Control of the Josephson current by varying a gate current has recently beendemonstrated in both 4-terminal and 3-terminal junctions. We show that, whenthe the gates are weakly coupled to the Josephson junction, the Josephsoncurrent versus gate current (or versus gate voltage) relation is the same forboth the 4- and 3- terminal geometries. At low temperature, the supercurrentswitches abruptly as a function of the gate voltage, but only slowly as afunction of the gate current.
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