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arXiv:1803.11314 · Physical review. E

Efficiency at maximum power of a laser quantum heat engine enhanced by noise-induced coherence

Konstantin E. Dorfman, Dazhi Xu, Jianshu Cao

Published Apr 13, 2018• 89 citations
arXivHTMLPDF

Abstract

Quantum coherence has been demonstrated in various systems including organic solar cells and solid state devices. In this article, we report the lower and upper bounds for the performance of quantum heat engines determined by the efficiency at maximum power. Our prediction based on the canonical three-level Scovil and Schulz-Dubois maser model strongly depends on the ratio of system-bath couplings for the hot and cold baths and recovers the theoretical bounds established previously for the Carnot engine. Further, introducing a fourth level to the maser model can enhance the maximal power and its efficiency, thus demonstrating the importance of quantum coherence in the thermodynamics and operation of the heat engines beyond the classical limit.

DOI
10.1103/physreve.97.042120

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Quantum coherence has been demonstrated in various systems including organic solar cells and solid state devices. In this article, we report the lower and upper bounds for the performance of quantum heat engines determined by the efficiency at maximum power. Our prediction based on the canonical three-level Scovil and Schulz-Dubois maser model strongly depends on the ratio of system-bath couplings for the hot and cold baths and recovers the theoretical bounds established previously for the Carnot engine. Further, introducing a fourth level to the maser model can enhance the maximal power and its efficiency, thus demonstrating the importance of quantum coherence in the thermodynamics and operation of the heat engines beyond the classical limit.
We consider a recently proposed four-level quantum heat engine (QHE) model to analyze the role of quantum coherences in determining the thermodynamic properties of the engine, such as flux, output power, and efficiency. A quantitative analysis of the relative effects of the coherences induced by the two thermal baths is brought out. By taking account of the dissipation in the cavity mode, we define useful work obtained from the QHE and present some analytical results for the optimal values of relative coherences that maximizes flux (hence output power) through the engine. We also analyze the role of quantum effects in inducing population inversion (lasing) between the states coupled to the cavity mode. The universal behavior of the efficiency at maximum power (EMP\mathrm{EMP}EMP) is examined. In accordance with earlier theoretical predictions, to leading order, we find that $\mathrm{EMP}\ensuremath{\sim}{\ensuremath{\eta}}_{c}/2$, where ${\ensuremath{\eta}}_{c}$ is Carnot efficiency. However, the next higher order coefficient is system dependent and hence nonuniversal.
We present a detailed study of a three-level quantum heat engine operating at maximum efficient power function, a trade-off objective function defined by the product of the efficiency and power output of the engine.The efficient power function represents a trade-off between the power output and efficiency of a heat engine.Engines working in the maximum efficient power regime operate at finite power, with finite efficiency lying in between the regimes of maximum power and maximum efficiency (Carnot efficiency).First, for near-equilibrium conditions, we find a general expression for the efficiency and establish the universal nature of efficiency at maximum power and maximum efficient power.Then in the high-temperature limit, optimizing with respect to one parameter while constraining the other one, we obtain the lower and upper bounds on the efficiency for both strong as well as weak matter-field coupling conditions.Except for the weak matter-field coupling condition, the obtained bounds on the efficiency exactly match with the bounds already known for some models of classical heat engines.Further for weak matter-field coupling, we derive some new bounds on the efficiency of the engine which lie beyond the range covered by bounds obtained for strong matter-field coupling.We conclude by comparing the performance of our three-level quantum heat engine in maximum power and maximum efficient power regimes and show that the engine operating at maximum efficient power produces at least 88.89% of the maximum power output while considerably reducing the power loss due to entropy production.Finally, to complete our analysis, we review the experimental setup of a recently realized effective three-level quantum engine.
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.
Abstract We work on a comprehensive theoretical investigation of a three-level quantum heat engine operating with engineered squeezed thermal reservoirs. Unlike conventional quantum heat engines that use thermal reservoirs, we demonstrate that squeezed reservoirs can significantly enhance the engine's performance by increasing both efficiency and output power. Using a rigorous open-quantum-system approach, we derive the full Lindblad master equation for a three-level system interacting with hot and cold squeezed thermal baths. Through a detailed analysis of the steady-state thermodynamics, we obtain explicit expressions for heat currents, work output, and efficiency. Our results reveal that moderate squeezing parameters (r≈0.5r \approx 0.5r≈0.5) combined with optimal squeezing phase (ϕ=π/2\phi = \pi/2ϕ=π/2) enhance the engine efficiency by up to 40\% compared to the classical Carnot limit for the same temperature ratio. The power output shows a non-monotonic behavior with squeezing, exhibiting an optimal squeezing parameter that maximizes performance. We identify three distinct operational regimes: (i) heat engine regime, (ii) refrigerator regime, and (iii) heat pump regime, which can be tuned by adjusting the squeezing phase. The efficiency at maximum power follows a universal scaling ηMP≈ηCarnot/2+Δη(r)\eta_{MP} \approx \eta_{Carnot}/2 + \Delta\eta(r)ηMP​≈ηCarnot​/2+Δη(r), where Δη(r)\Delta\eta(r)Δη(r) represents the squeezing-induced enhancement. Our findings provide fundamental insights into the role of non-thermal reservoirs in quantum thermodynamics and offer practical guidelines for designing high-performance quantum heat engines using squeezed light and engineered baths.
We investigate the efficiency at maximum power (EMP) of irreversible quantum Carnot engines that perform finite-time cycles between two temperature tunable baths. The temperature form we adopt can be experimentally realized in squeezed baths in the high temperature limit, which makes our proposal of practical relevance. Focusing on low dissipation engines, we first generalize the pervious upper as well as lower bounds for the EMP to temperature tunable cases in which they are solely determined by a generalized Carnot limit. As an illustrative example, we then consider a minimal heat engine model with a two-level spin as the working medium. It mimics a low dissipation engine as confirmed by finite time thermodynamic optimization results. The so-obtained EMP, being constrained by the generalized bounds, is well described by a generalized Curzon- Ahlborn efficiency as consequences of a left/right symmetry for a rate constant and low dissipations. Intriguing features of this minimal heat engine under optimal power output are also demonstrated.
The question of whether quantum coherence is a resource beneficial or detrimental to the performance of quantum heat engines has been thoroughly studied but remains undecided. To isolate the contribution of coherence, we analyze the performance of a purely coherence-driven quantum heat engine, a device that does not include any heat flow during the thermodynamic cycle. The engine is powered by the coherence of a multiqubit system, where each qubit is charged via interaction with a coherence bath using the Jaynes-Cummings model. We demonstrate that optimal coherence charging and hence extractable work is achieved when the coherence bath has an intermediate degree of coherence. In our model, the extractable work is maximized when four copies of the charged qubits are used. Meanwhile, the efficiency of the engine, given by the extractable work per input coherence flow, is optimized by avoiding the coherence being stored in the system-bath correlations that is inaccessible to work. We numerically find that the highest efficiency is obtained for slightly lower temperatures and weaker system-bath coupling than those for optimal coherence charging.