Josephson effect

The Josephson effect arises from the coherent tunneling of Cooper pairs between two superconductors separated by a thin insulating barrier, known as a Josephson junction. The supercurrent I is related to the phase difference φ between the superconducting wavefunctions by the first Josephson relation: I = I_c sin φ, where I_c is the critical current.¹ The second relation links the time derivative of φ to the voltage across the junction: dφ/dt = (2e/ħ)V, where e is the electron charge and ħ is the reduced Planck constant.²

In the DC Josephson effect, a constant supercurrent flows with zero voltage, up to the critical current. When a constant voltage V is applied, the phase evolves linearly, producing an alternating supercurrent with frequency f = (2e/h)V, known as the AC Josephson effect. This frequency-voltage relation is exact and is used to define the volt in metrology.

The most prominent application is the superconducting quantum interference device (SQUID), which exploits the sensitivity of the critical current to magnetic flux to measure extremely small magnetic fields.³ Josephson junctions are also used in voltage standards, where arrays of junctions produce precise voltages, and in quantum computing as qubits (e.g., transmon).⁴

Beyond the standard superconductor-insulator-superconductor junction, the Josephson effect occurs in other configurations, such as superconductor-normal metal-superconductor (SNS) junctions and constriction-type weak links. The effect also appears in exotic systems like superfluid helium-3 and ultracold atomic gases, where analogous phase coherence is observed.⁵ A lesser-known fact is that the Josephson effect was initially met with skepticism; John Bardeen argued against it, but the subsequent experimental confirmation by Anderson and Rowell in 1963 validated Josephson's theory.⁶

Cooper pair

A bound state of two electrons with opposite spin and momentum, responsible for superconductivity.

Critical current

The maximum supercurrent a Josephson junction can sustain without voltage.

SQUID

Superconducting Quantum Interference Device, a sensitive magnetometer based on Josephson junctions.

Weak link

A thin region connecting two superconductors that allows Josephson tunneling.