Optimizing one-qubit refrigerators in the strong-coupling regime

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 c RCPT ( λ ) . Numerical optimization reveals a critical coupling strength λ c ≈ 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 Ω , and a family of figures of merit ε I Qc 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.