DC SQUID Interferometer: Flux-Quantized Critical Current

Applied Flux

Φ / Φ₀ 0.00

Junction Parameters

Asymmetry I_c2/I_c1 1.00

Bias current I_b (mA) 0.00

Live State

SUPERCURRENT · V = 0

Critical current I_c(Φ)

2.40 mA

Voltage ⟨V⟩

0.00 mV

Loop phase φ mod 2π

0.0°

Flux quanta enclosed

How it works

A DC SQUID is a superconducting loop interrupted by two Josephson junctions. Each junction carries a supercurrent I = I_c,i sin(δ_i), and single-valuedness of the pair wavefunction around the loop locks the two phase differences to the enclosed flux:

δ2 − δ1 = 2π Φ / Φ0        (fluxoid quantization, negligible self-inductance)
Φ0 = h / 2e ≈ 2.068 × 10⁻¹⁵ Wb   (flux quantum, Cooper pairs → 2e)

Maximum (critical) current the loop can carry lossless:
Ic(Φ) = sqrt( Ic1² + Ic2² + 2·Ic1·Ic2·cos(2πΦ/Φ0) )
      → 2·Ic0·|cos(πΦ/Φ0)|   for identical junctions (Ic1 = Ic2 = Ic0)

Overdamped (RSJ) time-averaged voltage once biased past Ic:
⟨V⟩ = Rn · sqrt( Ib² − Ic(Φ)² )   for Ib > Ic(Φ), else ⟨V⟩ = 0

Φ/Φ0 slider — applied flux threading the loop. Ic(Φ) oscillates with period exactly one flux quantum: this interference pattern is what makes a SQUID the most sensitive magnetometer known (~10⁻¹⁵ T).
Asymmetry — unequal junctions (Ic2 ≠ Ic1) never fully cancel Ic at the destructive-interference points, filling in the oscillation minima.
Bias current — drive current through the loop. Below Ic(Φ) the loop is a dissipationless supercurrent (V = 0, particles glow steady blue); above it, the junctions switch to a resistive branch and a real time-averaged voltage appears (particles flicker orange).
The moving marker on the interference curve tracks your current Φ/Φ0 against the analytic Ic(Φ) trace.

Real-world relevance: this exact Ic(Φ) interference pattern is read out in every commercial SQUID magnetometer and susceptometer, and the same two-junction phase-locking is the operating principle behind flux qubits used in superconducting quantum processors.

Supercurrent (V = 0) Resistive branch (V > 0) Josephson junction

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