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A single spin in a Josephson junction can reverse the flow of the supercurrent by changing the sign of the superconducting phase difference across it. At mesoscopic length scales, these π-junctions are employed in various applications, such as finding the pairing symmetry of the underlying superconductor, as well as quantum computing. At the atomic scale, the counterpart of a single spin in a superconducting tunnel junction is known as a Yu–Shiba–Rusinov state. Observation of the supercurrent reversal in that setting has so far remained elusive. Here we demonstrate such a 0 to π transition of a Josephson junction through a Yu–Shiba–Rusinov state as we continuously change the impurity–superconductor coupling. We detect the sign change in the critical current by exploiting a second transport channel as reference in analogy to a superconducting quantum interference device, which provides our scanning tunnelling microscope with the required phase sensitivity. The measured change in the Josephson current is a signature of the quantum phase transition and allows its characterization with high resolution.

The global network of gravitational-wave observatories now includes five detectors, namely LIGO Hanford, LIGO Livingston, Virgo, KAGRA, and GEO 600. These detectors collected data during their third observing run, O3, composed of three phases: O3a starting in 2019 April and lasting six months, O3b starting in 2019 November and lasting five months, and O3GK starting in 2020 April and lasting two weeks. In this paper we describe these data and various other science products that can be freely accessed through the Gravitational Wave Open Science Center at https://gwosc.org. The main data set, consisting of the gravitational-wave strain time series that contains the astrophysical signals, is released together with supporting data useful for their analysis and documentation, tutorials, as well as analysis software packages.

Very recent experiments have reported the tunneling between Yu-Shiba-Rusinov (YSR) bound states at the atomic scale. These experiments have been realized with the help of a scanning tunneling microscope where a superconducting tip is functionalized with a magnetic impurity and is used to probe another magnetic impurity deposited on a superconducting substrate. In this way it has become possible to study for the first time the spin-dependent transport between individual superconducting bound states. Motivated by these experiments, we present here a comprehensive theoretical study of the tunneling processes between YSR bound states in a system in which two magnetic impurities are coupled to superconducting leads. Our theory is based on a combination of an Anderson model with broken spin degeneracy to describe the impurities and nonequilibrium Green's function techniques to compute the current-voltage characteristics. This combination allows us to describe the spin-dependent transport for an arbitrary strength of the tunnel coupling between the impurities. We first focus on the tunnel regime and show that our theory naturally explains the experimental observations of the appearance of current peaks in the subgap region due to both the direct and thermal tunneling between the YSR states in both impurities. Then, we study in detail the case of junctions with increasing transparency, which has not been experimentally explored yet, and predict the occurrence of a large variety of (multiple) Andreev reflections mediated by YSR states that give rise to a very rich structure in the subgap current. In particular, we predict the occurrence of multiple Andreev reflections that involve YSR states in different impurities. These processes have no analogue in single-impurity junctions and they are manifested as current peaks with negative differential conductance for subgap voltages. Overall, our work illustrates the unique physics that emerges when the spin degree of freedom is added to a system with superconducting bound states.