Josephson effect
Encyclopedia
The Josephson effect is the phenomenon of supercurrent (i.e. a current that flows indefinitely long without any voltage applied) across two superconductors coupled by a weak link. The weak link can consist of a thin insulating barrier (known as a superconductor–insulator–superconductor junction, or S-I-S), a short section of non-superconducting metal (S-N-S), or a physical constriction that weakens the superconductivity at the point of contact (S-s-S). Such a device is known as a Josephson junction (JJ). The term is named after British physicist Brian David Josephson
, who predicted in 1962 the mathematical relationships for the current and voltage across the weak link. Before his prediction it was only known that normal (i.e. non-superconducting) electrons can flow through an insulating barrier, by means of quantum tunneling. Josephson was the first to predict the tunneling of superconducting Cooper pair
s. For this work, Josephson received the Nobel prize in physics
in 1973. Josephson junctions have important applications in quantum-mechanical circuits
, such as SQUID
s, superconducting qubits
and RSFQ digital electronics.
A Dayem bridge is a thin-film variant of the Josephson junction in which the weak link consists of a superconducting wire with dimensions on the scale of a few micrometre
s or less.
(superconducting phase evolution equation)
(Josephson or weak-link current-phase relation)
where U(t) and I(t) are the voltage and current across the Josephson junction,
is the "phase difference" across the junction (i.e., the difference in phase factor
, or equivalently, argument, between the Ginzburg–Landau complex order parameter of the two superconductors composing the junction), and Ic 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 h/2e is the magnetic flux quantum
, the inverse of which is the Josephson constant.
The three main effects predicted by Josephson follow from these relations:
The DC Josephson effect: This refers to the phenomenon of a direct current crossing from 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 
.
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.
The inverse AC Josephson effect: If the phase takes the form
, the voltage and current will be
The DC components will then be
Hence, for distinct DC voltages, the junction may carry a DC current and the junction acts like a perfect frequency-to-voltage converter.
Brian David Josephson
Brian David Josephson, FRS is a Welsh physicist. He became a Nobel Prize laureate in 1973 for the prediction of the eponymous Josephson effect....
, who predicted in 1962 the mathematical relationships for the current and voltage across the weak link. Before his prediction it was only known that normal (i.e. non-superconducting) electrons can flow through an insulating barrier, by means of quantum tunneling. Josephson was the first to predict the tunneling of superconducting Cooper pair
Cooper pair
In condensed matter physics, a Cooper pair or BCS pair is two electrons that are bound together at low temperatures in a certain manner first described in 1956 by American physicist Leon Cooper...
s. For this work, Josephson received the Nobel prize in physics
Nobel Prize in Physics
The Nobel Prize in Physics is awarded once a year by the Royal Swedish Academy of Sciences. It is one of the five Nobel Prizes established by the will of Alfred Nobel in 1895 and awarded since 1901; the others are the Nobel Prize in Chemistry, Nobel Prize in Literature, Nobel Peace Prize, and...
in 1973. Josephson junctions have 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 quantum gates, which are reversible transformations on a quantum mechanical analog of an n-bit register...
, such as SQUID
SQUID
A SQUID is a very sensitive magnetometer used to measure extremely weak magnetic fields, based on superconducting loops containing Josephson junctions....
s, superconducting qubits
Superconducting quantum computing
Superconducting quantum computing is a promising implementation of quantum information that involves nanofabricated superconducting electrodes coupled through Josephson junctions...
and RSFQ digital electronics.
A Dayem bridge is a thin-film variant of the Josephson junction in which the weak link consists of a superconducting wire with dimensions on the scale of a few micrometre
Micrometre
A micrometer , is by definition 1×10-6 of a meter .In plain English, it means one-millionth of a meter . Its unit symbol in the International System of Units is μm...
s or less.
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 U(t) and I(t) are the voltage and current across the Josephson junction,
is the "phase difference" across the junction (i.e., the difference in phase factorPhase factor
For any complex number written in polar form , the phase factor is the exponential part, i.e. eiθ. As such, the term "phase factor" is similar to the term phasor, although the former term is more common in quantum mechanics. This phase factor is itself a complex number of absolute value 1...
, or equivalently, argument, between the Ginzburg–Landau complex order parameter of the two superconductors composing the junction), and Ic 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 h/2e is the magnetic flux quantum
Magnetic flux quantum
The magnetic flux quantum Φ0 is the quantum of magnetic flux passing through a superconductor. The phenomenon of flux quantization was discovered B. S. Deaver and W. M. Fairbank and, independently, by R. Doll and M. Nabauer, in 1961...
, the inverse of which is the Josephson constant.
The three main effects predicted by Josephson follow from these relations:
The DC Josephson effect: This refers to the phenomenon of a direct current crossing from 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 .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.The inverse AC Josephson effect: If the phase takes the form
, the voltage and current will beThe DC components will then be
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:- SQUIDSQUIDA SQUID is a very sensitive magnetometer used to measure extremely weak magnetic fields, based on superconducting loops containing Josephson junctions....
s, or superconducting quantum interference devices, are very sensitive magnetometerMagnetometerA magnetometer is a measuring instrument used to measure the strength or direction of a magnetic field either produced in the laboratory or existing in nature...
s that operate via the Josephson effect. They are widely used in science and engineering. (See main article: SQUIDSQUIDA SQUID is a very sensitive magnetometer used to measure extremely weak magnetic fields, based on superconducting loops containing Josephson junctions....
.)
- In precision metrologyMetrologyMetrology is the science of measurement. Metrology includes all theoretical and practical aspects of measurement. The word comes from Greek μέτρον , "measure" + "λόγος" , amongst others meaning "speech, oration, discourse, quote, study, calculation, reason"...
, the Josephson effect provides an exactly reproducible conversion between frequencyFrequencyFrequency 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 voltageVoltageVoltage, otherwise known as electrical potential difference or electric tension is the difference in electric potential between two points — or the difference in electric potential energy per unit charge between two points...
. Since the frequency is already defined precisely and practically by the caesium standardCaesium standardA caesium standard or caesium atomic clock is a primary frequency standard in which electronic transitions between the two hyperfine ground states of caesium-133 atoms are used to control the output frequency. They are one of the most accurate types of atomic clock...
, the Josephson effect is used, for most practical purposes, to give the definition of a voltVoltThe volt is the SI derived unit for electric potential, electric potential difference, and electromotive force. The volt is named in honor of the Italian physicist Alessandro Volta , who invented the voltaic pile, possibly the first chemical battery.- Definition :A single volt is defined as the...
(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." The Josephson effect is also used for the most precise measurements of elementary chargeElementary chargeThe elementary charge, usually denoted as e, is the electric charge carried by a single proton, or equivalently, the absolute value of the electric charge carried by a single electron. This elementary charge is a fundamental physical constant. To avoid confusion over its sign, e is sometimes called...
in terms of the Josephson constant and von Klitzing constant which is related to the quantum Hall effect.
- RSFQ digital electronics is based on shunted Josephson junctions. In this case, the junction switching event is associated to the emission of one magnetic flux quantumMagnetic flux quantumThe magnetic flux quantum Φ0 is the quantum of magnetic flux passing through a superconductor. The phenomenon of flux quantization was discovered B. S. Deaver and W. M. Fairbank and, independently, by R. Doll and M. Nabauer, in 1961...
that carries the digital information: the absence of switching is equivalent to 0, while one switching event carries a 1.
- Josephson junctions are integral in superconducting quantum computingSuperconducting quantum computingSuperconducting quantum computing is a promising implementation of quantum information that involves nanofabricated superconducting electrodes coupled through Josephson junctions...
as qubits such as in a flux qubitFlux qubitIn quantum computing, flux qubits are micrometer 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 variablesConjugate variablesConjugate variables are pairs of variables mathematically defined in such a way that they become Fourier transform duals of one-another, or more generally are related through Pontryagin duality. The duality relations lead naturally to an uncertainty in physics called the Heisenberg uncertainty...
.
- Superconducting tunnel junction detectors (STJs) may become a viable replacement for CCDs (charge-coupled devices) for use in astronomyAstronomyAstronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...
and astrophysicsAstrophysicsAstrophysics is the branch of astronomy that deals with the physics of the universe, including the physical properties of celestial objects, as well as their interactions and behavior...
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 TelescopeWilliam Herschel TelescopeThe William Herschel Telescope is a optical/near-infrared reflecting telescope located at the Observatorio del Roque de los Muchachos on the island of La Palma in the Canary Islands, Spain. The telescope, which is named after William Herschel, is part of the Isaac Newton Group of Telescopes...
in the SCAM instrument.
See also
- Andreev reflectionAndreev reflectionAndreev 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 . It is a charge-transfer process by which normal current in N is converted to supercurrent in S...
- Brian David JosephsonBrian David JosephsonBrian David Josephson, FRS is a Welsh physicist. He became a Nobel Prize laureate in 1973 for the prediction of the eponymous Josephson effect....
- Cooper pairCooper pairIn condensed matter physics, a Cooper pair or BCS pair is two electrons that are bound together at low temperatures in a certain manner first described in 1956 by American physicist Leon Cooper...
- Fractional vortices
- Ginzburg–Landau theory
- Macroscopic quantum self-trappingMacroscopic quantum self-trappingIn quantum mechanics, macroscopic quantum self-trapping is a phenomenon occurring in the state of matter called the Bose-Einstein condensate between two superconductors linked by a non-conducting barrier known as a Josephson junction....
- Pi Josephson junctionPi Josephson junctionA Josephson Junction is a voltage-to-frequency converter usefully sensitive to voltage, current and magnetic fields that is made of a superconducting wire interrupted by an insulating weak-link....
- Quantum computerQuantum computerA quantum computer is a device for computation that makes direct use of quantum mechanical phenomena, such as superposition and entanglement, to perform operations on data. Quantum computers are different from traditional computers based on transistors...
- Quantum gyroscopeQuantum gyroscopeA quantum gyroscope is a very sensitive device to measure angular rotation based on quantum mechanical principles. The first of these has been built by Richard Packard and his colleagues at the University of California, Berkeley...
- RSFQ digital electronics
- SemifluxonSemifluxonIn 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-π long Josephson junctions at the boundary between 0 and π regions. For a shorter junction length In superconductivity, a...
- Zero-point energyZero-point energyZero-point energy is the lowest possible energy that a quantum mechanical physical system may have; it is the energy of its ground state. All quantum mechanical systems undergo fluctuations even in their ground state and have an associated zero-point energy, a consequence of their wave-like nature...
- Rapid single flux quantumRapid single flux quantumIn electronics, rapid single flux quantum is a digital electronics technology that relies on quantum effects in superconducting devices, namely Josephson junctions, to process digital signals. Josephson junctions are the active elements for RSFQ electronics, like transistors are the active...
- Superconducting tunnel junction