of thermalization of the system and measure the temperature of the thermalized state, and compare to numerical simulations. We observe the formation of grey solitons in the thermalized state consistent with the Kibble-Zurek mechanism. We also present experiments on artificial gauge potentials with Bose-Einstein condensates. We benchmark the experiments with a uniform synthetic potential and extend to spin-orbit coupled systems. We take the spin-orbit coupled BEC out of equilibrium through the application of a synthetic electric field and measure the thermalization process of the system. We measure the rate at which the system reaches equilibrium as a function of the final Raman coupling strength, and measure the temperature of the thermalized states. We observe the system thermalize into a spin-orbit coupled state with a the final temperature decreasing with increasing Raman coupling.

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.

Following an explosion of research on Bose–Einstein condensation (BEC) ignited by demonstration of the effect by 2001 Nobel prize winners Cornell, Wieman and Ketterle, this book surveys the field of BEC studies. Written by experts in the field, it focuses on Bose–Einstein condensation as a universal phenomenon, covering topics such as cold atoms, magnetic and optical condensates in solids, liquid helium and field theory. Summarising general theoretical concepts and the research to date - including novel experimental realisations in previously inaccessible systems and their theoretical interpretation - it is an excellent resource for researchers and students in theoretical and experimental physics who wish to learn of the general themes of BEC in different subfields.

This work presents a series of experiments with ultracold one-dimensional Bose gases, which establish said gases as an ideal model system for exploring a wide range of non-equilibrium phenomena. With the help of newly developed tools, like full distributions functions and phase correlation functions, the book reveals the emergence of thermal-like transient states, the light-cone-like emergence of thermal correlations and the observation of generalized thermodynamic ensembles. This points to a natural emergence of classical statistical properties from the microscopic unitary quantum evolution, and lays the groundwork for a universal framework of non-equilibrium physics. The thesis investigates a central question that is highly contested in quantum physics: how and to which extent does an isolated quantum many-body system relax? This question arises in many diverse areas of physics, and many of the open problems appear at vastly different energy, time and length scales, ranging from high-energy physics and cosmology to condensed matter and quantum information. A key challenge in attempting to answer this question is the scarcity of quantum many-body systems that are both well isolated from the environment and accessible for experimental study.

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.

The realization of Bose Einstein condensation in ultra-cold dilute atomic gases, represented by a macroscopic occupation of ground state and the non-vanishing order parameter, makes the study of quantum many-body physics and condensed matter physics much easier. Especially, the quantum dynamics of condensate in the optical lattice serves as a perfect test-bed to study the condensed matter physics such as Josephson tunneling, Bloch oscillations, Landau-Zener tunneling. The interplay of mean field interaction and coherent Josephson tunneling leads to rich phases described by the Bose-Hubbard model such as Superfluid-Insulator transition at zero temperature and Berezinskii-Kosterlitz thouless transition at finite temperature. Furthermore, due to the extremely narrow momentum distribution of Bose Einstein condensate, it can be used to make interferometer as sensitive phase detector. The creation of number squeezed state of BEC enables the realization of Heisenberg-limited interferometer which can bring the noise below shot-noise level. The coherence time of such squeezed state interferometer can be longer than that of the coherent state interferometers. The quasi-2D geometry in 1D optical lattice can be used to study superfluid to normal fluid transition when topological order is broken. The studies of Kosterlitz-Thouless with inter-well coupling can lead to the interpretation of High TC superconductivity. This work will discuss the quantum dynamics of the Bose-Einstein condensate in 1D optical lattice.

This 2008 book, reissued as OA, captures the essence of nonequilibrium quantum field theory, graduate students and researchers.