---
title: "SQUID: Flux into Voltage Interactive Lab | Sandbox Physics"
description: "How can a magnetic flux change a superconducting circuit’s voltage? Flux changes the phase difference between the two junctions. Their supercurrents reinforce or cancel, changing the largest current the loop can carry at zero voltage. A fixed bias above that limit produces a voltage that varies periodically with flux."
canonical_url: "https://sandboxphysics.com/labs/squid-flux-response/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/squid-flux-response/"
last_modified: "2026-10-24"
---

C-X4 · Two junctions around one loop

# SQUID: Flux into Voltage

**How can a magnetic flux change a superconducting circuit’s voltage?** Flux changes the phase difference between the two junctions. Their supercurrents reinforce or cancel, changing the largest current the loop can carry at zero voltage. A fixed bias above that limit produces a voltage that varies periodically with flux.

Send current through a superconducting ring with two weak links. Sweep the flux and watch interference move the switching threshold and the voltage response.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

Two sinusoidal Josephson junctions have negligible loop inductance. Their critical currents can differ. A noiseless overdamped effective-junction model gives the dc voltage; capacitance, self-field screening, hysteresis and feedback electronics are omitted. Each mean junction critical current is ten microamperes and the effective resistance is ten ohms. The chip, flux marks and moving carriers are schematic; carrier motion illustrates current, not individual electron trajectories.

From the experiment

## Observe, then compare

Cyan: recorded model sweep. Amber marker: present setting. Current in microamperes, voltage in microvolts.

Recorded flux sweep

Voltage response

Nobel · Condensed matter

## What did the original experiments establish?

Follow the apparatus, observations and interpretation in the historical evidence. Each article explains where this teaching model fits.

[Read the historical evidence](https://sandboxphysics.com/stories/condensed-matter/josephson-phase-current/) [All six reading paths](https://sandboxphysics.com/stories/condensed-matter/)

Physics tutorial

## Interference in a superconducting loop

**Background** A dc SQUID places two Josephson junctions in parallel around a ring. Magnetic flux fixes their relative phase.

**Why it matters** A magnetic field becomes an electrical signal when the bias is chosen near the flux-dependent critical current.

Start with the essentials

- **Focus question**: How can a magnetic flux change a superconducting circuit’s voltage?
- **One-sentence intuition**: The phase difference determines how much the two junction supercurrents reinforce.

### Core mathematical model

#### Critical current without loop inductance

$$
I_c(\Phi)=2I_0\sqrt{\cos^2(\pi\Phi/\Phi_0)+d^2\sin^2(\pi\Phi/\Phi_0)}
$$

The mean single-junction critical current sets the scale. The dimensionless imbalance is the difference divided by the sum of the two junction critical currents.

#### Flux quantum

$$
\Phi_0=\frac{h}{2e}
$$

One flux quantum advances the relative phase by one full turn.

#### Overdamped effective-junction voltage

$$
\overline V=R\,\operatorname{sgn}(I_b)\sqrt{\max(0,I_b^2-I_c^2)}
$$

This noiseless dc approximation neglects junction capacitance and loop self-inductance.

### Common difficulties

#### Reading the model correctly

**Typical misconception** A flux quantum is a tiny magnetic particle moving through the hole.

**Better mental model** It is a unit of magnetic flux that sets the phase periodicity. The marks inside the ring indicate applied flux schematically.

### Run the experiment

1. 01

   #### Cancel the two paths

   Compare Constructive interference and Destructive interference.

   **What to observe:** At half a flux quantum the critical current reaches its minimum.

2. 02

   #### Choose a voltage-sensitive bias

   Select Flux-sensitive voltage, then move Applied flux.

   **What to observe:** The fixed current crosses the critical-current envelope and generates a periodic voltage.

3. 03

   #### Unbalance the junctions

   Select Unequal junctions and repeat the flux sweep.

   **What to observe:** The cancellation minimum rises because the supercurrent amplitudes differ.

Physical conclusion

Flux periodicity comes from phase interference; junction imbalance lifts the interference minimum.

Quantum & fields · Starter path

## Start from a single measurement

Predict an outcome, then count what the measurements actually give. The path starts with one qubit and moves on to wave packets, bound states and two-photon interference.

[Start here → **Quantum State & Born Measurement** Predict a probability, turn the analyzer, then compare your prediction with the measured frequency over many shots. Observe · 15 min](https://sandboxphysics.com/labs/qubit-state/)

1. [1 Quantum State & Born Measurement](https://sandboxphysics.com/labs/qubit-state/)
2. [2 Stern–Gerlach Sequence](https://sandboxphysics.com/labs/stern-gerlach-sequence/)
3. [3 Wave Packet & Uncertainty](https://sandboxphysics.com/labs/wave-packet-uncertainty/)
4. [4 Quantum Harmonic Oscillator](https://sandboxphysics.com/labs/quantum-harmonic-oscillator/)
5. [5 Which Path & Quantum Eraser](https://sandboxphysics.com/labs/quantum-eraser/)
6. [6 Hong–Ou–Mandel Two-Photon Interference](https://sandboxphysics.com/labs/hong-ou-mandel/)

[View the full path →](https://sandboxphysics.com/topics/quantum/#starter-path)