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arXiv:2403.11645 · Physical review. B./Physical review. B

Many-body quantum heat engines based on free fermion systems

Vincenzo Roberto Arezzo, Davide Rossini, G. Piccitto

Published Jun 20, 2024• 10 citations
arXivHTMLPDF

Abstract

Devising and constructing quantum many-body heat engines is a key challenge of quantum thermodynamics. Most of the research in this field assumes the strokes to be ideal transformations. Here, the authors study the performance of realistic Otto engines with finite-time duration, whose working substance is made of free-fermion systems. They provide analytic expressions for the work and the power delivered through imperfect adiabatic and isochoric strokes. These findings are applied to the case study of an Ising-like quantum Otto cycle.

DOI
10.1103/physrevb.109.224309

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Devising and constructing quantum many-body heat engines is a key challenge of quantum thermodynamics. Most of the research in this field assumes the strokes to be ideal transformations. Here, the authors study the performance of realistic Otto engines with finite-time duration, whose working substance is made of free-fermion systems. They provide analytic expressions for the work and the power delivered through imperfect adiabatic and isochoric strokes. These findings are applied to the case study of an Ising-like quantum Otto cycle.
Abstract The efficiency of a quantum heat engine is maximum when the unitary strokes of the quantum Otto cycle are adiabatic. On the other hand, this may not be always possible due to small energy gaps in the system, especially at the critical point (CP) where the gap between the ground state and the first excited state vanishes and the system gets excited. With the aim to regain this lost adiabaticity, we modify one of the unitary strokes of the Otto cycle by allowing the system to first evolve with a time dependent Hamiltonian as in the case of a usual Otto cycle, followed by an additional evolution with a different time independent Hamiltonian so that the system reaches a less excited state. This will help in increasing the magnitude of the heat absorbed from the hot bath so that the work output and efficiency of the engine can be increased. We demonstrate this method using an integrable model and a non-integrable model as the working medium and discuss the generality and limitations of this method. In the case of a two spin system, the optimal value for the time till which the system needs to be freely evolved is calculated analytically in the adiabatic limit. The results show that implementing this modified unitary stroke significantly improves the work output and efficiency of the engine, especially when it crosses the CP.
We investigate the finite-power performance of quantum heat engines working in the linear response regime where the temperature gradient is small. The engine cycles with working substances of ideal harmonic systems consist of two heat transfer and two adiabatic processes, such as the Carnot cycle, Otto cycle, and Brayton cycle. By analyzing the optimal protocol under maximum power we derive the explicitly analytic expression for the irreversible entropy production, which becomes the low dissipation form in the long duration limit. Assuming the engine to be endoreversible, we derive the universal expression for the efficiency at maximum power, which agrees well with that obtained from the phenomenological heat transfer laws holding in the classical thermodynamics. Through appropriate identification of the thermodynamic fluxes and forces that a linear relation connects, we find that the quantum engines under consideration are tightly coupled, and the universality of efficiency at maximum power is confirmed at the linear order in the temperature gradient.
Abstract We propose a quantum Otto heat engine using a finite-size Dicke-Stark model as the working substance. In the extended coherent state space, the complete energy spectrum and eigenstates are obtained through numerical calculations. Within the infinite-time and finite-time thermodynamics frameworks, we find that the output work, efficiency, and power can be optimized by adjusting the Stark field strength, the qubit–boson coupling strength, stroke times, and number of atoms. Our results reveal that output work and efficiency are maximized near the coupling strength at the superradiant phase transition (SPT). Tuning the Stark field strength modifies the energy level structure and SPT, effectively suppressing entropy generation and quantum friction during nonequilibrium evolution. We also show that asymmetric heat engines—where the two isochoric strokes operate with different Stark field strengths and durations—further improve engine performance. These results may guide future implementations of efficient quantum heat engines.
In order to describe quantum heat engines, here we systematically study isothermal and isochoric processes for quantum thermodynamic cycles. Based on these results the quantum versions of both the Carnot heat engine and the Otto heat engine are defined without ambiguities. We also study the properties of quantum Carnot and Otto heat engines in comparison with their classical counterparts. Relations and mappings between these two quantum heat engines are also investigated by considering their respective quantum thermodynamic processes. In addition, we discuss the role of Maxwell's demon in quantum thermodynamic cycles. We find that there is no violation of the second law, even in the existence of such a demon, when the demon is included correctly as part of the working substance of the heat engine.
In this work we investigate a finite-time quantum Otto-like heat engine with a single-qubit working substance, distinguished from the standard Otto cycle by introducing a unitary operation before the cold isochore. This operation suppresses the slowest decaying mode of the open-system dynamics and broadens the spectral gap, thereby inducing an exponential to accelerate the subsequent thermalization process toward stationarity. We derive analytic expressions for the work, heat, and efficiency, and perform numerical simulations comparing the standard Otto engine, the shortcut to adiabatic engine, and our proposed Otto-like engine. Our analysis demonstrates that with an appropriate parameter selection, the additional unitary operation can significantly boost the system's power and efficiency. Finally, using the unified optimization criterion Φ, we further show that the modified cycle consistently outperforms both the conventional cycle and the shortcut to adiabatic protocol.
We study a quantum Otto engine at finite time, where the working substance is composed of a two-level system interacting with a harmonic oscillator, described by the quantum Rabi model. We obtain the limit cycle and calculate the total work extracted, efficiency, and power of the engine by numerically solving the master equation describing the open system dynamics. We relate the total work extracted and the efficiency at maximum power with the quantum correlations embedded in the working substance, which we consider through entanglement of formation and quantum discord. Interestingly, we find that the engine can overcome the Curzon-Ahlborn efficiency when the working substance is in the ultrastrong coupling regime. This high-efficiency regime roughly coincides with the cases where the entanglement in the working substance experiences the greatest reduction in the hot isochoric stage. Our results highlight the efficiency performance of correlated working substances for quantum heat engines.