Josephson effect

Josephson effect. The Josephson effect is a quantum mechanical phenomenon where a supercurrent flows continuously through a barrier separating two superconductors without an applied voltage. This remarkable effect, predicted theoretically by Brian David Josephson in 1962 while he was a graduate student at the University of Cambridge, arises from the phase coherence of the macroscopic wavefunctions describing the superconducting condensates. Its discovery, for which Josephson shared the Nobel Prize in Physics in 1973, provided profound confirmation of the BCS theory and has led to highly precise measurement devices and novel computing architectures.

Physical basis

The effect occurs in a device known as a Josephson junction, which typically consists of two superconducting electrodes separated by a thin insulating barrier, a normal metal, or a constriction. This structure is central to the field of superconducting electronics. The underlying physics is described by the laws of quantum mechanics and the concept of Cooper pair tunneling, where pairs of electrons quantum-mechanically penetrate the barrier. The key parameter is the phase difference between the complex order parameters of the two superconductors, a concept deeply rooted in the Ginzburg-Landau theory. This phase coherence across the junction is maintained by the Josephson coupling energy, which favors a fixed phase relationship.

DC Josephson effect

The DC Josephson effect describes a direct supercurrent that flows across the junction in the absence of any external electric or magnetic fields. This current, Is, is a function of the phase difference, φ, according to the relation Is = Ic sin(φ), where Ic is the junction's critical current. This critical current depends on the properties of the superconductors and the barrier, and was first experimentally verified by researchers including Philip Warren Anderson and John Rowell at Bell Labs. The phenomenon demonstrates dissipationless current flow and is highly sensitive to externally applied magnetic fields, leading to quantum interference patterns analogous to the Aharonov-Bohm effect in superconducting loops.

AC Josephson effect

When a constant voltage V is applied across the junction, the phase difference evolves linearly in time, causing an alternating supercurrent to oscillate across the barrier. This is known as the AC Josephson effect. The frequency f of this oscillation is directly proportional to the applied voltage through the fundamental relation f = (2e/h)V, where e is the elementary charge and h is the Planck constant. This exact frequency-voltage linkage provides a direct connection between macroscopic voltages and fundamental constants. The effect enables the highly precise definition of the volt via the Josephson voltage standard, maintained by institutions like the National Institute of Standards and Technology and the Physikalisch-Technische Bundesanstalt.

Applications

The precision of the Josephson relations has revolutionized electrical metrology. The Josephson voltage standard is a primary standard for the SI volt, used globally by national laboratories. Arrays of thousands of junctions, developed at institutions like the National Institute of Standards and Technology, generate quantized voltages. Furthermore, the extreme sensitivity of Josephson junctions to magnetic fields is exploited in SQUIDs, which are among the most sensitive magnetometers known, with applications in geophysics, medicine for magnetoencephalography, and materials science. The junctions are also fundamental components in the development of quantum computing architectures, such as those pursued by IBM and Google, and form the basis for rapid single flux quantum digital logic.

Mathematical description

The dynamics of a Josephson junction are governed by two coupled equations first derived by Brian David Josephson. The current-phase relation is I = Ic sin φ. The voltage-phase relation is given by the Josephson-Anderson equation: V = (ħ/2e) (dφ/dt), where ħ is the reduced Planck constant. These equations can be combined with the resistively and capacitively shunted junction model to analyze real device behavior under bias. In the presence of an external magnetic field, the gauge-invariant phase difference must be used, incorporating the vector potential as described by the theories of Lev Landau and Vitaly Ginzburg. This formalism is essential for modeling complex circuits in superconducting electronics and quantum information science.

Category:Superconductivity Category:Quantum mechanics Category:Electrical phenomena Category:Condensed matter physics