Josephson Effect

Core Idea

When two superconductors are connected by a weak link (thin insulating barrier, narrow constriction, or normal metal), a supercurrent flows that depends on the phase difference phi = phi_1 - phi_2 between the two superconducting order parameters: I = I_c sin(phi) (DC Josephson effect). If a voltage V is applied across the junction, the phase evolves as d(phi)/dt = 2eV/hbar, producing an AC current at frequency f = 2eV/h (AC Josephson effect). The Josephson effects are macroscopic quantum phenomena that directly manifest the phase of the superconducting wavefunction and form the basis of SQUIDs (superconducting quantum interference devices), voltage standards, and superconducting qubits.

Explainer

The Josephson effects, predicted by Brian Josephson in 1962 (Nobel Prize 1973), are among the most remarkable manifestations of macroscopic quantum mechanics. They arise whenever two superconductors are connected by a weak link — a region where the superconducting order parameter is suppressed but not zero. The weak link can be a thin insulating barrier (~1-2 nm of oxide), a point contact, a narrow constriction, or a short normal-metal bridge.

The DC Josephson effect states that a supercurrent I = I_c sin(phi) flows through the junction with zero voltage, where phi = phi_1 - phi_2 is the phase difference between the two superconductors and I_c is the critical current of the junction. The current is carried by Cooper pairs tunneling coherently through the barrier. This is truly remarkable: a macroscopic current (microamps to milliamps) flows through an insulating barrier with no applied voltage, driven entirely by the quantum phase difference. The maximum current I_c depends exponentially on the barrier thickness and on the gap values of the superconductors.

The AC Josephson effect emerges when a DC voltage V is applied across the junction. The phase evolves as d(phi)/dt = 2eV/hbar, so the supercurrent oscillates: I = I_c sin(phi_0 + 2eVt/hbar), with frequency f = 2eV/h. For V = 1 mV, f = 484 GHz — in the far-infrared range. The frequency-voltage ratio 2e/h = 483.5979 GHz/mV is a fundamental constant with no material dependence, making the AC Josephson effect the basis of the international voltage standard. When microwaves at frequency f are applied simultaneously, the junction develops constant-voltage steps at V_n = nhf/2e (Shapiro steps), providing a precise voltage reference.

The combination of Josephson junctions with superconducting loops produces SQUIDs — the most sensitive magnetic flux detectors known. A DC SQUID (two junctions in a loop) exploits the interference of supercurrents from the two junctions, modulated by the magnetic flux through the loop via flux quantization. SQUIDs can detect flux changes of 10^{-6} Phi_0, corresponding to magnetic fields of ~10^{-15} T. Beyond sensing, Josephson junctions are the active elements in superconducting qubits: their nonlinear inductance creates the anharmonic energy spectrum needed to define a two-level quantum system, and the absence of dissipation enables coherence times sufficient for quantum computation. Superconducting quantum processors from IBM, Google, and others are built entirely from Josephson junction circuits.