# Two-Impurity Yu-Shiba-Rusinov States in Coupled Quantum Dots

## TL;DR

This paper demonstrates a superconducting analog of the two-impurity Kondo model using coupled quantum dots, revealing gate-tunable ground state transitions and quantum phase boundaries in YSR states.

## Contribution

It introduces a novel superconducting device that models the two-impurity Kondo effect and explores the quantum phase transitions between different YSR ground states.

## Key findings

- Gate-tunable transition from inter-dot singlet to YSR singlets.
- Observation of quantum phase boundaries to doublet YSR phases.
- Cusped current-voltage characteristic modeled by an overdamped circuit.

## Abstract

Using double quantum dots as the weak link of a Josephson junction, we realize the superconducting analog of the celebrated two-impurity Kondo model. The device shows a cusped current-voltage characteristic, which can be modelled by an overdamped circuit relating the observed cusp current to the Josephson critical current. The gate dependence of the cusp current and of the subgap spectra are used as complementary ground-state indicators to demonstrate gate-tuned changes of the ground state from an inter-dot singlet to independently screened Yu-Shiba-Rusinov (YSR) singlets. In contrast to the two-impurity Kondo effect in normal-state systems, the crossover between these two singlets is heralded by quantum phase boundaries to nearby doublet YSR phases in which only a single spin is screened.