# Theory of quantum-circuit refrigeration by photon-assisted electron tunneling

## TL;DR

This paper develops a first-principles theory for photon-assisted electron tunneling in superconductor-normal metal junctions coupled to resonators, accurately describing their refrigeration and heating effects and guiding quantum device initialization.

## Contribution

It introduces a comprehensive theoretical framework validated by experiments, providing analytical estimates and optimization principles for quantum-circuit refrigeration.

## Key findings

- Quantitative agreement with experimental refrigeration and heating data
- Analytical estimates of coupling strength and reservoir temperature
- Guidelines for optimizing quantum device initialization

## Abstract

We focus on a recently experimentally realized scenario of normal-metal-insulator-superconductor tunnel junctions coupled to a superconducting resonator. We develop a first-principles theory to describe the effect of photon-assisted electron tunneling on the quantum state of the resonator. Our results are in very good quantitative agreement with the previous experiments on refrigeration and heating of the resonator using the photon-assisted tunneling, thus providing a stringent verification of the developed theory. Importantly, our results provide simple analytical estimates of the voltage-tunable coupling strength and temperature of the thermal reservoir formed by the photon-assisted tunneling. Consequently, they are used to introduce optimization principles for initialization of quantum devices using such a quantum-circuit refrigerator. Thanks to the first-principles nature of our approach, extension of the theory to the full spectrum of quantum electric devices seems plausible.