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Floquet-Tomasch mechanism for long-range correlations between Cooper pairs in a BCS three-terminal Josephson junction
The Josephson effect originates from tunneling of Cooper pairs between two superconductors, through a non-superconducting insulating region. The current-phase relation deviates from sinusoidal for higher transparency : two, three or more correlated Cooper pairs can be transmitted in a single tunneling event. Three-terminal Josephson junctions have been used to implement [1,2] detection of these correlated Cooper pairs, through their splitting into different leads . The phase rigidity of a BCS superconductor has infinite range, but quartets made of two correlated Cooper pairs do no show infinite range phase rigidity, because they originate from the interfaces in absence of glue between Cooper pairs in the bulk. The question is then to put numbers on this length scale, in connection with experimental results  obtained at the Weizmann Institute on a double-SQUID interferometer . Extending the 1960s McMillan-Anderson model of Tomasch oscillations leads to an original Floquet-Tomasch mechanism for quantum coherent synchronization between two superconductor-quantum dot-superconductor Josephson junctions biased with significant voltages. The effect combines multiple Andreev reflections at each junction to long-range Tomasch propagation in the electron-hole channel above the gap. Simple physical pictures will be presented, in analogy with the tilted band picture for Wannier resonances in solid state physics. The range is limited by inelastic scattering, also in the dirty limit.
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