Evidence for 4e charge of Cooper quartets in a biased multi-terminal graphene-based Josephson junction.

In a Josephson junction (JJ) at zero bias, Cooper pairs are transported between two superconducting contacts via the Andreev bound states (ABSs) formed in the Josephson channel. Extending JJs to multiple superconducting contacts, the ABSs in the Josephson channel can coherently hybridize Cooper pairs among different superconducting electrodes. Biasing three-terminal JJs with antisymmetric voltages, for example, results in a direct current (DC) of Cooper quartet (CQ), which involves a four-fermion entanglement. Here, we report half a flux periodicity in the interference of CQ formed in graphene based multi-terminal (MT) JJs with a magnetic flux loop. We observe that the quartet differential conductance associated with supercurrent exhibits magneto-oscillations associated with a charge of 4e, thereby presenting evidence for interference between different CQ processes. The CQ critical current shows non-monotonic bias dependent behavior, which can be modeled by transitions between Floquet-ABSs. Our experimental observation for voltage-tunable non-equilibrium CQ-ABS in flux-loop-JJs significantly extends our understanding of MT-JJs, enabling future design of topologically unique ABS spectrum.

Nonlocal supercurrent of quartets in a three-terminal Josephson junction.

A novel nonlocal supercurrent, carried by quartets, each consisting of four electrons, is expected to appear in a voltage-biased three-terminal Josephson junction. This supercurrent results from a nonlocal Andreev bound state (ABS), formed among three superconducting terminals. While in a two-terminal Josephson junction the usual ABS, and thus the dc Josephson current, exists only in equilibrium, the ABS, which gives rise to the quartet supercurrent, persists in the nonlinear regime. In this work, we report such resonance in a highly coherent three-terminal Josephson junction made in an InAs nanowire in proximity to an aluminum superconductor. In addition to nonlocal conductance measurements, cross-correlation measurements of current fluctuations provided a distinctive signature of the quartet supercurrent. Multiple device geometries had been tested, allowing us to rule out competing mechanisms and to establish the underlying microscopic origin of this coherent nondissipative current.

Production of nonlocal quartets and phase-sensitive entanglement in a superconducting beam splitter.

Three BCS superconductors Sa, Sb, and S and two short normal regions Na and Nb in a three-terminal SaNaSNb Sb setup provide a source of nonlocal quartets spatially separated as two correlated pairs in Sa and Sb, if the distance between the interfaces Na S and SNb is comparable to the coherence length in S. Low-temperature dc transport of nonlocal quartets from S to Sa and Sb can occur in equilibrium, and also if Sa and Sb are biased at opposite voltages. At higher temperatures, thermal excitations result in correlated current fluctuations which depend on the superconducting phases Φa and Φb in Sa and Sb. Phase-sensitive entanglement is obtained at zero temperature if Na and Nb are replaced by discrete levels.