Ultralong-distance quantum correlations in three-terminal Josephson junctions

Abstract

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 ξ 0 is smaller than the superconducting coherence length), and the "ultralong-distance Floquet-Tomasch clusters of Cooper pairs" if R 0 l ϕ , where l ϕ ξ 0 is the mesoscopic coherence length of the BCS quasiparticles. Analytical theory is presented for the simplest cluster at voltage eV > ∆/2, i.e. the ultralong-distance Floquet-Tomasch octets, where ∆ 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 ≈ 30 µm which is orders of magnitude larger than the zero-energy BCS coherence length ξ 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.