Optimizing one-qubit refrigerators in the strong-coupling regime

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 $$Q_{\text {c}}^{\text {RCPT}}(\lambda )$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup> <mml:mi>Q</mml:mi> <mml:mrow> <mml:mtext>c</mml:mtext> </mml:mrow> <mml:mtext>RCPT</mml:mtext> </mml:msubsup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>λ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> . Numerical optimization reveals a critical coupling strength $$\lambda _{\text {c}} \approx 0.71$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>λ</mml:mi> <mml:mtext>c</mml:mtext> </mml:msub> <mml:mo>≈</mml:mo> <mml:mn>0.71</mml:mn> </mml:mrow> </mml:math> beyond which cooling performance deteriorates sharply. We analyze the impact of coupling strength on the maximum cooling power, the trade-off function $$\Omega$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Ω</mml:mi> </mml:math> , and a family of figures of merit $$\varepsilon ^I Q_{\text {c}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>ε</mml:mi> <mml:mi>I</mml:mi> </mml:msup> <mml:msub> <mml:mi>Q</mml:mi> <mml:mtext>c</mml:mtext> </mml:msub> </mml:mrow> </mml:math> . 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.