Inductance bridge for current-quantum phase measurements in superconductors at zero frequency

A zero-frequency bridge has been developed for measuring the inductance and the current-vs-quantum-phase relation of superconductors. The current null detector is a SQUID magnetometer coupled to the bridge by a superconducting transformer. The bridge is balanced by adjusting precision resistors at room temperature. The theory of the bridge and analysis of the null-detector circuit for optimizing the sensitivity are given. For current-dependent inductors, a definition of inductance based on the quantum-phase difference is shown to be useful. Construction and operation of the bridge are described and measurements of inductance vs temperature for Al thin-film meander lines are presented. Zero-frequency measurements avoid the stray coupling to capacitances and normal metal inductances found in high-frequency measurements and the method could give high-precision absolute measurements. The sensitivity of the present instrument is such that an inductor of 4×10−7 H was measured to a relative precision of one part in 104 with a measuring current of 5×10−6 A. Considerable improvement is possible, especially for circuit elements of very small inductance such as Josephson junctions and weak-link superconductors.