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Physical Review Research

Quantum-dot heat engines with irreversible heat transfer

Jianying Du, Wei Shen, Xin Zhang, Shanhe Su, Jincan Chen

Published Mar 4, 2020• 22 citations
Publisher

Abstract

This work establishes a quantum heat engine considering qubits as the external heat transfer mediums. The authors find that the efficiency and the power output of the quantum heat engine are closely dependent on the microproperties of qubits, and consequently relate the irreversible heat transfer with quantum effects. The equivalent conditions between the quantum heat engines and the classical endoreversible Carnot heat engines are revealed

DOI
10.1103/physrevresearch.2.013259

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This work establishes a quantum heat engine considering qubits as the external heat transfer mediums. The authors find that the efficiency and the power output of the quantum heat engine are closely dependent on the microproperties of qubits, and consequently relate the irreversible heat transfer with quantum effects. The equivalent conditions between the quantum heat engines and the classical endoreversible Carnot heat engines are revealed
The unavoidable irreversible loss of power in a heat engine is found to be of quantum origin. Following thermodynamic tradition, a model quantum heat engine operating in an Otto cycle is analysed, where the working medium is composed of an ensemble of harmonic oscillators and changes in volume correspond to changes in the curvature of the potential well. Equations of motion for quantum observables are derived for the complete cycle of operation. These observables are sufficient to determine the state of the system and with it all thermodynamical variables. Once the external controls are set, the engine settles to a limit cycle. Conditions for optimal work, power and entropy production are derived. At high temperatures and quasistatic operating conditions, the efficiency at maximum power coincides with the endoreversible result . The optimal compression ratio varies from in the quasistatic limit where the irreversibility is dominated by heat conductance to in the sudden limit when the irreversibility is dominated by friction. When the engine deviates from adiabatic conditions, the performance is subject to friction. The origin of this friction can be traced to the noncommutability of the kinetic and potential energy of the working medium.
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.
Continuous particle exchange thermal machines require no time-dependent driving, can be realised in solid-state electronic devices, and miniaturised to nanometre scale. Quantum dots, providing a narrow energy filter and allowing to manipulate particle flow between the hot and cold reservoirs are at the heart of such devices. It has been theoretically shown that by mitigating passive heat flow, Carnot efficiency can be approached arbitrarily closely in a quantum dot heat engine, and experimentally, values of 0.7ηC have been reached. However, for practical applications, other parameters of a thermal machine, such as maximum power, efficiency at maximum power, and noise - stability of the power output or heat extraction - take precedence over maximising efficiency. We explore the effect of internal microscopic dynamics of a quantum dot on these quantities and demonstrate that its performance as a thermal machine depends on few parameters - the overall conductance and three inherent asymmetries of the dynamics. These parameters will act as a guide to engineering the quantum states of the quantum dot, allowing to optimise its performance beyond that of the simplest case of a two-fold spin-degenerate transmission level.
Heat engines constitute the major building blocks of modern technologies. However, conventional heat engines with higher power yield lesser efficiency and vice versa and respect various power-efficiency trade-off relations. This is also assumed to be true for the engines operating in the quantum regime. Here we show that these relations are not fundamental. We introduce quantum heat engines that deliver maximum power with Carnot efficiency in the one-shot finite-size regime. These engines are composed of working systems with a finite number of quantum particles and are restricted to one-shot measurements. The engines operate in a one-step cycle by letting the working system simultaneously interact with hot and cold baths via semilocal thermal operations. By allowing quantum entanglement between its constituents and, thereby, a coherent transfer of heat from hot to cold baths, the engine implements the fastest possible reversible state transformation in each cycle, resulting in maximum power and Carnot efficiency. Finally, we propose a physically realizable engine using quantum optical systems.
The unavoidable irreversible losses of power in a heat engine are found to be of quantum origin. Following thermodynamic tradition a model quantum heat engine operating by the Otto cycle is analyzed. The working medium of the model is composed of an ensemble of harmonic oscillators. A link is established between the quantum observables and thermodynamical variables based on the concept of canonical invariance. These quantum variables are sufficient to determine the state of the system and with it all thermodynamical variables. Conditions for optimal work, power and entropy production show that maximum power is a compromise between the quasistatic limit of adiabatic following on the compression and expansion branches and a sudden limit of very short time allocation to these branches. At high temperatures and quasistatic operating conditions the efficiency at maximum power coincides with the endoreversible result. The optimal compression ratio varies from the square root of the temperature ratio in the quasistatic limit where their reversibility is dominated by heat conductance to the temperature ratio to the power of 1/4 in the sudden limit when the irreversibility is dominated by friction. When the engine deviates from adiabatic conditions the performance is subject to friction. The origin of this friction can be traced to the noncommutability of the kinetic and potential energy of the working medium.
We study the efficiency at maximum power, ${\ensuremath{\eta}}_{m}$, of irreversible quantum Carnot engines (QCEs) that perform finite-time cycles between a hot and a cold reservoir at temperatures Th{T}_{h}Th​ and Tc{T}_{c}Tc​, respectively. For QCEs in the reversible limit (long cycle period, zero dissipation), ${\ensuremath{\eta}}_{m}$ becomes identical to the Carnot efficiency ${\ensuremath{\eta}}_{{}_{C}}=1\ensuremath{-}{T}_{c}/{T}_{h}$. For QCE cycles in which nonadiabatic dissipation and the time spent on two adiabats are included, the efficiency ${\ensuremath{\eta}}_{m}$ at maximum power output is bounded from above by ${\ensuremath{\eta}}_{{}_{C}}/(2\ensuremath{-}{\ensuremath{\eta}}_{{}_{C}})$ and from below by ${\ensuremath{\eta}}_{{}_{C}}/2$. In the case of symmetric dissipation, the Curzon-Ahlborn efficiency ${\ensuremath{\eta}}_{{}_{\mathit{CA}}}=1\ensuremath{-}\sqrt{{T}_{c}/{T}_{h}}$ is recovered under the condition that the time allocation between the adiabats and the contact time with the reservoir satisfy a certain relation.