Four-quadrant flux quanta counting for wide-range SQUID amplifiers

We have studied flux quanta counting in an open loop as a way to implement superconducting quantum interference device (SQUID) amplifiers with a large dynamic range and small power dissipation simultaneously. Good signal-to-noise ratio at all flux values is provided by using two SQUIDs, one yielding sin(Φ) and the other cos(Φ) proportional signals. In principle, the lack of feedback lifts the slew rate limitation due to the loop causality present in previously implemented flux quanta counters. Experimental results are shown for up to 180 Φ₀ peak-to-peak flux ranges with a 1.5 μΦ₀ Hz^−1/2 noise floor, dominated by the digitizer noise. The SQUID and low-noise amplifier would allow a 0.07 μΦ₀ Hz^−1/2 noise floor with a more silent digitizer. Operation up to a 13 Φ₀ μs⁻¹ slew rate was demonstrated, but this is not a fundamental limitation. In our experiment, the mismatch between the sin(Φ) and cos(Φ) channels limited the practically achievable slew rate.