SQUID Magnetometer

The intuition — a flux ruler with quantum tick marks

Imagine a tiny superconducting ring, about the size of a grain of sand, sliced open in two places by ultra-thin insulating barriers. Each barrier is a Josephson junction: thin enough that Cooper pairs tunnel straight through it without losing their quantum coherence. The whole ring behaves like a single quantum wavefunction wrapped into a circle.

Now thread a magnetic field through that ring. A superconductor insists that the total flux enclosed by a closed loop be an exact integer multiple of one flux quantum Φ₀. To enforce that rule when the outside world tries to push a fractional amount of flux through, the ring spontaneously runs a circulating screening current that adds or subtracts just enough flux to land on the nearest allowed value. That screening current is the SQUID's answer to "how much field is here?"

Because there are two junctions, the two paths around the ring act like the two slits in a double-slit experiment — the supercurrent that can flow before the device "breaks" into a voltage state interferes, and that interference pattern repeats every single flux quantum. Counting those fringes is like reading a ruler whose tick marks are spaced 2.07×10⁻¹⁵ weber apart. That is why a SQUID can resolve fields no other instrument comes close to.

How a dc SQUID works, step by step

1. Bias the loop. A constant current I_bias is fed across the ring, split between the two junctions. It is set slightly above the loop's critical current so the device is permanently in the resistive state and develops a small dc voltage.
2. External flux arrives. The field you want to measure threads the loop (usually funneled in by a separate superconducting pickup coil, not the field acting on the bare ring directly).
3. Screening current responds. The ring sets up a circulating current to push the enclosed flux toward the nearest integer × Φ₀.
4. Critical current is modulated. That circulating current adds to one junction and subtracts from the other, so the maximum zero-voltage supercurrent the device can carry oscillates with flux, period Φ₀.
5. Voltage tracks flux. Because the bias current is fixed, the changing critical current shows up as a changing voltage V(Φ) that rises and falls with period Φ₀ — typically tens of microvolts of swing.
6. Flux-lock and read out. A feedback loop injects an opposing flux to hold the SQUID at the steepest part of its V–Φ curve. The feedback current required to cancel the incoming flux is the linearized output.

The governing physics

Two equations underpin everything. The first is the dc Josephson relation: the supercurrent through a junction depends on the difference in the quantum phase φ across it,

I = I_c · sin(φ)

The second is flux quantization plus phase continuity: going once around the loop, the phase must return to itself modulo 2π, which links the two junction phases to the enclosed flux,

φ₂ − φ₁ = 2π · Φ / Φ₀      with   Φ₀ = h / (2e)

Combining the two junction currents (assuming identical junctions) gives the total maximum supercurrent the dc SQUID can carry as a function of applied flux:

I_max(Φ) = 2 · I_c · |cos(π · Φ / Φ₀)|

This is the two-junction interference pattern. It is exactly periodic in Φ₀, so as flux increases by one quantum the device returns to the same state. The numbers:

Φ₀ = h / (2e)
   = (6.626 × 10⁻³⁴ J·s) / (2 × 1.602 × 10⁻¹⁹ C)
   = 2.068 × 10⁻¹⁵ Wb

The factor 2e — not e — in the denominator is the smoking gun that the supercurrent is carried by paired electrons (Cooper pairs), not single electrons.

Worked example — how small a field can it see?

Suppose the SQUID loop encloses an area A = 0.01 mm² = 1×10⁻⁸ m². One flux quantum threading that area corresponds to a field

B₀ = Φ₀ / A = (2.07 × 10⁻¹⁵ Wb) / (1 × 10⁻⁸ m²) ≈ 2 × 10⁻⁷ T = 0.2 µT

That alone isn't impressive. The magic is in the resolution: a good SQUID resolves a few micro-flux-quanta per √Hz — roughly 1×10⁻⁶ Φ₀/√Hz. So the smallest flux change it can register is

δΦ ≈ 10⁻⁶ · Φ₀ ≈ 2 × 10⁻²¹ Wb
δB ≈ δΦ / A ≈ 2 × 10⁻¹³ T  (bare loop)

In practice the bare loop is tiny, so a large superconducting pickup coil (centimetres across) collects flux over a big area and funnels it into the small SQUID loop via a transformer. That flux concentration pushes field resolution down into the 1–10 femtotesla per √Hz range. A neuron firing produces a field of order 100 fT at the scalp — comfortably above that floor — which is why magnetoencephalography is possible at all.

SQUID vs other magnetometers

Sensor	Typical resolution	Operating temp	Bandwidth	Cost / complexity	Best for
dc SQUID	~1–10 fT/√Hz (10⁻¹⁵ T)	4.2 K (Nb) / 77 K (YBCO)	DC–~MHz	Very high — needs cryogenics + shielding	Biomagnetism (MEG/MCG), geophysics, metrology
Optically pumped (SERF) atomic	~1–10 fT/√Hz	Room temp (heated cell)	DC–~kHz	High; no cryogenics	Portable MEG, zero-field magnetometry
Fluxgate	~10 pT–1 nT	Room temp	DC–~kHz	Low–moderate	Space probes, navigation, surveying
Hall-effect sensor	~1 µT	Room temp	DC–~MHz	Very low (chip)	Current sensing, position, automotive
Magnetoresistive (AMR/GMR)	~1–100 nT	Room temp	DC–~MHz	Low (chip)	Compasses, hard-drive heads, IoT
Proton precession	~0.1–1 nT	Room temp	Slow (seconds)	Moderate	Absolute field surveys, archaeology

Note the scale: a SQUID's 10⁻¹⁵ T floor is roughly a billion times finer than a Hall sensor's 10⁻⁶ T, and about fifty billion times finer than Earth's 50 µT field.

Where SQUIDs show up — and what they cost

• Magnetoencephalography (MEG). A whole-head MEG system packs roughly 200–300 SQUID channels in a helmet-shaped dewar, mapping the ~100 fT magnetic signatures of neural currents with millisecond timing. Systems cost on the order of US$2–3 million and live inside a magnetically shielded room.
• Magnetocardiography (MCG). The heart's field is ~50 picotesla at the chest — large for a SQUID — enabling contactless, electrode-free cardiac mapping.
• Geophysics and mineral exploration. Airborne and ground SQUID systems measure tiny anomalies from ore bodies and map the conductivity of the crust (transient electromagnetics).
• Non-destructive evaluation. Detecting cracks, corrosion, and reinforcement-bar flaws by their distortion of an applied field, without contact.
• Metrology and standards. SQUIDs underpin the most precise current comparators and noise thermometers, and the Josephson effect itself defines the SI volt.
• Fundamental physics. Searches for dark matter (axion detectors), tests of gravity, and readout of superconducting qubits all lean on SQUID amplifiers as near-quantum-limited detectors.
• Materials characterization. The commercial "SQUID magnetometer" most labs own is a MPMS — a sample is moved through a SQUID pickup coil to measure its magnetic moment to ~10⁻⁸ emu.

dc SQUID vs rf SQUID

Feature	dc SQUID	rf SQUID
Number of junctions	Two	One
Bias	Steady dc current	Inductively coupled rf tank circuit
Physics of readout	Two-path quantum interference	Periodic loading of a resonant circuit
Noise performance	Best; near quantum limit	Generally higher noise
Fabrication (historic)	Harder — two matched junctions	Easier — single junction
Modern usage	Dominant in instruments	Niche / legacy

Common misconceptions and edge cases

• "It measures field directly." A SQUID measures magnetic flux through its loop, not field. Field resolution depends entirely on the pickup-coil geometry that converts field to flux.
• "The output reads off the voltage." The raw V–Φ curve is periodic and nonlinear, so a bare voltage is ambiguous. Real instruments run a Flux-Locked Loop and report the feedback flux, giving a single-valued linear output over many quanta.
• "More junctions would be even better." Two junctions give the sharpest practical interference; the device is fundamentally a two-path interferometer. Arrays of SQUIDs (SQIFs) exist but serve different goals like absolute-field linearity.
• "It needs a strong field to work." The opposite — SQUIDs excel at the faintest fields and saturate or require careful flux counting in large ones. They run inside heavy magnetic shielding precisely to keep Earth's field and 50/60 Hz mains hum out.
• "High-T SQUIDs replaced the helium ones." 77 K YBCO SQUIDs are cheaper to cool but noisier, owing to grain-boundary junctions and flux creep. The lowest-noise work still uses 4 K niobium devices.
• "The factor of 2 in Φ₀ is arbitrary." It is the experimental fingerprint of Cooper pairing — the carriers have charge 2e, so flux quantizes in units of h/2e, half of what single-electron quantization would give.