 Josephson effect

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 SIS), a short section of nonsuperconducting metal (SNS), or a physical constriction that weakens the superconductivity at the point of contact (SsS). 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.^{[1]}^{[2]} Before his prediction it was only known that normal (i.e. nonsuperconducting) electrons can flow through an insulating barrier, by means of quantum tunneling. Josephson was the first to predict the tunneling of superconducting Cooper pairs. For this work, Josephson received the Nobel prize in physics in 1973.^{[3]} Josephson junctions have important applications in quantummechanical circuits, such as SQUIDs, superconducting qubits and RSFQ digital electronics.
A Dayem bridge is a thinfilm variant of the Josephson junction in which the weak link consists of a superconducting wire with dimensions on the scale of a few micrometres or less.^{[4]}^{[5]}
Contents
The effect
The basic equations governing the dynamics of the Josephson effect are^{[6]}
 (superconducting phase evolution equation)
 (Josephson or weaklink currentphase relation)
where U(t) and I(t) are the voltage and current across the Josephson junction, Φ(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 composing the junction), and 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 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 voltagetofrequency 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 frequencytovoltage 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 frequency 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^{[7]}).
 Singleelectron 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 singleelectron transistor."^{[8]} The Josephson effect is also used for the most precise measurements of elementary charge 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 quantum 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 computing as qubits such as in a flux qubit or others schemes where the phase and charge act as the conjugate variables.^{[9]}
 Superconducting tunnel junction detectors (STJs) may become a viable replacement for CCDs (chargecoupled devices) for use in astronomy and astrophysics in a few years. These devices are effective across a wide spectrum from ultraviolet to infrared, and also in xrays. The technology has been tried out on the William Herschel Telescope in the SCAM instrument.
See also
 Andreev reflection
 Brian David Josephson
 Cooper pair
 Fractional vortices
 Ginzburg–Landau theory
 Macroscopic quantum selftrapping
 Pi Josephson junction
 Quantum computer
 Quantum gyroscope
 RSFQ digital electronics
 Semifluxon
 Zeropoint energy
 Rapid single flux quantum
 Superconducting tunnel junction
References
 ^ B. D. Josephson, "Possible new effects in superconductive tunnelling," Physics Letters 1, 251 (1962), doi:10.1016/00319163(62)913690
 ^ Josephson, B. D. (1974). "The discovery of tunnelling supercurrents". Rev. Mod. Phys. 46 (2): 251–254. Bibcode 1974RvMP...46..251J. doi:10.1103/RevModPhys.46.251.
 ^ The Nobel prize in physics 1973, accessed 81811
 ^ P.W. Anderson and A.H. Dayem, "Radiofrequency effects in superconducting thin film bridges," Physical Review Letters 13, 195 (1964), doi:10.1103/PhysRevLett.13.195
 ^ Dawe, Richard (28th October 1998). "SQUIDs: A Technical Report  Part 3: SQUIDs" (website). http://rich.phekda.org. http://rich.phekda.org/squid/technical/part3.html. Retrieved 21/04/2011.
 ^ Barone, A.; Paterno, G. (1982). Physics and Applications of the Josephson Effect. New York: John Wiley & Sons. ISBN 0471014699.
 ^ http://www.bipm.org/en/si/si_brochure/chapter2/21/
 ^ 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. Bibcode 1989PhRvL..63.1307F. doi:10.1103/PhysRevLett.63.1307. PMID 10040529.
 ^ Bouchiat, V.; Vion, D.; Joyez, P.; Esteve, D.; Devoret, M. H. (1998). "Quantum coherence with a single Cooper pair". Physica Scripta T 76: 165. http://wwwdrecam.cea.fr/drecam/spec/Pres/Quantro/Qsite/archives/reprints/SSBox.pdf.
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