# Josephson effect

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Josephson effect
Josephson junction array chip developed by NIST as a standard volt

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.[1][2] 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 pairs. For this work, Josephson received the Nobel prize in physics in 1973.[3] Josephson junctions have important applications in quantum-mechanical circuits, such as SQUIDs, 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 micrometres or less.[4][5]

## The effect

The basic equations governing the dynamics of the Josephson effect are[6]

$U(t) = \frac{\hbar}{2 e} \frac{\partial \phi}{\partial t}$ (superconducting phase evolution equation)
$\frac{}{} I(t) = I_c \sin (\phi (t))$ (Josephson or weak-link current-phase relation)

where 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 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 $\scriptstyle -I_c$ and $\scriptstyle I_c$.
The AC Josephson effect
With a fixed voltage $\scriptstyle U_{DC}$ across the junctions, the phase will vary linearly with time and the current will be an AC current with amplitude $\scriptstyle I_c$ and frequency $\scriptstyle\frac{1}{h}2e \cdot U_{DC}$. The complete expression for the current drive $\scriptstyle I_\text{ext}$ becomes $\scriptstyle I_\text{ext} \;=\; C_J \frac{dv}{dt} \,+\, I_J \sin \phi \,+\, \frac{V}{R}$. 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 $\scriptstyle \phi (t) \;=\; \phi_0 \,+\, n \omega t \,+\, a \sin( \omega t)$, the voltage and current will be
$U(t) = \frac{\hbar}{2 e} \omega ( n + a \cos( \omega t) ), \ \ \ I(t) = I_c \sum_{m \,=\, -\infty}^\infty J_n (a) \sin (\phi_0 + (n + m) \omega t)$

The DC components will then be

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

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 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]).
• 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."[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 $\scriptstyle\frac{1}{2 e}h$ that carries the digital information: the absence of switching is equivalent to 0, while one switching event carries a 1.
• Superconducting tunnel junction detectors (STJs) may become a viable replacement for CCDs (charge-coupled 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 x-rays. The technology has been tried out on the William Herschel Telescope in the SCAM instrument.

## References

1. ^ B. D. Josephson, "Possible new effects in superconductive tunnelling," Physics Letters 1, 251 (1962), doi:10.1016/0031-9163(62)91369-0
2. ^ 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.
3. ^ The Nobel prize in physics 1973, accessed 8-18-11
4. ^ P.W. Anderson and A.H. Dayem, "Radio-frequency effects in superconducting thin film bridges," Physical Review Letters 13, 195 (1964), doi:10.1103/PhysRevLett.13.195
5. ^ Dawe, Richard (28th October 1998). "SQUIDs: A Technical Report - Part 3: SQUIDs" (website). http://rich.phekda.org. Retrieved 21/04/2011.
6. ^ Barone, A.; Paterno, G. (1982). Physics and Applications of the Josephson Effect. New York: John Wiley & Sons. ISBN 0471014699.
7. ^ http://www.bipm.org/en/si/si_brochure/chapter2/2-1/
8. ^ 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.
9. ^ Bouchiat, V.; Vion, D.; Joyez, P.; Esteve, D.; Devoret, M. H. (1998). "Quantum coherence with a single Cooper pair". Physica Scripta T 76: 165.

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• Josephson effect — /ˈdʒoʊsəfsən əˌfɛkt/ (say johsuhfsuhn uh.fekt) noun the effect whereby electric current can flow from one superconducting metal to another through a sufficiently thin layer of insulator, the application of a potential difference causing the… …   Australian English dictionary

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• josephson effect — ˈjōzə̇fsən also ōsə̇ noun Usage: usually capitalized J Etymology: after Brian D. Josephson b1940 British physicist : the movement of electron pairs through a thin insulator separating two superconductors carrying low current that can be stopped… …   Useful english dictionary

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• Josephson-Effekt — Josephson o reiškinys statusas T sritis automatika atitikmenys: angl. Josephson effect vok. Josephson Effekt, m rus. эффект Джозефсона, m pranc. effet de Josephson, m ryšiai: sinonimas – Džozefsono reiškinys …   Automatikos terminų žodynas

• JOSEPHSON, BRIAN DAVID — (1940– ), British physicist. Josephson was born in Cardiff, Wales, where he was a brilliant pupil. He studied physics at Cambridge, receiving his doctorate in 1964. In 1962, at the age of only 22, he discovered the Josephson effect, showing the… …   Encyclopedia of Judaism