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arXiv:2412.18476

Effects of noise-induced coherence on the performance of a four-level laser heat engine

Kirandeep Kaur

Published Dec 24, 2024• 0 citations
arXivHTMLPDF

Abstract

In this work, we study the effect of noise-induced coherence on the performance analysis of a degenerate four-level quantum heat engine with particular focus on the universal nature of efficiency, which refers to the appearance of the first two universal terms $η_C/2$ and $η_C^2/8$ in series expansion of the efficiency at maximum power under a left-right symmetry in the system. Firstly, for a two-parameter optimization scheme, we derive an analytic expression for the efficiency at maximum power for the near-equilibrium condition and show that presence of noise-induced coherence breaks the left-right symmetry of the system. However, when the operation of the engine is restricted to either high-temperature or low-temperature regime, we discuss the conditions under which the left-right symmetry can be retained in each case, giving rise to the universal characteristic of efficiency. In case of one-parameter optimization, we show that while the universality of the first linear term $η_c/2$ is robust and holds consistently across all conditions, the universality of the quadratic term $η_C^2/8$ depends on the constraints imposed on the control parameters. Finally, we examine the behavior of power as a function of noise-induced coherence parameter highlighting the role of matter-field coupling in determining the suitable operation regime for the heat engine to reap the benefits of noise-induced coherence.

DOI
10.48550/arxiv.2412.18476

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In this work, we study the effect of noise-induced coherence on the performance analysis of a degenerate four-level quantum heat engine with particular focus on the universal nature of efficiency, which refers to the appearance of the first two universal terms ηC/2η_C/2ηC​/2 and ηC2/8η_C^2/8ηC2​/8 in series expansion of the efficiency at maximum power under a left-right symmetry in the system. Firstly, for a two-parameter optimization scheme, we derive an analytic expression for the efficiency at maximum power for the near-equilibrium condition and show that presence of noise-induced coherence breaks the left-right symmetry of the system. However, when the operation of the engine is restricted to either high-temperature or low-temperature regime, we discuss the conditions under which the left-right symmetry can be retained in each case, giving rise to the universal characteristic of efficiency. In case of one-parameter optimization, we show that while the universality of the first linear term ηc/2η_c/2ηc​/2 is robust and holds consistently across all conditions, the universality of the quadratic term ηC2/8η_C^2/8ηC2​/8 depends on the constraints imposed on the control parameters. Finally, we examine the behavior of power as a function of noise-induced coherence parameter highlighting the role of matter-field coupling in determining the suitable operation regime for the heat engine to reap the benefits of noise-induced coherence.
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.
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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 present a detailed thermodynamic analysis of a three-level quantum heat engine coupled continuously to hot and cold reservoirs. The system is driven by an oscillating external field and is described by the Markovian quantum master equation. We use the general form of the dissipator which is consistent with thermodynamics. We calculate the heat, power, and efficiency of the system for the heat-engine operating regime and also examine the thermodynamic uncertainty relation. The efficiency of the system is strongly dependent on the structure of the dissipator, and the correlations between different levels can be an obstacle for ideal operation. In quantum systems, the heat flux is decomposed into the population and coherent parts. The coherent part is specific to quantum systems, and in contrast to the population part, it cannot be expressed by a simple series expansion in the linear-response regime. We discuss how the interplay between the population and coherent parts affects the performance of the heat engine.
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.
The two-level quantum heat engines have been studied extensively. Before that, the optimization of most heat engines was mainly concentrated in non-degenerate cases. We consider the level degeneracy, then calculate the maximum operation time and the irreversible dissipation coefficient of the two-level system under the scheme of linear tuned levels. In the high-temperature limit, we find that the level degeneracy affects the maximum power of the two-level heat engine. Especially in the case of the same degeneracy of the ground state and the excited state, the influence is the greatest. In addition, we also show that the degeneracy does not affect the efficiency at maximum power and the consistent relation of the two-level Carnot-like heat engine.