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The European Physical Journal Plus

Optimizing one-qubit refrigerators in the strong-coupling regime

J. J. Fernández

Published Feb 3, 2026• 0 citations
Publisher

Abstract

Abstract Real refrigerators operate in finite time, deviating from classical thermodynamics, which predicts zero cooling power at Carnot efficiency. Finite-time thermodynamics (FTT) addresses this by incorporating realistic constraints, but quantum extensions often rely on the weak-coupling approximation. This approximation fails in systems—such as superconducting circuits or nanomechanical resonators—where qubit-bath interactions are strong. To overcome this, we study a one-qubit refrigerator using the non-perturbative reaction-coordinate polaron transform (RCPT), which systematically captures strong-coupling effects through an exact mapping and dressing of a collective bath mode. We derive the renormalized qubit energy and effective dissipation rates, leading to a closed expression for the steady-state cooling power $$Q_{\text {c}}^{\text {RCPT}}(\lambda )$$ Q c RCPT ( λ ) . Numerical optimization reveals a critical coupling strength $$\lambda _{\text {c}} \approx 0.71$$ λ c ≈ 0.71 beyond which cooling performance deteriorates sharply. We analyze the impact of coupling strength on the maximum cooling power, the trade-off function $$\Omega$$ Ω , and a family of figures of merit $$\varepsilon ^I Q_{\text {c}}$$ ε I Q c . Our results establish the validity bounds of the weak-coupling approximation and demonstrate that excessive coupling suppresses energy extraction, providing essential guidelines for designing robust quantum thermal devices in the strong-coupling regime.

DOI
10.1140/epjp/s13360-026-07341-0

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Abstract Real refrigerators operate in finite time, deviating from classical thermodynamics, which predicts zero cooling power at Carnot efficiency. Finite-time thermodynamics (FTT) addresses this by incorporating realistic constraints, but quantum extensions often rely on the weak-coupling approximation. This approximation fails in systems—such as superconducting circuits or nanomechanical resonators—where qubit-bath interactions are strong. To overcome this, we study a one-qubit refrigerator using the non-perturbative reaction-coordinate polaron transform (RCPT), which systematically captures strong-coupling effects through an exact mapping and dressing of a collective bath mode. We derive the renormalized qubit energy and effective dissipation rates, leading to a closed expression for the steady-state cooling power QcRCPT(λ)Q_{\text {c}}^{\text {RCPT}}(\lambda )QcRCPT​(λ) Q c RCPT ( λ ) . Numerical optimization reveals a critical coupling strength λc≈0.71\lambda _{\text {c}} \approx 0.71λc​≈0.71 λ c ≈ 0.71 beyond which cooling performance deteriorates sharply. We analyze the impact of coupling strength on the maximum cooling power, the trade-off function Ω\OmegaΩ Ω , and a family of figures of merit εIQc\varepsilon ^I Q_{\text {c}}εIQc​ ε I Q c . Our results establish the validity bounds of the weak-coupling approximation and demonstrate that excessive coupling suppresses energy extraction, providing essential guidelines for designing robust quantum thermal devices in the strong-coupling regime.
The study of nanoscopic thermal devices attracts an increasing attention, not only because of their key role in understanding the emergence of thermodynamics from quantum theory, but also for the potential use of quantum-mechanical thermal cycles, especially refrigerators, in quantum technologies. This thesis, is devoted to the performance optimization of autonomous (heat-driven) refrigerators. For a quantum refrigerator, one has a full microscopic description of the simple system serving as a working medium, and of its interaction with the external heat baths. This enables a consistent `finite-time? thermodynamic analysis, not relying on any phenomenological assumptions about the leading sources of irreversibility, and allows to establish arguably general performance bounds, essential to benchmark the operation of realistic devices. In particular, tight and model-independent upper bounds for the coefficient of performance at maximum power, are derived here for a class of strongly coupled refrigerators, and seen to hold more generally for other types of heat and power-driven cycles. Remarkably, these ultimate limitations only depend on the particulars of the system-baths interaction at the interface with the object to be cooled. Strategies might be then defined so as to saturate those limits: It is shown how the working medium of the refrigerator may be, for instance, scaled up into a parallel multi-stage configuration, resembling that of macroscopic multi-effect absorption chillers, as a means to increase its cooling power. Similarly, by applying reservoir engineering techniques on selected transitions between the energy states of the working medium, one can mimic exploitable non-equilibrium fluctuations in the baths, capable of boosting the overall power and COP beyond what would be otherwise allowed by the second law of thermodynamics. In this way, heat-driven chillers could be set to compete on a equal footing with the best power-driven refrigerators.
We study the performance of three-level quantum absorption refrigerators, paradigmatic autonomous quantum thermal machines, and reveal central impacts of strong couplings between the working system and the thermal baths. Using the reaction coordinate quantum master equation method, which treats system-bath interactions beyond weak coupling, we demonstrate that in a broad range of parameters the cooling window at strong coupling can be captured by a weak-coupling theory, albeit with parameters renormalized by the system-bath coupling energy. As a result, at strong system-bath couplings the window of cooling is significantly reshaped compared to predictions of weak-coupling treatments. We further show that strong coupling admits direct transport pathways between the thermal reservoirs. Such beyond-second-order transport mechanisms are typically detrimental to the performance of quantum thermal machines. Our study reveals that it is inadequate to claim for either a suppression or an enhancement of the cooling performance as one increases system-bath coupling-when analyzed against a single parameter and in a limited domain. Rather, a comprehensive approach should be adopted so as to uncover the reshaping of the operational window.
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Abstract We study several optimal working regimes of one-qubit quantum refrigerators having one qubit at their cold side. We demonstrate that they can be optimized using the techniques of finite-time thermodynamics on the solutions of the Lindblad equation. Our results show that differently to what happens in classic refrigerators, in our quantum ones the optimization of the cooling power does not lead to an optimal working regime but that using the Ω\OmegaΩ Ω function we can find it. Then, we generalize the study using a family of target functions defined by powers of the coefficient of performance times the cooling power to carry out a more general optimization. These last optimizations reveal the importance that every parameter defining the refrigerator has on the performance of the refrigerators when they work optimally.
We study the performance of quantum absorption refrigerators, paradigmatic autonomous quantum thermal machines, and reveal central impacts of strong couplings between the working system and the thermal baths. Using the reaction coordinate quantum master equation method, which treats system-bath interactions beyond weak coupling, we discover that reshaping of the window of performance is a central outcome of strong system-bath couplings. This alteration of the cooling window stems from the dominant role of parameter renormalization at strong couplings. We further show that strong coupling admits direct transport pathways between the thermal reservoirs. Such beyond-second-order transport mechanisms are typically detrimental to the performance of quantum thermal machines. Our study reveals that it is inadequate to claim for either a suppression or an enhancement of the cooling performance at strong coupling when analyzed against a single parameter and in a limited domain. Rather, a comprehensive approach should be adopted so as to uncover the reshaping of the operation window.
We investigate the performance of a three-spin quantum absorption refrigerator using a refined open quantum system model valid across all inter-spin coupling strengths. It describes the transition between previous approximate models for the weak and the ultrastrong coupling limit, and it predicts optimal refrigeration for moderately strong coupling, where both approximations are inaccurate. Two effects impede a more effective cooling: the coupling between the spins no longer reduces to a simple resonant energy exchange (the rotating wave approximation fails), and the interactions with the thermal baths become sensitive to the level splitting, thus opening additional heat channels between the reservoirs. We identify the modified conditions of refrigeration as a function of the inter-spin coupling strength, and we show that, contrary to intuition, a high-temperature work reservoir thwarts refrigeration in the strong coupling regime.