We investigate quantum Otto engines operating with a weakly interacting Bose gas confined in a cubic box with periodic boundary conditions. Our study focuses on two approaches to realizing adiabatic processes: varying the system volume and adjusting the interaction strength. We analyze the impact of Bose-Einstein condensation and interparticle interaction effects on engine performance, particularly power output and efficiency. Additionally, we explore the advantages of operating near the critical point of condensation, where quantum phenomena may enhance engine performance. Our findings underscore the significance of phase transitions and many-body effects in improving machine performance.
We investigate quantum Otto engines operating with a weakly interacting Bose gas confined in a cubic box with periodic boundary conditions. Our study focuses on two approaches to realizing adiabatic processes: varying the system volume and adjusting the interaction strength. We analyze the impact of Bose-Einstein condensation and interparticle interaction effects on engine performance, particularly power output and efficiency. Additionally, we explore the advantages of operating near the critical point of condensation, where quantum phenomena may enhance engine performance. Our findings underscore the significance of phase transitions and many-body effects in improving machine performance.
Bose-Einstein condensation is a quintessential characteristic of Bose systems. We investigate the finite-time performance of an endoreversible quantum Brayton heat engine operating with an ideal Bose gas with a finite number of particles confined in a d-dimensional harmonic trap. The working medium of these engines may work in the condensation, noncondensation, and near-critical point regimes, respectively. We demonstrate that the existence of the phase transition during the cycle leads to enhanced engine performance by increasing power output and efficiencies corresponding to maximum power and maximum efficient power. We also show that the quantum engine working across the Bose-Einstein condensation in N-particle Bose gas outperforms an ensemble of independent single-particle heat engines. The difference in the machine performance can be explained in terms of the behavior of specific heat at constant pressure near the critical point regime.
It was reported that, if and only if the specific heat, correlation length, and dynamical exponents α,ν and z, fulfill the condition α−zν>0, the phase transitions can enable a quantum heat engine to approach Carnot efficiency at finite power. We start our analysis via a different approach in which the effects of interaction and fluctuations on the Hamiltonian of a trapped dilute Bose gas belonging to the same universality as XY model. Based on models of quantum Otto heat engines, we find the general expression of the efficiency which includes the correction due to interaction and fluctuations at the critical point, and show that, near the Bose-Einstein-condensation point with α−zν<0, energy fluctuations could enable attaintment of the Carnot efficiency with nonvanishing power. Such quantum heat engines can also be realized by changing the shape of the trap confining the ideal and weakly interacting Bose gas during the adiabatic processes of the cycle. These quantum heat engines working with the trapped Bose gases, which are based on techniques of cooling Bose condensates and could be realizable at present technology.
At low-temperatures a gas of bosons will undergo a phase transition into a quantum state of matter known as a Bose-Einstein condensate (BEC), in which a large fraction of the particles will occupy the ground state simultaneously. Here we explore the performance of an endoreversible Otto cycle operating with a harmonically confined Bose gas as the working medium. We analyze the engine operation in three regimes, with the working medium in the BEC phase, in the gas phase, and driven across the BEC transition during each cycle. We find that the unique properties of the BEC phase allow for enhanced engine performance, including increased power output and higher efficiency at maximum power.
Abstract At low-temperatures a gas of bosons will undergo a phase transition into a quantum state of matter known as a Bose–Einstein condensate (BEC), in which a large fraction of the particles will occupy the ground state simultaneously. Here we explore the performance of an endoreversible Otto cycle operating with a harmonically confined Bose gas as the working medium. We analyze the engine operation in three regimes, with the working medium in the BEC phase, in the gas phase, and driven across the BEC transition during each cycle. We find that the unique properties of the BEC phase allow for enhanced engine performance, including increased power output and higher efficiency at maximum power.
The development of the theory of thermodynamics dates back nearly two centuries, to when the need arose to comprehend and enhance the performance of a novel technology of that era, the heat engine. Extending the classical concepts related to the properties of heat and work into the quantum realm forms the foundation of an emerging field of research known as quantum thermodynamics. To unify the disparate theories of classical thermodynamics and quantum mechanics, a thoroughly developed theoretical framework is necessary. Quantum heat engines provide a fundamental platform for this purpose. Many-body quantum heat engines, in particular, can provide important insights into the potential utilisation of exotic quantum phenomena, such as entanglement and quantum coherence, for building quantum devices that can surpass their classical counterparts in performance. One-dimensional (1D) Bose gases are a paradigmatic example of an interacting quantum many-body system that can be used as a versatile platform for building heat engines to test the thermodynamic theories in the quantum regime. The versatility of this platform comes through the routine experimental realisability of 1D Bose gases, with precise control of their internal and external properties, such as the strength of inter-atomic interactions and external confinement, and the presence of quantum many-body effects. In recent years, there has been an increased focus on exploiting the unique properties of ultracold atomic gases to realize many-body quantum heat engines. Despite this heightened attention and the resulting significant advances at the level of theoretical proposals, experimental feasibility and practical utilization of such engines remains at its infancy. Achieving significant advances at the experimental level requires a deeper understanding of the fundamental components of quantum-gas heat engines. Motivated by this goal, in this thesis we propose a novel and experimentally realistic quantum many-body heat engine that operates in an Otto cycle and uses a weakly interacting harmonically trapped 1D Bose gas as a working fluid. To execute work during the work strokes, we use a quench of the strength of interparticle interactions; when the quench is sudden with respect to the longitudinal dynamics, it maximises the power output. The interaction-induced work strokes are implemented by treating the working fluid as an isolated quantum many-body system undergoing a dynamical evolution starting from a finite temperature thermal equilibrium state. Furthermore, to optimize the performance of this interaction-driven quantum Otto cycle in an experimental scenario, we undertake a comprehensive numerical investigation of the dynamics of the system-reservoir coupling during the heat transfer strokes. We model the heat transfer strokes by treating the working substance as an open quantum many-body system that is coupled to a reservoir.After providing an overview of recent advances in the field of quantum thermodynamics and the background theory of 1D Bose gases in Chapters 1 and 2 we present the main results of this thesis in Chapters 3, 4 and 5. In Chapter 3, we study the individual interaction-induced work strokes of the Otto cycle with a weakly interacting 1D Bose gas as the working fluid. We evaluate the instantaneity of the sudden quench, specifically, identifying the minimum timescales required to perform the sudden quench of the interaction strength without invoking the transverse dynamics. Knowledge of these timescales enables us to perform the sudden quench in an experimental setting while ensuring that the system retains its 1D characteristics and the theory of 1D Bose gas is applicable. Additionally, we determine the time scales governing the opposite scenario of near-adiabatic quench which corresponds to minimum irreversible work in the engine cycle and hence maximum efficiency. This will help us benchmark the sudden quench engine's performance compared to a nearly ideal (near-adiabatic) scenario corresponding to maximum efficiency.Next, in Chapter 4, we analyze the heat transfer strokes of the Otto cycle, where the system is coupled to a reservoir. Using the c-field approach, we simulate the coupling dynamics of the system with both finite and infinite-size reservoirs. During the heat transfer stroke of the quantum Otto cycle, we treat the working fluid as an open quantum many-body system that is in thermal and diffusive contact with another quantum many-body system serving as the reservoir. In our real-time dynamical simulations of the engine strokes, we use a c-field approach based on the stochastic projected Gross-Pitaevskii equation. This approach enables us to treat both the working fluid and the hot and cold reservoirs as independent quantum many-body systems with chemical potential and temperature imbalances. To model the heat transfer strokes of such an engine with a finite-size reservoir, we use a tunnel-coupled model of two quasicondensates that treats both the system and the reservoir microscopically. Our analysis incorporates the impact of both finite-time operation and finite-size reservoirs in the engine cycle to gain a deeper understanding of the operational feasibility of such engines. Our results indicate that, in contrast to the common assumption of near-instantaneous heat transfer between the system and the reservoir, the thermalisation time of the system during these heat transfer strokes is non-negligible when compared to the duration of work strokes even in the near-adiabatic quench. This observation holds true even in the case of coupling the system with an infinite reservoir during the heat transfer strokes. Moreover, we demonstrate that for a finite-size reservoir, the initial dynamics (namely fast initial energy transfer) in the tunnel-coupled model of two quasicondensates can be leveraged to reduce the total driving time and hence increase the power output of the engine. Finally, in Chapter 5, we explore an alternate protocol that involves performing chemical work on the system during the heat transfer strokes to boost the efficiency and power output of the quantum Otto engines with a 1D Bose gas as a working fluid. We compare the performance of the sudden quench engine with an engine driven by a near-adiabatic and a finite-time quench of the interaction strength with respect to the longitudinal dynamics. We then conclude the thesis by summarising our main findings and presenting open questions for future work in the final chapter, Chapter 6.
We investigate a quantum Otto engine with a quantum Ising spin glass as the working medium to explore the scaling behavior of work output and thermodynamic performance concerning system size, particularly near the critical point. Specifically, we explore the two operating modes of the Otto engine, namely the heat engine and refrigerator modes. We observe a double-peaked structure in the heat engine regime, leading to superlinear scaling in both work output and thermodynamic performance near the critical point. Additionally, in the refrigerator regime, superlinear scaling in refrigerator efficiency can be achieved at high and low temperatures, significantly outperforming models with uniform Ising interactions. These findings suggest that disorder and frustration in quantum Ising spin-glass systems could significantly impact thermodynamic performance in quantum heat engines and refrigerators, potentially opening up new avenues for improvement.