Non-equilibrium thermodynamics can provide strong advantages when compared to more standard equilibrium situations. Here, we present a general framework to study its application to concrete problems, which is valid also beyond the assumption of a Gaussian dynamics. We consider two different problems: 1) the dynamics of a levitated nanoparticle undergoing the transition from an harmonic to a double-well potential; 2) the transfer of a quantum state across a double-well potential through classical and quantum protocols. In both cases, we assume that the system undergoes to decoherence and thermalisation. In case 1), we construct a numerical approach to the problem and study the non-equilibrium thermodynamics of the system. In case 2), we introduce a new figure of merit to quantify the efficiency of a state-transfer protocol and apply it to quantum and classical versions of such protocols.
Non-equilibrium thermodynamics can provide strong advantages when compared to more standard equilibrium situations. Here, we present a general framework to study its application to concrete problems, which is valid also beyond the assumption of a Gaussian dynamics. We consider two different problems: 1) the dynamics of a levitated nanoparticle undergoing the transition from an harmonic to a double-well potential; 2) the transfer of a quantum state across a double-well potential through classical and quantum protocols. In both cases, we assume that the system undergoes to decoherence and thermalisation. In case 1), we construct a numerical approach to the problem and study the non-equilibrium thermodynamics of the system. In case 2), we introduce a new figure of merit to quantify the efficiency of a state-transfer protocol and apply it to quantum and classical versions of such protocols.
Many advanced quantum techniques feature non-Gaussian dynamics, and the ability to manipulate the system in that domain is the next stage in many experiments.One example of meaningful non-Gaussian dynamics is that of a double-well potential.Here we study the dynamics of a levitated nanoparticle undergoing the transition from a harmonic potential to a double well in a realistic setting, subjected to both thermalization and localization.We characterize the dynamics of the nanoparticle from a thermodynamic point of view, investigating the dynamics with the Wehrl entropy production and its rates.Furthermore, we investigate coupling regimes where the the quantum effect and thermal effect are of the same magnitude, and look at suitable squeezing of the initial state that provides the maximum coherence.The effects and the competitions of the unitary and the dissipative parts onto the system are demonstrated.We quantify the requirements to relate our results to a bonafide experiment with the presence of the environment, and discuss the experimental interpretations of our results in the end.
Quantum computing promises exponential speedups for specific computational tasks compared to classical computing. However, the inherent fragility of quantum states—their susceptibility to decoherence—poses a significant challenge to realizing this potential. This work investigates the crucial role of non-equilibrium thermodynamics in governing the dynamics of quantum computation. It argues that the efficiency of quantum algorithms is fundamentally linked to the non-equilibrium interactions between the quantum system (qubits) and its environment. A novel thermodynamic framework is proposed, moving beyond the traditional assumptions of equilibrium. This framework utilizes concepts from non-equilibrium statistical mechanics to model energy transfer and information flow between qubits and the surrounding environment, offering a pathway to understand and potentially mitigate decoherence. Specifically, we introduce a quantum computing heat engine model, formulated using non-equilibrium statistical ensembles, to quantify the impact of environmental fluctuations on qubit coherence. The core claim is that a new thermodynamic understanding is required for optimal quantum algorithm design and control. Key mathematical concepts include the Boltzmann entropy, the Landau free energy, and the quantum master equation. The analysis highlights the need for sophisticated control strategies that actively manage environmental fluctuations rather than passively attempting to isolate the quantum system.
Manipulating quantum systems undergoing non-Gaussian dynamics in a fast and accurate manner is becoming fundamental to many quantum applications. Here, we focus on classical and quantum protocols transferring a state across a double-well potential. The classical protocols are achieved by deforming the potential, while the quantum ones are assisted by a counterdiabatic driving. We show that quantum protocols perform more quickly and accurately. Finally, we design a figure of merit for the performance of the transfer protocols---namely, the protocol grading---that depends only on fundamental physical quantities, and which accounts for the quantum speed limit, the fidelity, and the thermodynamics of the process. We test the protocol grading with classical and quantum protocols, and show that quantum protocols have higher protocol grading than the classical ones.
Quantum thermodynamics is an emerging research field aiming to extend standard thermodynamics and non-equilibrium statistical physics to ensembles of sizes well below the thermodynamic limit, in non-equilibrium situations and with the full inclusion of quantum effects. Fuelled by experimental advances and the potential of future nanoscale applications, this research effort is pursued by scientists with different backgrounds, including statistical physics, many-body theory, mesoscopic physics and quantum information theory, who bring various tools and methods to the field. A multitude of theoretical questions are being addressed ranging from issues of thermalisation of quantum systems and various definitions of ‘work’ to the efficiency and power of quantum engines. This overview provides a perspective on a selection of these current trends accessible to postgraduate students and researchers alike.
Quantum thermodynamics (QT) is an emerging field of research that aims to investigate how the laws of thermodynamics and quantum mechanics merge together in small quantum systems.With advances at the necessary technology to control and measure those small physical systems this field has acquired even more importance, not only in the sense that it can be tested, which is a good thing for basic research, but that new applications could be implemented at these scales, so a better comprehension of the limitations imposed by quantum thermodynamics turns out to be of crucial importance for these goals, which forces theoreticians to produce experimentally relevant versions of these new concepts.Another important aspect present at those systems is that part of them work in a regime where its constituents are described by non-thermal states, and in particular non-thermal steady states, which brings to light a different thermodynamic description, usually called steady-state thermodynamics, therefore one of the goals that we are willing to achieve with this thesis is to give an introduction to QT of systems out-of-equilibrium.One of the related subtopics that physicists deal with in QT and the one that we will be focusing on this work are the use of non-thermal stationary states to build heat engines in the quantum domain, and the analyses of the features that this new regime could possibly allow, like the use of quantum resources as a way to overcome classical limitations imposed on its performance, like to attain efficiencies higher than Carnot's or operate in certain regimes unattainable using only classical resources.Therefore, in order to clarify the underlying physics of those systems in a non-thermal regime, any experimentally well suited content is more than welcome.So keeping that in mind we devised an experimentally relevant thermodynamic cycle for a transmon qubit WS interacting with a non-thermal environment composed by two subsystems, an externally excited cavity and a classical heat bath with temperature T. The WS undergoes a non-conventional cycle (different from Otto, Carnot, etc.) through a succession of non-thermal stationary states obtained by slowly varying its bare frequency and the amplitude of the field applied on the cavity.The efficiency of this engine obtains a maximum value up to 47% in the regime of operation used.We also wanted to look for the role played by the different types of coherences, present at the WS, on the behavior of the engine and its efficiency.By different types of coherence we mean the so called modes of coherence, whose definition is based on how they respond to symmetry transformations.We did that for the trivial case of the qubit, that only contains the modes 1 and -1, and that has shown to be extremely important for the efficiency of the machine.The same procedure was repeated for a 3-level system WS.The modes 1 and -1 was again very important, not only to the absolute value of the engine's efficiency but to the regime of operation of the machine.The additional modes, 2 and -2, had a negative impact on the efficiency, reducing its absolute value.This result appears to show some evidences that quantumness won't necessarily bring improvements to the operation of those machines.
The results of analytical and numerical investigation of quantum dissipative dynamics a particle moving in a potential well with two equilibrium states is presented. A classical analogue of this problem is the capture into the resonance a particle in a double-well potential, when two states of equilibrium in the phase space are separated by a separatrix. The probability of finding the system in one of states of equilibrium for the quantum particle, depending on initial conditions and noise, is discussed.