DC SQUID Flux Interference

Worked Example

Consider a SQUID with completely asymmetric junctions (Junction ratio r = 0). Let the applied flux be half a flux quantum (f = 0.5) and the mean phase be 90 degrees. We compute the sine coefficient, cosine coefficient, total current and critical envelope.

Given:
f = 0.5 (flux quanta)
r = 0 (junction ratio)
phi = 90 degrees (pi/2 radians)

1. Compute Coefficients:
Sine coefficient = (1 + r) * cos(pi * f)
                 = (1 + 0) * cos(pi/2)
                 = 1 * 0 = 0.0

Cosine coefficient = (1 - r) * sin(pi * f)
                   = (1 - 0) * sin(pi/2)
                   = 1 * 1 = 1.0

2. Compute Total Current (I):
I = SineCoefficient * sin(phi) + CosineCoefficient * cos(phi)
  = 0.0 * sin(pi/2) + 1.0 * cos(pi/2)
  = 0.0 * 1.0 + 1.0 * 0.0
  = 0.0

3. Compute Critical Envelope:
Envelope = sqrt(SineCoefficient^2 + CosineCoefficient^2)
         = sqrt(0.0^2 + 1.0^2)
         = 1.0

Experiment

Open the DC SQUID Flux Interference module. Test the dependence of the total current on phase and flux asymmetry.

1. Set Flux quanta to 0.5.
2. Set Junction ratio to 1 (symmetric junctions). Observe complete cancellation (critical envelope = 0).
3. Change Junction ratio to 0 (completely asymmetric). The critical envelope becomes 1.0, meaning interference is incomplete.
4. Set Mean phase degrees to 90. Notice how the total current changes based on these parameters. The calculated total current will be 0.0 for this case, while the envelope is 1.0.

Limitations

This simulation models an ideal, static DC SQUID with negligible loop self-inductance. It does not compute voltage or resistance dynamics. Furthermore, self-screening effects and finite-temperature noise are neglected in this simple model.

References

The following resource explains the phase and flux dependence of Josephson junctions used in a DC SQUID.

• SQUID Operations and Theory