Josephson Junction: Quantum Tunnelling Through a Superconducting Barrier

The DC effect: current without voltage

In a superconductor, electrons bind into Cooper pairs sharing a single macroscopic wavefunction with a well-defined phase. When two superconductors are separated by a barrier thin enough — a few nanometres of oxide, a sliver of normal metal — their wavefunctions overlap weakly and Cooper pairs tunnel coherently between them. Remarkably, a steady supercurrent flows even at zero voltage. First predicted by Brian Josephson in 1962 (Nobel Prize 1973), the current depends only on the phase difference φ between the two superconductors:

I = I_c · sin(φ)          ← DC Josephson effect
dφ/dt = (2e/ħ) · V         ← AC Josephson effect
f = 2eV / h                ← voltage-to-frequency conversion
K_J = 2e/h ≈ 483.6 GHz/mV  ← Josephson constant

Because the relationship is sinusoidal, current can never exceed the critical current I_c: push harder and the junction abruptly develops a voltage and becomes resistive. What makes this striking is its non-local character — current is set by a shared quantum phase, not by Ohm's law.

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The AC effect: a perfect voltage-to-frequency converter

Hold a constant voltage V across the junction and the phase difference winds forward steadily, making the supercurrent oscillate sinusoidally at f = 2eV/h. Because the Josephson constant K_J = 2e/h is built entirely from fundamental constants, it links voltage to frequency with extraordinary reproducibility — frequency can be measured against atomic clocks with breathtaking precision. This is exactly why national metrology laboratories realise the modern volt from Josephson junction arrays rather than chemical reference cells, and why applied microwaves produce flat Shapiro steps in the current–voltage curve.

SQUIDs, qubits and everyday electronics

A loop containing one or two junctions — a SQUID — exploits flux quantisation to detect magnetic fields a billion times weaker than Earth's, used in brain imaging and geophysical surveys. Arrays of thousands of junctions driven by microwaves realise the volt to parts per billion. Superconducting qubits (transmon and flux qubits) use a junction's non-linear inductance to carve out an addressable two-level system, and single-flux-quantum logic stores information as discrete magnetic flux quanta for very low-power, high-speed computing. All of this rests on two compact equations and a single quantum idea: coherent tunnelling of paired electrons.

Frequently asked questions

What is a Josephson junction?

A Josephson junction is two superconductors separated by a thin barrier through which Cooper pairs can tunnel coherently, producing a supercurrent with no voltage applied. It is the building block of superconducting electronics, predicted by Brian Josephson in 1962.

What is the difference between the DC and AC Josephson effects?

The DC effect is a steady supercurrent I = Ic·sin(φ) that flows with zero voltage across the junction, set entirely by the phase difference φ. The AC effect appears when a constant voltage V is applied: the phase evolves as dφ/dt = 2eV/ħ and the current oscillates at frequency f = 2eV/h.

What is a SQUID and why is it so sensitive?

A SQUID (Superconducting Quantum Interference Device) is a loop containing one or two Josephson junctions. It exploits magnetic flux quantisation through the loop to detect magnetic fields roughly a billion times weaker than Earth's, making it central to brain imaging, geophysical surveys and materials research.

Try it live

Everything above runs in your browser — open Josephson Junction and watch the DC and AC effects emerge as you vary the drive current, bias voltage and damping. Nothing is installed, nothing is uploaded.

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