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The European Physical Journal Plus

Optimization of inverse one-qubit refrigerators

J. J. Fernández

Published May 26, 2025• 1 citation
Publisher

Abstract

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 $$\Omega$$ 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.

DOI
10.1140/epjp/s13360-025-06313-0

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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.
Abstract We study the performance of one-qubit quantum and semiclassic refrigerators with the qubit on the hot side. We obtain the cooling power and the Ω\OmegaΩ Ω function. We discover that the quantum refrigerators perform differently to classic ones. We also prove that even in the high-temperature limit, where the semiclassic version of the refrigerator is valid, the results of the optimization are different to those obtained by optimizing classic refrigerators.
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.
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.
We study the optimal performance of a three-level quantum refrigerator using two different objective functions: cooling power and χ function. For both cases, we obtain general expressions for the coefficient of performance (COP) and derive its well-known lower and upper bounds for the limiting cases when the ratio of system-bath coupling constants at the hot and cold contacts approaches infinity and zero, respectively. We also show that the cooling power can be maximized with respect to one control frequency, while χ function can be maximized globally with respect to two control frequencies. Additionally, we show that in the low-temperature regime, our model of refrigerator can be mapped to Feynman's ratchet and pawl model, a classical mesoscopic heat engine. In the parameter regime where both cooling power and χ function can be maximized, we compare the cooling power of the quantum refrigerator at maximum χ function with the maximum cooling power.
Abstract We discuss a quantum refrigerator to increase the ground state probability of a target qubit whose energy difference between the ground and excited states is less than the thermal energyof its environment. We consider two types of quantum refrigerators: (1) one extra qubit with frequent pulse operations and(2) two extra qubits without them. These two types of refrigerators are evaluated from the viewpoint of quantum thermodynamics. More specifically,we calculate the heat removed from the target qubit, the work done for the system, and the coefficient of performance (COP), the ratio between the heat ant work.We show that the COP of the second type outperforms that of the first one.Our results are useful to design a high-performance quantum refrigerator cooling down a qubit.
The derivation of general performance benchmarks is important in the design of highly optimized heat engines and refrigerators. To obtain them, one may model phenomenologically the leading sources of irreversibility ending up with results that are model independent, but limited in scope. Alternatively, one can take a simple physical system realizing a thermodynamic cycle and assess its optimal operation from a complete microscopic description. We follow this approach in order to derive the coefficient of performance at maximum cooling rate for any endoreversible quantum refrigerator. At striking variance with the universality of the optimal efficiency of heat engines, we find that the cooling performance at maximum power is crucially determined by the details of the specific system-bath interaction mechanism. A closed analytical benchmark is found for endoreversible refrigerators weakly coupled to unstructured bosonic heat baths: an ubiquitous case study in quantum thermodynamics.