Josephson Junction — Quantum Tunnelling Through a Superconducting Barrier

Written by MySimulator Team · Reviewed by MySimulator Editorial Review

A Josephson junction is a deceptively simple device — two superconductors separated by a barrier so thin that quantum mechanics lets a supercurrent flow straight through it without any applied voltage. First predicted by Brian Josephson in 1962, this behaviour seems to violate everyday intuition: a current crosses an insulating gap of its own accord. The explanation lies in quantum tunnelling of paired electrons, and the consequences have proved enormous. Josephson junctions sit at the heart of the world's most sensitive magnetometers, define the international standard for the volt, and form the active element of most superconducting quantum computers. Understanding the junction means understanding how coherence — the shared quantum phase of a vast number of particles — can produce measurable, controllable electrical effects in a circuit you can hold in your hand.

The DC Josephson Effect: Current Without Voltage

In a superconductor, electrons bind into Cooper pairs that all share a single macroscopic wavefunction with a well-defined phase. When two superconductors are brought close together with only a thin barrier between them — a few nanometres of oxide, a sliver of normal metal, or a narrow constriction — their wavefunctions overlap weakly. Cooper pairs can then tunnel coherently from one side to the other. Remarkably, a steady supercurrent flows even with zero voltage across the junction. This is the DC Josephson effect.

The size of this supercurrent depends only on the difference in phase between the two superconductors. Josephson's first equation expresses this relationship:

I = I_c · sin(φ)

Here I is the current, φ is the phase difference between the two condensates, and I_c is the critical current — the maximum supercurrent the junction can sustain. Because the relationship involves a sine, the current can never exceed I_c. Push harder than that and the junction can no longer carry a dissipationless current; it abruptly develops a voltage and becomes resistive. The critical current depends on the barrier's thickness and area and on the properties of the superconducting electrodes. What makes the effect so striking is its non-local character: the current is set not by a voltage drop, as Ohm's law would demand, but by the geometry of a quantum phase shared across the whole device. This is macroscopic quantum behaviour made visible in a laboratory measurement.

The AC Josephson Effect and the Quantum of Frequency

The story becomes richer when a constant voltage V is held across the junction. Josephson's second equation describes how the phase difference then evolves in time:

dφ/dt = (2e / ħ) · V

The factor 2e appears because the charge carriers are pairs of electrons, not single ones, and ħ is the reduced Planck constant. With a fixed voltage the phase winds steadily forwards, and through the first equation the supercurrent oscillates sinusoidally. The junction becomes a perfect voltage-to-frequency converter. This is the AC Josephson effect, and the oscillation frequency is given by f = 2eV / h.

The proportionality constant, the Josephson constant K_J = 2e / h, is approximately 483.6 GHz per millivolt. Because it is built entirely from fundamental constants, it provides an extraordinarily reproducible link between voltage and frequency — and frequency can be measured with breathtaking precision against atomic clocks. This is precisely why Josephson junctions underpin the modern voltage standard: by counting microwave-driven oscillations, metrology laboratories realise the volt from first principles rather than from a physical reference cell. The same equations also explain how an applied microwave field produces flat steps, known as Shapiro steps, in the junction's current–voltage curve. The depth of the effect is that two fundamental constants, the electron charge and Planck's constant, govern the behaviour of a practical circuit element, tying everyday electronics to the foundations of quantum theory.

Real-World Applications

• SQUID magnetometers: A loop containing one or two junctions exploits flux quantisation to detect magnetic fields a billion times weaker than the Earth's. They are used in brain imaging (magnetoencephalography), geophysical surveys, and materials research.
• The voltage standard: Arrays of thousands of junctions driven by microwaves realise the volt to parts per billion, replacing fragile chemical reference cells in national measurement institutes worldwide.
• Superconducting qubits: Quantum computers from leading research groups and companies use junctions to build transmon and flux qubits, where the junction supplies the non-linearity needed to define a two-level system.
• Fast digital electronics: Single-flux-quantum logic uses junctions to switch and store information as discrete magnetic flux quanta, promising very low-power, high-speed processing.

Common Misconceptions

A frequent misunderstanding is that current crosses the barrier because electrons are simply "pushed" through, as in an ordinary wire. In fact the supercurrent flows with no voltage at all; it is driven by a phase difference, not a potential difference. Another error is to picture single electrons tunnelling — it is Cooper pairs, carrying charge 2e, that make the effect distinctive. People also assume a thicker, "stronger" barrier carries more current, when the opposite is true: increasing the barrier thickness sharply reduces the critical current. Finally, the Josephson effect is sometimes confused with ordinary tunnelling of normal electrons. Both occur, but only the coherent pair tunnelling is dissipationless and phase-dependent. Research suggests these distinctions trip up many newcomers, so testing them in a simulation is genuinely instructive.

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.

Who discovered the Josephson effect? Brian Josephson predicted the effect in 1962 while a graduate student at Cambridge, and he shared the 1973 Nobel Prize in Physics for the work. The effect was confirmed experimentally soon after his prediction.

What is the difference between the DC and AC Josephson effects? The DC effect is a steady supercurrent that flows with zero voltage across the junction. The AC effect appears when a constant voltage is applied: the phase difference evolves and the current oscillates at a frequency proportional to that voltage.

Try It Yourself

Explore the behaviour of superconducting tunnelling with these interactive simulations:

• josephson-junction — vary the phase and voltage and watch the DC and AC effects emerge.
• quantum-tunnel — see how particles penetrate a barrier they classically could not cross.
• superconductivity — model Cooper pairing and the loss of electrical resistance.

Conclusion

The Josephson junction shows how a fundamentally quantum idea — the coherent tunnelling of Cooper pairs across a barrier — becomes a practical, controllable circuit element. Two compact equations, one relating current to phase and the other relating phase to voltage, capture behaviour that powers magnetometers sensitive enough to map the brain, defines the volt through fundamental constants, and provides the heartbeat of superconducting quantum computers. Few devices link such deep physics to such broad technology so directly. By experimenting with the simulations above you can build a genuine feel for how phase, current and voltage interact, and appreciate why this small junction continues to shape the frontier of modern physics.