Kerr-type nonlinear baths enhance cooling in quantum refrigerators

We study the self-contained three-qubit quantum refrigerator, with a three-body interaction enabling cooling of the target qubit, in presence of baths composed of anharmonic quantum oscillators with Kerr-type nonlinearity. We show that such baths, locally connected to the three qubits, opens up the opportunity to implement superior steady-state cooling compared to using harmonic oscillator baths, aiding in access to the free energy required for empowering the refrigerator function autonomously. We find that in spite of providing significant primacy in steady-state cooling, such anharmonic baths do not impart much edge over using harmonic oscillator baths if one targets transient cooling. However, we gain access to steady-state cooling in the parameter region where only transient cooling could be achieved by using harmonic baths. Subsequently, we also study the scaling of steady-state cooling advantage and the minimum attainable temperature for varying levels of anharmonicity present in the bath oscillators. Finally, we analyse heat currents and coefficients of performance of quantum refrigerators using bath modes involving Kerr-type nonlinearity, and present a comparison with the case of using bosonic baths made of simple harmonic oscillators. On the way, we derive the decay rates in the Gorini-Kossakowski-Sudarshan-Lindblad quantum master equation for Kerr-type anharmonic oscillator baths.