Non-local Supercurrent of Quartets in a Three-Terminal Josephson Junction

We report an observation of a new, non dissipative and non local supercurrent, carried by quartets; each consisting of four entangled electrons. The supercurrent is a result of a novel 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, exist only in equilibrium, in the present realization the ABS exists also in the strongly nonlinear regime (biased terminals). The presence of supercurrent carried by quartets was established by performing non-local conductance and cross-correlation of current fluctuations measurements, in different devices made of aluminum-InAs nanowire junctions. An extensive and detailed theoretical study is intertwined with the experimental results

Proposal for detecting the π−\pi-shifted Cooper quartet supercurrent

The multiterminal Josephson effect aroused considerable interest recently, in connection with theoretical and experimental evidence for correlations among Cooper pairs, that is, the so-called Cooper quartets. It was further predicted that the spectrum of Andreev bound states in such devices could host Weyl-point singularities. However, the relative phase between the Cooper pair and quartet supercurrents has not yet been addressed experimentally. Here, we propose an experiment involving four-terminal Josephson junctions with two independent orthogonal supercurrents, and calculate the critical current contours (CCCs) from a multiterminal Josephson junction circuit theory. We predict a generically $\pi$-shifted contribution of both the local or nonlocal second-order Josephson harmonics. Furthermore, we show that these lead to marked nonconvex shapes for the CCCs in zero magnetic field, where the dissipative state reenters into the superconducting one. Eventually, we discuss distinctive features of the non-local Josephson processes in the CCCs. The experimental observation of the latter could allow providing firm evidence of the $\pi$-shifted Cooper quartet current-phase relation.Comment: Third revision: manuscript in final for

Interference of Cooper quartet Andreev bound states in a multi-terminal graphene-based Josephson junction

In a Josephson junction (JJ), Cooper pairs are transported via Andreev bound states (ABSs) between superconductors. The ABSs in the weak link of multi-terminal (MT) JJs can coherently hybridize two Cooper pairs among different superconducting electrodes, resulting in the Cooper quartet (CQ) involving four fermions entanglement. The energy spectrum of these CQ-ABS can be controlled by biasing MT-JJs due to the AC Josephson effect. Here, using gate tunable four-terminal graphene JJs complemented with a flux loop, we construct CQs with a tunable spectrum. The critical quartet supercurrent exhibits magneto-oscillation associated with a charge of 4e; thereby presenting the evidence for interference between entangled CQ-ABS. At a finite bias voltage, we find the DC quartet supercurrent shows non-monotonic bias dependent behavior, attributed to Landau-Zener transitions between different Floquet bands. Our experimental demonstration of coherent non-equilibrium CQ-ABS sets a path for design of artificial topological materials based on MT-JJs

Ultralong-distance quantum correlations in three-terminal Josephson junctions

In the paper, we address nonlocality and quantum correlations in three-terminal Josephson junctions, where the BCS superconductors $S_a$, $S_b$ and $S_c$ are voltage-biased at $(V_a,V_b,V_c)=(V,-V,0)$ and $V$ is a significant fraction of the gap. The constituting two-terminal $S_a$-dot-$S_c$ and $S_c$-dot-$S_b$ are connected at arbitrary distance $R_0$ on the grounded $S_c$. The proposed interpretation of the numerical experiments relies on the interplay between the time-periodic Floquet-Josephson dynamics, Cooper pair splitting and the long-range Tomasch effect. We find cross-over between the "Floquet-Andreev quartets" (if $R_0<\xi_0$ is smaller than the superconducting coherence length), and the "ultralong-distance Floquet-Tomasch clusters of Cooper pairs" if $R_0 < l_\varphi$, where $l_\varphi\gg\xi_0$ is the mesoscopic coherence length of the BCS quasiparticles. Analytical theory is presented for the simplest cluster at voltage $eV>\Delta/2$, i.e. the ultralong-distance Floquet-Tomasch octets, where $\Delta$ is the superconducting gap. The range of the effect is conjectured to be the same as in the Tomasch experiment, i.e. the junctions can be remotely separated by the mesoscopic $R_0\approx 30\,\mu$m which is orders of magnitude larger than the zero-energy BCS coherence length $\xi_0$. Our results go beyond the paradigm of classical synchronization in the macroscopic Josephson circuits. The effect can be detected with dc-transport and zero-frequency quantum current-noise cross-correlation experiments, and it can be used for fundamental studies of superconducting quasiparticle quantum coherence in the circuits of quantum engineering.Comment: 12 pages, 9 figures, a reference was adde

Proposal for the observation of nonlocal multipair production: the biSQUID

We propose an all-superconducting three-terminal setup consisting in a carbon nanotube (or semiconducting nanowire) contacted to three superconducting leads. The resulting device, referred to as a "biSQUID", is made of four quantum dots arranged in two loops of different surface area. We show how this biSQUID can prove a useful tool to probe nonlocal quantum phenomena in an interferometry setup. We study the measured critical current as a function of the applied magnetic field, which shows peaks in its Fourier spectrum, providing clear signatures of multipair Josephson processes. The device does not require any specific fine-tuning as these features are observed for a wide range of microscopic parameters -- albeit with a non-trivial dependence. Competing effects which may play a significant role in actual experimental realizations are also explored.Comment: 13 pages, 9 figure

A quantum interferometer for quartets in superconducting three-terminal Josephson junctions

An interferometric device is proposed in order to analyze the quartet mode in biased three-terminal Josephson junctions (TTJs), and to provide experimental evidence for emergence of a single stationary phase, the so-called quartet phase. In such a quartet-Superconducting Quantum Interference Device (quartet-SQUID), the flux sensitivity exhibits period ${hc}/{4e}$, which is the fingerprint of a transient intermediate state involving two entangled Cooper pairs. The quartet-SQUID provides two informations: an amplitude that measures a total ``quartet critical current'', and a phase lapse coming from the superposition of the following two current components: the quartet supercurrent that is odd in the quartet phase, and the phase-sensitive multiple Andreev reflection (phase-MAR) quasiparticle current, that is even in the quartet phase. This makes a TTJ a generically "$\theta$-junction". Evidence for phase-MARs plays against conservative scenarii involving synchronization of AC Josephson currents, based on ``adiabatic'' phase dynamics and RSJ-like models.Comment: 6 pages, 2 figures, revised manuscript (minor modifications