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The Josephson effect is the phenomenon of current flow across two weakly coupled superconductors, separated by a very thin insulating barrier. This arrangement—two superconductors linked by a non-conducting barrier—is known as a Josephson junction; the current that crosses the barrier is the Josephson current. The terms are named after British physicist Brian David Josephson
Brian David Josephson

Brian David Josephson is a Welsh physics. He became a Nobel Prize for Physics in 1973 at the age of 33 with Leo Esaki and Ivar Giaever, and he predicted the Josephson effect....
, who predicted the existence of the effect in 1962.






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The Josephson effect is the phenomenon of current flow across two weakly coupled superconductors, separated by a very thin insulating barrier. This arrangement—two superconductors linked by a non-conducting barrier—is known as a Josephson junction; the current that crosses the barrier is the Josephson current. The terms are named after British physicist Brian David Josephson
Brian David Josephson

Brian David Josephson is a Welsh physics. He became a Nobel Prize for Physics in 1973 at the age of 33 with Leo Esaki and Ivar Giaever, and he predicted the Josephson effect....
, who predicted the existence of the effect in 1962. It has important applications in quantum-mechanical circuits
Quantum circuit

In quantum information theory, a quantum circuit is a model for quantum computation in which a computation is a sequence of reversible transformations on a quantum mechanics analog of an n bit register....
, such as SQUID
Squid

Squid are marine cephalopods of the order Teuthida, which comprises around 300 species. Like all other cephalopods, squid have a distinct head, Symmetry #Bilateral_symmetry, a mantle , and cephalopod arms....
s.

The effect

The basic equations governing the dynamics of the Josephson effect are

(superconducting phase evolution equation)

(Josephson or weak-link current-phase relation)

where and are the voltage and current across the Josephson junction, is the "phase difference" across the junction (i.e., the difference in phase factor
Phase factor

In Quantum Mechanics, a phase factor is a complex number scalar number of absolute value 1 that multiplies a Bra-ket notation. It does not, in itself, have any physical meaning, but differences in phase factors between two interacting states can have important physical effects....
, or equivalently, argument, between the Ginzburg-Landau complex order parameter
Ginzburg-Landau theory

In physics, Ginzburg?Landau theory is a mathematical theory used to model superconductivity. It does not purport to explain the microscopic mechanisms giving rise to superconductivity....
 of the two superconductors comprising the junction), and is a constant, the critical current of the junction. The critical current is an important phenomenological parameter of the device that can be affected by temperature as well as by an applied magnetic field. The physical constant, is the magnetic flux quantum
Magnetic flux quantum

The magnetic flux quantum F0 is the quantum of magnetic flux passing through a superconductor. The quantization of magnetic flux is closely related to the Aharonov?Bohm effect, but was predicted earlier by Fritz London in 1948 using a phenomenological model....
, the inverse of which is the Josephson constant.

The three main effects predicted by Josephson follow from these relations:

  1. The DC Josephson effect. This refers to the phenomenon of a direct current crossing the insulator in the absence of any external electromagnetic field, owing to tunneling. This DC Josephson current is proportional to the sine of the phase difference across the insulator, and may take values between and .
  2. The AC Josephson effect. With a fixed voltage across the junctions, the phase will vary linearly with time and the current will be an AC current with amplitude and frequency . The complete expression for the current drive becomes . This means a Josephson junction can act as a perfect voltage-to-frequency converter.
  3. The inverse AC Josephson effect. If the phase takes the form , the voltage and current will be

  4. The DC components will then be

  5. Hence, for distinct DC voltages, the junction may carry a DC current and the junction acts like a perfect frequency-to-voltage converter.



Applications

The Josephson effect has found wide usage, for example in the following areas:

  • SQUID
    Squid

    Squid are marine cephalopods of the order Teuthida, which comprises around 300 species. Like all other cephalopods, squid have a distinct head, Symmetry #Bilateral_symmetry, a mantle , and cephalopod arms....
    s, or superconducting quantum interference devices, are very sensitive magnetometer
    Magnetometer

    A magnetometer is a scientific instrument used to measure the strength and/or direction of the magnetic field in the vicinity of the instrument....
    s that operate via the Josephson effect. They are widely used in science and engineering. (See main article: SQUID
    Squid

    Squid are marine cephalopods of the order Teuthida, which comprises around 300 species. Like all other cephalopods, squid have a distinct head, Symmetry #Bilateral_symmetry, a mantle , and cephalopod arms....
    .)


  • In precision metrology
    Metrology

    Metrology is the science of measurement. Metrology includes all theoretical and practical aspects of measurement....
    , the Josephson effect provides an exactly reproducible conversion between frequency
    Frequency

    Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency....
     and voltage
    Voltage

    Electrical tension is the potential difference between two points of an electrical or electronic circuit, expressed in volts. It is the measurement of the potential for an electric field to cause an electric current in an electrical conductor....
    . Since the frequency is already defined precisely and practically by the caesium standard
    Caesium standard

    A caesium standard is a primary frequency standard in which electronic transitions between the two hyperfine level ground states of caesium atoms are used to control the output frequency....
    , the Josephson effect is used, for most practical purposes, to give the definition of a volt
    Volt

    The volt is the SI SI derived unit of electric potential difference or electromotive force, commonly known as voltage. It is named in honor of the Lombard physicist Alessandro Volta , who invented the voltaic pile, possibly the first chemical battery ....
     (although, as of July 2007, this is not the official BIPM definition ).


  • Single-electron transistors are often constructed of superconducting materials, allowing use to be made of the Josephson effect to achieve novel effects. The resulting device is called a "superconducting single-electron transistor".


  • Josephson junctions are integral in Superconducting quantum computing
    Superconducting quantum computing

    This promising implementation of quantum information involves nanofabricated superconducting electrodes coupled through Josephson effect. As in a superconducting electrode, the phase and the charge are Cannonical conjugate variables, there exists three families of superconducting qubits, depending if the charge, the phase or neither of the two are...
     as qubits such as in a Flux qubit
    Flux qubit

    In quantum computing, flux qubits are micro-metre sized loops of superconducting metal interrupted by a number of Josephson junctions. The junction parameters are engineered during fabrication so that a persistent current will flow continuously when an external flux is applied....
     or others schemes where the phase and charge act as the Conjugate variables
    Conjugate variables

    In physics, conjugate variables are pair of variables mathematically defined in such a way that they become Fourier transform dual of one-another, or more generally are related through Pontryagin duality....
    .


  • Superconducting Tunnel Junction Detectors (STJs) may become a viable replacement for CCDs (charge-coupled devices) for use in astronomy
    Astronomy

    Astronomy is the science of Astronomical object and Phenomenon that originate outside the Earth's atmosphere . It is concerned with the evolution, physics, chemistry, meteorology, and motion of celestial objects, as well as the physical cosmology....
     and astrophysics
    Astrophysics

    Astrophysics is the branch of astronomy that deals with the physics of the universe, including the physical properties of astronomical objects such as galaxy, stars, planets, exoplanets, and the interstellar medium, as well as their interactions....
     in a few years. These devices are effective across a wide spectrum from ultraviolet to infrared, and also in x-rays. The technology has been tried out on the William Herschel Telescope
    William Herschel Telescope

    The William Herschel Telescope or WHT was first conceived in the late 1960s, when the Anglo-Australian Observatory was being designed. The British astronomical community saw the need for telescopes of comparable power in the Northern Hemisphere....
    .


See also

  • Brian D. Josephson
  • Quantum gyroscope
    Quantum gyroscope

    A quantum gyroscope is a very sensitive device to measure angular rotation based on quantum mechanics principles. The first of these has been built by Richard Packard and his colleagues at the University of California, Berkeley....
  • Quantum computer
    Quantum computer

    A quantum computer is a device for computation that makes direct use of quantum mechanical phenomena, such as quantum superposition and quantum entanglement, to perform operations on data....
  • Andreev reflection
    Andreev reflection

    Andreev reflection named after the Russian physicist Alexander F. Andreev, is a type of particle scattering whichoccurs at interfaces between a superconductor and a normal state material ....
  • Pi Josephson junction
    Pi Josephson junction

    A Josephson Junction is a specific instance of a Josephson Junction where the Josephson phase is equal to in the ground state, i.e. when no external currents or magnetic fields are applied to the Josephson junction....
  • Semifluxon
    Semifluxon

    In superconductivity, a Semifluxon is a vortex of supercurrent carrying the magnetic flux equal to the half of the magnetic flux quantum. Semifluxons exist in the so-called 0-p long Josephson junctions at the boundary between 0 and p regions....
  • Fractional vortices
    Fractional vortices

    In a standard superconductor, described by a complex field , vortices carry quantized magnetic field: a consequence of -invariance of the phase of the condensate wave function ....
  • Ginzburg-Landau theory
    Ginzburg-Landau theory

    In physics, Ginzburg?Landau theory is a mathematical theory used to model superconductivity. It does not purport to explain the microscopic mechanisms giving rise to superconductivity....
  • Zero-point energy
    Zero-point energy

    In physics, the zero-point energy is the lowest possible energy that a quantum mechanical physical system may have and is the energy of the ground state....
  • Josephson diode
  • Peptide molecular photodiode