Recently, there has been significant interest in extending thermodynamic concepts—particularly thermal machines—into the quantum regime to better understand the exchange of physical quantities such as energy and information between a system and its environment. In this thesis, we present the theoretical framework necessary to develop the concept of a quantum thermal machine from a quantum mechanical perspective. Leveraging these tools, we propose a two-qubit system, which can be prepared either in a separable state or a correlated state, and subject it to a thermodynamic cycle by immersing the system in an environment while externally controlling its energy gap Δ. We evaluate the performance of the system in both configurations under ultra-weak and weak coupling regimes, employing an endoreversible cycle and dynamics governed by a Lindblad master equation, respectively. Our findings show that the efficiency η exhibits similar behavior in both regimes, indicating potential for optimization through correlations. However, the power output P displays distinct behaviors across the two regimes, attributed to the specific protocol applied in the weak coupling scenario. Despite this difference, our results suggest that correlations offer opportunities for enhancing efficiency and power in quantum thermal machines.
Recently, there has been significant interest in extending thermodynamic concepts—particularly thermal machines—into the quantum regime to better understand the exchange of physical quantities such as energy and information between a system and its environment. In this thesis, we present the theoretical framework necessary to develop the concept of a quantum thermal machine from a quantum mechanical perspective. Leveraging these tools, we propose a two-qubit system, which can be prepared either in a separable state or a correlated state, and subject it to a thermodynamic cycle by immersing the system in an environment while externally controlling its energy gap Δ. We evaluate the performance of the system in both configurations under ultra-weak and weak coupling regimes, employing an endoreversible cycle and dynamics governed by a Lindblad master equation, respectively. Our findings show that the efficiency η exhibits similar behavior in both regimes, indicating potential for optimization through correlations. However, the power output P displays distinct behaviors across the two regimes, attributed to the specific protocol applied in the weak coupling scenario. Despite this difference, our results suggest that correlations offer opportunities for enhancing efficiency and power in quantum thermal machines.
We present a detailed study of quantum thermal machines employing quantum systems as working substances. In particular, we study two different types of two-stroke cycles where two collections of identical quantum systems with evenly spaced energy levels are initially prepared at thermal equilibrium by putting them in contact with a cold and a hot thermal bath, respectively. The two cycles differ in the absence or the presence of a mediator system, while, in both cases, nonresonant exchange Hamiltonians are exploited as particle interactions. We show that the efficiencies of these machines depend only on the energy gaps of the systems composing the collections and are equal to the efficiency of ``equivalent'' Otto cycles. Focusing on the cases of qubits or harmonic oscillators for both models, we maximize the engine power and analyze, in the model without the mediator, the role of the waiting time between subsequent interactions. It turns out that the case with the mediator can bring performance advantages when the interaction times are comparable with the waiting time of the correspondent cycle without the mediator. We find that in both cycles, the power peaks of qubit systems can surpass the Curzon-Ahlborn efficiency. Finally, we compare our cycle without the mediator with previous schemes of the quantum Otto cycle showing that high coupling is not required to achieve the same maximum power.
We present a detailed study of quantum thermal machines employing quantum systems as working substances. In particular, we study two different types of two-stroke cycles where two collections of identical quantum systems with evenly spaced energy levels are initially prepared at thermal equilibrium by putting them in contact with a cold and a hot thermal bath, respectively. The two cycles differ in the absence or the presence of a mediator system, while, in both cases, non-resonant exchange Hamiltonians are exploited as particle interactions. We show that the efficiencies of these machines depend only on the energy gaps of the systems composing the collections and are equal to the efficiency of equivalent Otto cycles. Focusing on the cases of qubits or harmonic oscillators for both models, we maximize the engine power and analyze, in the model without the mediator, the role of the waiting time between subsequent interactions. It turns out that the case with the mediator can bring performance advantages when the interaction times are comparable with the waiting time of the correspondent cycle without the mediator. We find that in both cycles, the power peaks of qubit systems can surpass the Curzon-Ahlborn efficiency. Finally, we compare our cycle without the mediator with previous schemes of the quantum Otto cycle showing that high coupling is not required to achieve the same maximum power.
Quantum thermodynamics seeks to address the emergence of thermodynamic laws, which govern how energy is exchanged between physical systems, from a quantum mechanical description of light and matter. As such, the workhorse model for an underlying description of such energy exchange processes is the open quantum system: a quantum system which may interact with an external environment. Open quantum systems are well-understood in regimes where the interaction between the system and the environment is weak enough that perturbative methods may be employed to arrive at dynamical equations of motion for the evolution of the system. How to tackle the strong coupling regime is an open question and much research is still being devoted in this area. In this project we employ a technique developed for studying an open quantum system in regimes of strong reservoir coupling in problems in thermodynamics which have so far been restricted to the weak coupling regime. We spend some time developing our strong coupling framework and then use it to analyse a quantum heat engine to find that strong coupling leads to a particular set of operational costs which are not present in more well-understood weak coupling versions. We also identify effects purely quantum in nature, present in the engine cycle only at strong coupling, which lead to a degradation in the engine's performance. Finally we address the issue of quantum coherence more generally in archetypal open quantum system models beyond weak coupling, and identify a thermodynamic cost to its erasure.
This thesis deals with energy management in open quantum systems. Three different systems are under study in the limit of weak system-environment coupling, and their dynamics is described by Markovian quantum master equations. In the first chapter, the complete derivation of such equation is performed in a specific case, and several notions of quantum thermodynamics are introduced. In the first system, energy transport is investigated along atomic chains (between 2 and 7 atoms) embedded in blackbody radiation around room temperature. It is shown that the transport efficiency can reach remarkable values, exceeding 100% and reaching 1400% in some configurations. Moreover, when the efficiency is amplified, the transport range is also considerably increased. The following chapter also deals with energy transport in atomic chains. The quantum system is located at the interface of a photonic topological insulator (PTI), supporting a unidirectional surface-plasmon-polariton (SPP) immune to backscattering. The SPP propagates along the chain and assists energy transport. Comparison is made between reciprocal and unidirectional SPPs in terms of transport efficiency, and it is shown that the latter can yield an efficiency larger by one order of magnitude. In addition, several practical aspects stemming from PTIs are highlighted, including the robustness of energy transport in the presence of defects on the SPP path. In the last chapter, a quantum system embedded in an out-of-thermal-equilibrium electromagnetic field is investigated. It is composed of a three-level atom playing the role of an absorption quantum thermal machine, as well as N two-level atoms ('qubits'), with N=1,...,6, which are the target bodies. It is demonstrated that the machine is able to perform significant thermal tasks on the qubits, even when their number is increased. Moreover, it is pointed out that due to qubit-qubit interactions, the tasks delivered by the machine are distributed throughout the system of interacting qubits, such that in some cases the temperature of the qubits which are completely decoupled from the machine can still be considerably affected by it. This task-distribution mechanism is investigated by means of the correlations between different subparts of the system. In addition, the tuning of thermal tasks is discussed.
Do quantum correlations lead to better performance with respect to several different systems working independently? For quantum thermal machines, the question is whether a working medium (WM) made of N constituents exhibits better performance than N independent engines working in parallel. Here, by inspecting a microscopic model with the WM composed by two non-interacting quantum harmonic oscillators, we show that the presence of a common environment can mediate non-trivial correlations in the WM leading to better quantum heat engine performance—maximum power and efficiency—with respect to an independent configuration. Furthermore, this advantage is striking for strong dissipation, a regime in which two independent engines cannot deliver any useful power. Our results show that dissipation can be exploited as a useful resource for quantum thermal engines and are then corroborated by optimization techniques here extended to non-Markovian quantum heat engines.
Quantum mechanics has given us a new playground in which to experiment that boasts several unique features. In this thesis, we explore it in the context of thermodynamics: looking at what kind of thermal devices can be constructed and how quantum behaviour affects them. We consider three research strands. In the first part we formulate a selection of heat engines with two-qubit systems, utilising environments that induce quantum correlations into the system. We see that these correlations can have some effects on the work of the engine, but this effect is system dependent. Describing the dynamics of a quantum system in contact with an external environment is often achieved with a master equation. When considering systems comprised of multiple subsystems, the description becomes more complicated and some of the master equations that have been used previously produce unphysical results. In the second part of this thesis we show that if one does the proper analysis of the microscopic derivation of these master equations, then no thermodynamical inconsistencies occur. When one considers a system connected to three or more environments, a whole new set of possible thermodynamical machines becomes available. One notable case of these is the absorption refrigerator, which performs refrigeration without the need for an external work source. For the third part, we show how one can construct an absorption refrigerator using a three-qubit system with two-body interactions and describe its operation. We also show some thermal control properties of the three-qubit system.