This paper provides a theoretical and experimental approach that allows characterizing and optimizing generic nonequilibrium processes of few-particle systems. The authors present experimental protocols to measure thermodynamic quantities, such as entropy production and thermodynamic length, in an ultra cold few-atom system, and introduce general optimization criteria based on these quantities.
This paper provides a theoretical and experimental approach that allows characterizing and optimizing generic nonequilibrium processes of few-particle systems. The authors present experimental protocols to measure thermodynamic quantities, such as entropy production and thermodynamic length, in an ultra cold few-atom system, and introduce general optimization criteria based on these quantities.
One-dimensional quantum many-body systems exhibit peculiar and intriguing behaviors as a consequence of the reduced dimensionality, which enhances the effect of fluctuations and correlations. The high degree of isolation and controllability of experiments manipulating ultra-cold atomic gases allows for the experimental simulation of text-book models, for which many theory tools are available for quantitative comparison. I will present instances of such efforts carried out during my PhD thesis, namely, the studies performed to investigate the behavior of 1D Bose gas (Lieb-Liniger gas) at equilibrium and beyond. An overview of the toolbox available to date to characterize the equilibrium thermodynamics of a Lieb-Liniger gas will be shown, followed by a detailed study of the breathing mode of such a system.
Thermodynamics is a phenomenological theory describing the energy conversion of work and heat. At its origins thermodynamics was developed in order to understand and improve heat engines. In conventional thermodynamics, however, only such processes are completely describable which are slow enough to keep the system of interest in an equilibrium state with its thermal environment at all times. On the contrary, all real physical processes are accompanied by non-equilibrium phenomena. These are mathematically described with the help of the irreversible entropy production, i.e. the dissipated work divided by the temperature of the bath. The second law of thermodynamics merely states that the irreversible entropy production is on average always positive. The modern trend of miniaturization, however, leads to smaller and smaller devices. On short length scales thermal noise as well as quantum fluctuations become important. Thus, usual thermodynamic quantities as work and heat acquire stochastic nature. Moreover, in the quantum regime a completely new theory had to be invented, since classical notions of work and heat are no longer valid. The present dissertation contributes to this prevailing field by the derivation of analytical expressions for the entropy production in open and closed quantum system far from thermal equilibrium. The theoretical treatment is motivated by an experimental point of view. The obtained results were derived from the reduced dynamics of the quantum mechanical system, which may be coupled to a thermal bath. To this end, it was dealt with methods and approaches of statistical physics, conventional thermodynamics, quantum information theory and the theory of open quantum systems. In this dissertation the most important physical systems are treated. First, an isolated system is considered before later on a heat bath is included. The limit of weak as well as of strong coupling are analyzed in detail. For isolated systems it turns out that a geometric approach is able to capture the thermodynamic properties, completely. To this end, the irreversible entropy production is sharply estimated from below by the angle between the real non-equilibrium state and the corresponding equilibrium one. Further, it is shown that the Heisenberg uncertainty relation for energy and time can be formulated more precisely in terms of that angle. As experimental system cold ion traps are introduced, in which the theoretical predictions can be verified. For weakly coupled systems, then, the irreversible entropy production is identified and a fluctuation theorem is derived by merely thermodynamic arguments. As experimental system we, again, propose the cold ion traps, where the heat bath can be simulated with the help of LASER light. In the limit of strong coupling a semiclassical description of the reduced quantum system is discussed. Again, an analytically exact expression for the entropy production and the corresponding fluctuation theorem is derived. A physical system, in which strong coupling to the environment can be analyzed, is given by Josephson junctions. This dissertation discusses the entropy production for isolated, weakly coupled, and overdamped quantum systems. For these physical regimes analytical relation are derived and experimental systems proposed, with which the predictions can be verified.
Among the few lessons that Physics teaches us on a daily basis, one in particular is hard to miss: thermalization processes are ubiquitous. With the same degree of certainty, one can predict an apple to fall onto the ground if its stalk is cut, or a cup of tea to be found cold if left on the table for too long. In this respect, generic classical and quantum mechanical systems seem to behave in the same way. This is also one of the main difficulties in the experimental observation of the bizarre effects predicted from the quantum theory, as several of these are known to disappear at finite temperatures. It has been known for a long time that thermalization is associated with “chaotic” behavior at the microscopic level, but recently systematic efforts, both theoretical and experimental, have allowed us to understand its mechanisms at an unprecedented level of accuracy. Indeed, it has been realized that thermalization generally occurs also in isolated systems, where the absence of interactions with the environment allows for first principle theoretical investigations1. In this case thermalization takes place locally, as the whole system acts as a thermal bath for its own subsystems. Theoretical research has been motivated and paralleled by exciting experimental progress in cold-atom physics, which has provided robust, nearly ideal realizations of several theoretical models2. As an established piece of knowledge, recent research has now confirmed that two outstanding exceptions actually exist in the quantum realm, where thermalization is prevented to occur. These are many-body localized systems3, where disorder plays a crucial role, and integrable ones, which are protected by the existence of higher conservation laws. By their own nature, these systems display exceptional non-equilibrium features, which are not washed out by the onset of thermalization as relaxation occurs. At the core of the present thesis lie the remarkable properties of integrable systems out of equilibrium, with a special attention to physical effects which could be observed in cold-atom realizations. The work collected here is part of a large theoretical effort4 which in the past decade has focused on the study of relatively simple protocols to bring a quantum system out of equilibrium, such as the so-called quantum quench. In these “theoretical laboratories” it has been possible to provide quantitative predictions which helped us to develop an intuition on general questions regarding non-equilibrium and thermalization processes. Furthermore, in some cases these studies have highlighted interesting physical effects which could be directly probed experimentally within cold-atom settings. The contribution of the present thesis is two-fold. On the one hand, we have developed new technical tools for the study of integrable systems out of equilibrium, and for the computation of measurable physical quantities such as correlation functions. The techniques employed are mainly analytical and rooted within the mathematical structures of integrability. On the other hand, we have singled out physically relevant nonequilibrium situations where exotic, non-thermal states of matter emerge after relaxation occurs, and provided quantitative analytical predictions in these cases. A comprehensive discussion of the motivations and results of our work will be presented in Chapter 1, where we provide a complete overview of this thesis and discuss the organization of its content.
In this thesis, we explore various aspects of equilibrium and nonequilibrium thermodynamics for ultracold atomic gases, with a focus on the experimentally realisable one-dimensional (1D) Bose gas. This is a paradigmatic example of an interacting many-body system, which is integrable in the uniform limit and near-integrable otherwise. We first investigate a quantum thermodynamic Otto cycle driven by a quench of interaction strength of a 1D Bose gas. For the case of a sudden quench in a uniform 1D Bose gas, we demonstrate how the performance of this highly nonequilibrium quantum thermal machine may be expressed in terms of atom-atom correlations. Further, we derive a new Maxwell relation which allows one to express entropy, which is generally difficult to ascertain in quantum systems, in terms of Glauber's local second-order correlation function, which are experimentally measurable. We next perform benchmarks of GHD in order to ascertain the regimes where such a theory may be applied, and then utilize it to investigate the interaction strength-driven quantum Otto cycle in a harmonically trapped 1D Bose gas. However, to realise such an engine in an experimentally realistic manner would require modelling thermalisation with external reservoirs, which is currently beyond the scope of GHD. Yet, the classical c-field stochastic-projected Gross-Pitaevskii equation (SPGPE) method is capable of simulating tunnel-coupling pairs of 1D Bose gases in the weakly interacting regime. We therefore utilise this numerical method to simulate the \emph{full} quantum Otto engine cycle, realised through a single working fluid tunnel-coupled to two 1D Bose gases, which constitute the external (hot and cold) reservoirs.
The relaxation of isolated quantum many-body systems is a major unsolved problem connecting statistical and quantum physics. Studying such relaxation processes remains a challenge despite considerable efforts. Experimentally, it requires the creation and manipulation of well-controlled and truly isolated quantum systems. In this context, ultracold neutral atoms provide unique opportunities to understand nonequilibrium phenomena because of the large set of available methods to isolate, manipulate, and probe these systems. Here, we give an overview of the rapid experimental progress that has been made in the field over the past few years and highlight some of the questions that may be explored in the future.
Optimizing thermodynamic processes far from equilibrium is a challenge. We report the experimental optimization of cooling and thermalization of a gas of few noninteracting Cesium atoms confined in a nonharmonic optical dipole trap. To this end, we combine degenerate Raman sideband cooling and nonequilibrium thermodynamics. We determine the axial phase-space distribution of the atoms after each Raman cooling pulse by tracing the evolution of the gas with position-resolved fluorescence imaging. We further minimize the entropy production to a target thermal state to specify the optimal spacing between a sequence of pulses, thus achieving optimal thermalization. We finally study the dynamics of the cooling process by measuring the statistical distance between each cooling step. Our results provide a method to systematically optimize the cooling of nonharmonically trapped dilute gases and illustrate the power of nonequilibrium thermodynamics.