We theoretically investigate the finite-time performance of a quantum thermochemical engine utilizing a harmonically trapped one-dimensional (1D) Bose gas in the quasicondensate regime as the working fluid. The proposed engine operates in an Otto cycle, where the unitary work strokes are simulated through a quench of the interatomic interactions of the 1D Bose gas. In the work strokes, the working fluid is treated as a closed quantum many-body system that undergoes dynamic evolution, beginning from an initial thermal equilibrium state at a nonzero temperature. On the other hand, during the thermalization strokes, the working fluid is treated as an open many-body quantum system in diffusive contact with a thermal reservoir, allowing particle exchange alongside the transfer of heat. Using a c-field approach, we demonstrate that the engine's operation is enabled by the chemical work done on the working fluid through the flow of particles from the hot reservoir. We examine the finite-time performance of the proposed quantum thermochemical engine in two extreme regimes: (i) the out-of-equilibrium regime (sudden quench), which yields near-maximum power (due to fast driving of the system) while compromising efficiency, and (ii) the quasistatic (near-adiabatic) limit, which approaches maximum efficiency but generates zero power output due to slow driving of the system. Notably, we show that using chemical work allows the engine to achieve efficiencies close to the near-maximum (quasistatic) limit, even in the out-of-equilibrium regime, while maintaining high power output. Thus, in the out-of-equilibrium operational regime, our proposed engine provides a favorable trade-off between efficiency and power output. We also draw connections to previous research, particularly the case of an adiabatic engine cycle operating at zero temperature. We show that this zero-temperature scenario establishes an upper bound on the efficiency and work of our proposed thermochemical engine operating at nonzero temperatures.
We theoretically investigate the finite-time performance of a quantum thermochemical engine utilizing a harmonically trapped one-dimensional (1D) Bose gas in the quasicondensate regime as the working fluid. The proposed engine operates in an Otto cycle, where the unitary work strokes are simulated through a quench of the interatomic interactions of the 1D Bose gas. In the work strokes, the working fluid is treated as a closed quantum many-body system that undergoes dynamic evolution, beginning from an initial thermal equilibrium state at a nonzero temperature. On the other hand, during the thermalization strokes, the working fluid is treated as an open many-body quantum system in diffusive contact with a thermal reservoir, allowing particle exchange alongside the transfer of heat. Using a c-field approach, we demonstrate that the engine's operation is enabled by the chemical work done on the working fluid through the flow of particles from the hot reservoir. We examine the finite-time performance of the proposed quantum thermochemical engine in two extreme regimes: (i) the out-of-equilibrium regime (sudden quench), which yields near-maximum power (due to fast driving of the system) while compromising efficiency, and (ii) the quasistatic (near-adiabatic) limit, which approaches maximum efficiency but generates zero power output due to slow driving of the system. Notably, we show that using chemical work allows the engine to achieve efficiencies close to the near-maximum (quasistatic) limit, even in the out-of-equilibrium regime, while maintaining high power output. Thus, in the out-of-equilibrium operational regime, our proposed engine provides a favorable trade-off between efficiency and power output. We also draw connections to previous research, particularly the case of an adiabatic engine cycle operating at zero temperature. We show that this zero-temperature scenario establishes an upper bound on the efficiency and work of our proposed thermochemical engine operating at nonzero temperatures.
Abstract We undertake a theoretical study of a finite-time quantum Otto engine cycle driven by inter-particle interactions in a weakly interacting one-dimensional (1D) Bose gas in the quasicondensate regime. Utilizing ac-field approach, we simulate the entire Otto cycle, i.e. the two work strokes and the two equilibration strokes. More specifically, the interaction-induced work strokes are modelled by treating the working fluid as an isolated quantum many-body system undergoing unitary evolution. The equilibration strokes, on the other hand, are modelled by treating the working fluid as an open quantum system tunnel-coupled to another quasicondensate which acts as either the hot or cold reservoir, albeit of finite size. We find that, unlike a uniform 1D Bose gas, a harmonically trapped quasicondensate cannot operate purely as aheatengine; instead, the engine operation is enabled by additionalchemicalwork performed on the working fluid, facilitated by the inflow of particles from the hot reservoir. The microscopic treatment of dynamics during equilibration strokes enables us to evaluate the characteristic operational time scales of this Ottothermochemicalengine, crucial for characterizing its power output, without any ad hoc assumptions about typical thermalization timescales. We analyse the performance and quantify the figures of merit of the proposed Otto thermochemical engine, finding that it offers a favourable trade-off between efficiency and power output, particularly when the interaction-induced work strokes are implemented via a sudden quench. We further demonstrate that in the sudden quench regime, the engine operates with an efficiency close to the near-adiabatic (near maximum efficiency) limit, while concurrently achieving maximum power output.
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.
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.
Abstract We study the performance of a quantum Otto cycle using a harmonic work medium and undergoing collisional dynamics with finite-size reservoirs. We span the dynamical regimes of the work strokes from strongly non-adiabatic to quasi-static conditions, and address the effects that non-Markovianity of the open-system dynamics of the work medium can have on the efficiency of the thermal machine. While such efficiency never surpasses the classical upper bound valid for finite-time stochastic engines, the behaviour of the engine shows clear-cut effects induced by both the finiteness of the evolution time, and the memory-bearing character of the system-environment evolution.
The finite-time operation of a quantum heat engine that uses a single particle as a working medium generally increases the output power at the expense of inducing friction that lowers the cycle efficiency. We propose to scale up a quantum heat engine utilizing a many-particle working medium in combination with the use of shortcuts to adiabaticity to boost the nonadiabatic performance by eliminating quantum friction and reducing the cycle time. To this end, we first analyze the finite-time thermodynamics of a quantum Otto cycle implemented with a quantum fluid confined in a time-dependent harmonic trap. We show that nonadiabatic effects can be controlled and tailored to match the adiabatic performance using a variety of shortcuts to adiabaticity. As a result, the nonadiabatic dynamics of the scaled-up many-particle quantum heat engine exhibits no friction, and the cycle can be run at maximum efficiency with a tunable output power. We demonstrate our results with a working medium consisting of particles with inverse-square pairwise interactions that includes non-interacting and hard-core bosons as limiting cases.
We analyze the performance of a quantum Otto cycle, employing a time-dependent harmonic oscillator as the working fluid undergoing sudden expansion and compression strokes during the adiabatic stages, coupled to a squeezed reservoir. First, we show that the maximum efficiency that our engine can achieve is 1/2 only, which is in contrast with earlier studies claiming unit efficiency under the effect of a squeezed reservoir. Then, in the high-temperature limit, we obtain analytic expressions for the upper bound on the efficiency as well as on the coefficient of performance of the Otto cycle. The obtained bounds are independent of the parameters of the system and depend on the reservoir parameters only. Additionally, with a hot squeezed thermal bath, we obtain an analytic expression for the efficiency at maximum work which satisfies the derived upper bound. Further, in the presence of squeezing in the cold reservoir, we specify an operational regime for the Otto refrigerator otherwise forbidden in the standard case. Finally, we find the cost of creating a squeezed state from the thermal state and show that in order to harvest the benefits of squeezing, it is sufficient to squeeze only one mode of the reservoir in resonance with the transition frequency of the working fluid. Further, we show that when the cost of squeezing is included in the definition of the operational efficiency of the engine, the advantages of squeezing fade away. Still, being purely quantum mechanical fuel in nature, squeezed reservoirs are beneficial in their own way by providing us with more compact energy storage medium or offering effectively high-temperature baths without being actually too hot.