High linearity superconducting radio frequency magnetic field detector

A method for transducing a flux Φ into an electrical signal, comprising:

• providing a plurality of Josephson junction circuits, each having an output responsive to a nonlinear impedance which depends on a respective flux Φ0 in a periodic manner, with periodicity Φ0=h/2e, where h is Planck's constant and e is the charge on an electron;
• and
• harmonically superposing the respective outputs of the plurality of Josephson junction circuits to increase a linearity with respect to the periodic flux Φ0.

A transducer, comprising:

• an irregular array of Josephson junction circuits, each Josephson junction circuit comprising an input configured to receive a bias current, a first Josephson junction having a critical current Ic1, a second Josephson junction having a critical current Ic1, a loop having a loop inductance, and a shunt Josephson junction in parallel with the loop, having a critical current Ic3, and a shunt inductance L=Φ/2π√{square root over (Ic2+Ish2)}, where Ish is a shunt current passing through the shunt Josephson junction;
• and
• a harmonic combiner, configured to superpose respective outputs of the irregular array of Josephson junction circuits, to at amplify a flux coupled to the respective loops of the irregular array of Josephson junction circuits, and to produce a linearized superposed output.