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8.1 Squid I/V Response
As explained in Chapters 2.3.4 and 4.1.3, SQuIDs (Superconducting Quantum
Interference Devices) can be used as highly sensitive magnetometers.
To first
order, a squid can be understood to behave like a single Josephson function (see
Chapter 2.2.2) whose critical current I c depends on the magnetic flux bias that is
applied to the squid’s inductive loop. The mutual inductance between the qubit
and the squid loop then makes it possible to measure the qubit’s magnetic flux
state by probing the squid’s critical current, i.e. it causes the critical current I c to
depend monotonically on the qubit state’s position along the δ-axis.
To verify that the squid is operating correctly and to calibrate the readout
procedure, it is useful to measure the squid’s voltage response to an applied sinusoidal
current bias (its I/V curve) as shown in Figure 8.1. The current bias in
this case is done by placing a 10 kΩ resistor in series with the squid and voltage
biasing the two elements. Since the squid’s resistance is much lower than 10 kΩ,
this results in a current bias I bias ≈ V bias / 10 kΩ. Since the qubit circuit at this
point is still unbiased, the qubit will have settled into a random magnetic flux
state which corresponds to an unknown (and potentially fluctuating) flux bias applied
to the squid. The resulting X-Y trace should look similar to the one shown
in Figure 8.1b. The trace should be symmetric except for an offset on the critical
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