What Is Josephson effect?

The Josephson effect is a quantum mechanical phenomenon in which an electrical current flows between two superconductors separated by a thin insulating barrier without any applied voltage, and in which an applied voltage produces a precisely defined alternating current whose frequency is proportional to that voltage. The effect was predicted theoretically in 1962 by Brian D. Josephson, then a graduate student at Cambridge University, and confirmed experimentally shortly afterward. Josephson's theoretical predictions earned him a share of the 1973 Nobel Prize in Physics, recognized by the Nobel Committee for his theoretical derivation of the properties of a supercurrent through a tunnel barrier.

The physical structure that exhibits the Josephson effect, a Josephson junction, consists of two superconducting electrodes separated by a barrier thin enough for Cooper pairs to tunnel across quantum mechanically. The barrier may be an insulating oxide layer, a normal metal, a semiconductor, or a weak link in the superconducting material itself, and each configuration produces variants of the underlying effect.

The DC Josephson Effect

The DC Josephson effect describes the flow of a supercurrent through a junction in the absence of any applied voltage. The supercurrent is determined by the sine of the quantum mechanical phase difference between the macroscopic wave functions of the two superconductors: I = I_c sin(φ), where I_c is the critical current of the junction and φ is the phase difference. Below this critical current, the junction behaves as a lossless conductor. The effect is a direct consequence of the long-range phase coherence that characterizes the superconducting state, and it provided early experimental confirmation that the Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity correctly describes macroscopic quantum behavior.

The AC Josephson Effect

When a constant voltage V is applied across a Josephson junction, the phase difference evolves in time at a rate governed by the second Josephson equation: dφ/dt = 2eV/ℏ. This produces an oscillating supercurrent at a frequency ν = 2eV/h, where e is the electron charge and h is Planck's constant. The ratio of frequency to voltage, known as the Josephson constant K_J = 2e/h, equals approximately 483.6 GHz per millivolt and is one of the most precisely determined quantities in physics. The AC effect is the physical basis for Josephson voltage standards, which define the volt in terms of the fundamental constants e and h rather than artifact standards, providing reproducibility at the sub-part-per-billion level. The NIST Josephson voltage standards program maintains and disseminates these standards for national metrology.

Josephson Effect in Metrology and Quantum Computing

The precision of the Josephson frequency-voltage relationship made it the foundation for the international volt standard well before the 2019 redefinition of the SI base units. Josephson junction arrays, consisting of thousands of junctions fabricated on a single chip and biased on quantized voltage steps called Shapiro steps, now generate arbitrary programmable waveforms traceable to quantum constants. In quantum computing, Josephson junctions serve as the nonlinear circuit elements needed to build artificial two-level quantum systems. Superconducting qubits of types including the transmon and flux qubit exploit the junction's nonlinear inductance, which arises directly from the phase-dependent supercurrent relationship, to create an anharmonic energy spectrum where a specific pair of levels can be addressed as a qubit. Research documented through arxiv on Josephson junctions and qubit design details how junction parameters are engineered to achieve target qubit frequencies and anharmonicities.

Applications

The Josephson effect has practical applications in a wide range of fields, including:

• Primary voltage standards in national metrology institutes worldwide
• Superconducting quantum interference devices (SQUIDs) for magnetic field sensing
• Superconducting qubit circuits for quantum computing processors
• Single-flux-quantum (SFQ) digital logic operating at hundreds of gigahertz
• Terahertz radiation detection and generation in scientific instrumentation