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We study the self-contained three-qubit quantum refrigerator, with athree-body interaction enabling cooling of the target qubit, in presence ofbaths composed of anharmonic quantum oscillators with Kerr-type nonlinearity.We show that such baths, locally connected to the three qubits, opens up theopportunity to implement superior steady-state cooling compared to usingharmonic oscillator baths, aiding in access to the free energy required forempowering the refrigerator function autonomously. We find that in spite ofproviding significant primacy in steady-state cooling, such anharmonic baths donot impart much edge over using harmonic oscillator baths if one targetstransient cooling. However, we gain access to steady-state cooling in theparameter region where only transient cooling could be achieved by usingharmonic baths. Subsequently, we also study the scaling of steady-state coolingadvantage and the minimum attainable temperature for varying levels ofanharmonicity present in the bath oscillators. Finally, we analyse heatcurrents and coefficients of performance of quantum refrigerators using bathmodes involving Kerr-type nonlinearity, and present a comparison with the caseof using bosonic baths made of simple harmonic oscillators. On the way, wederive the decay rates in the Gorini-Kossakowski-Sudarshan-Lindblad quantummaster equation for Kerr-type anharmonic oscillator baths.

Kerr-type nonlinear baths enhance cooling in quantum refrigerators