NationMaster - Encyclopedia: Josephson effect

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, who predicted the existence of the effect in 1962^[1]. It has important applications in quantum-mechanical circuits, such as SQUIDs. Superconductivity is a phenomenon occurring in certain materials at low temperatures, characterised by the complete absence of electrical resistance and the damping of the interior magnetic field (the Meissner effect. ... Brian David Josephson (born Cardiff, Wales, UK, January 4, 1940) is a British physicist whose discovery of the Josephson effect as a 22-year-old graduate student won him the 1973 Nobel Prize for Physics, which he shared with Leo Esaki and Ivar Giaever. ... In quantum mechanics, a quantum circuit is a specific model for a quantum computational device. ... For other uses, see Squid (disambiguation). ...

1 The effect
2 Applications
3 See also
4 References

The effect

The basic equations ^[2] governing the dynamics of the Josephson effect are

$U(t) = frac{h}{2 e} frac{partial phi}{partial t}$ (superconducting phase evolution equation)

$frac{}{} I(t) = I_c sin (phi (t))$ (Josephson or weak-link current-phase relation)

where $displaystyle U(t)$ and $displaystyle I(t)$ are the voltage and current across the Josephson junction, $displaystylephi (t)$ 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 comprising the junction), and $displaystyle I_c$ 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, $frac{h}{2 e}$ is the magnetic flux quantum, the inverse of which is the Josephson constant. There are very few or no other articles that link to this one. ... Wikibooks Algebra has more about this subject: Complex numbers In mathematics, a complex number is an expression of the form where a and b are real numbers, and i is a specific imaginary number, called the imaginary unit, with the property i 2 = âˆ’1. ... In physics, Ginzburg-Landau theory is a mathematical theory used to model superconductivity. ... The magnetic flux quantum Î¦0 is the quantum of magnetic flux passing through a superconductor. ... The magnetic flux quantum Φ0 is the quantum of magnetic flux passing through a superconductor. ...

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 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 $displaystyle-I_c$ and $displaystyle I_c$ .
The AC Josephson effect. With a fixed voltage $displaystyle U_{DC}$ across the junctions, the phase will vary linearly with time and the current will be an AC current with amplitude $displaystyle I_c$ and frequency $frac{2 e}{hbar}cdot U_{DC}$ . The complete expression for the current drive $I e x t$ becomes $I_{ext} = C_J frac{dv}{dt} + I_J sin phi + frac{V}{R}$ . 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 $displaystyle phi (t) = phi_0 + n omega t + a sin( omega t)$ , the voltage and current will be

$U(t) = frac{h}{2 e} omega ( n + a cos( omega t) ), I(t) = I_c sum_{m = -infty}^{infty} J_n (a) sin (phi_0 + (n + m) omega t)$
The DC components will then be Quantum tunneling is the quantum-mechanical effect of transitioning through a classically-forbidden energy state. ...

$U_{DC} = n frac{h}{2 e} omega, I(t) = I_c J_{-n} (a) sin phi_0$
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:

SQUIDs, or superconducting quantum interference devices, are very sensitive magnetometers that operate via the Josephson effect. They are widely used in science and engineering. (See main article: SQUID.)

In precision metrology, the Josephson effect provides an exactly reproducible conversion between frequency and voltage. Since the second is already defined precisely and practically by the caesium standard, the Josephson effect is used, for most practical purposes, to give the definition of a volt (although, as of July 2007, this is not the official BIPM definition [1]).

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"^[3].

For other uses, see Squid (disambiguation). ... A magnetometer is a scientific instrument used to measure the strength and/or direction of the magnetic field in the vicinity of the instrument. ... For other uses, see Squid (disambiguation). ... Metrology (from Greek metron (measure), and -logy) is the science of measurement. ... For other uses, see Frequency (disambiguation). ... International safety symbol Caution, risk of electric shock (ISO 3864), colloquially known as high voltage symbol. ... This article is about the unit of time. ... A caesium standard is a primary frequency standard in which electronic transitions between the two hyperfine ground states of caesium-133 atoms is used to control the output frequency. ... Josephson junction array chip developed by NIST as a standard volt. ... The Bureau International des Poids et Mesures (International Bureau of Weights and Measures, or BIPM) is a standards organization, one of the three organizations established to maintain the SI system under the terms of the Metre Convention. ... In physics, a Coulomb blockade, named after Charles-Augustin de Coulomb, is the increased resistance at small bias voltages of an electronic device comprising at least one low-capacitance tunnel junction. ... Superconductivity is a phenomenon occurring in certain materials at low temperatures, characterised by the complete absence of electrical resistance and the damping of the interior magnetic field (the Meissner effect. ...

References

^ B. D. Josephson. The discovery of tunnelling supercurrents. Rev. Mod. Phys. 1974; 46(2): 251-254.
^ Barone A, Paterno G. Physics and Applications of the Josephson Effect. New York: John Wiley & Sons; 1982.
^ Fulton, T.A.; et al. (1989). "Observation of Combined Josephson and Charging Effects in Small Tunnel Junction Circuits". Physical Review Letters 63 (12): 1307-1310.

Categories: Condensed matter physics | Superconductivity | Josephson effect | Sensors

Results from FactBites:

Josephson effect: Definition and Much More from Answers.com (1443 words)
	Josephson also predicted that if a constant nonzero voltage were maintained across the tunnel barrier, an alternating supercurrent would flow through the barrier in addition to the dc current produced by the tunneling of unpaired electrons.
	The Josephson effect is a term given to the phenomenon of current flow across two superconductors separated by a very thin insulating barrier.
	Josephson junctions are used as microwave detectors in the giga- and terahertz range.

LNE, Quantum metrology : the josephson effect, Research and Development (1369 words)
	The Josephson effect [1] is one of the notable effects of
	DC Josephson effect: If no voltage is applied to the junction terminals, a direct current - a current of Cooper pairs Ij, - flows through the junction up to a critical value Ic, which depends on the geometry, temperature and magnetic field (Fig.2a).
	Development of voltage standards based on the Josephson effect is closely linked to the advances in junction manufacture and nanotechnologies (nanofabrication techniques such as thin layer deposition and microlithography).

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Applications

See also

References

The effect