Josephson effect

Dictionary: Jo·seph·son effect (jō'zəf-sən, -səf-) pronunciation

The effect associated with the tunneling of electron pairs across an insulating barrier separating two superconductors.

[After Brian David Josephson (born 1940), British physicist.]

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Sci-Tech Encyclopedia: Josephson effect

The passage of paired electrons (Cooper pairs) through a weak connection (Josephson junction) between superconductors, as in the tunnel passage of paired electrons through a thin dielectric layer separating two superconductors.

Quantum-mechanical tunneling of Cooper pairs through a thin insulating barrier (on the order of a few nanometers thick) between two superconductors was theoretically predicted by Brian D. Josephson in 1962. Josephson found that a current of paired electrons (supercurrent) would flow in addition to the usual current that results from the tunneling of single electrons. Josephson predicted that if the current did not exceed a limiting value (the critical current), there would be no voltage drop across the tunnel barrier. This zero-voltage current flow is known as the dc Josephson effect. 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. This phenomenon is known as the ac Josephson effect. See also Tunneling in solids.

Josephson pointed out that the magnitude of the maximum zero-voltage supercurrent would be reduced by a magnetic field. In fact, the magnetic field dependence of the magnitude of the critical current is one of the more striking features of the Josephson effect. Circulating supercurrents flow through the tunnel barrier to screen an applied magnetic field from the interior of the Josephson junction just as if the tunnel barrier itself were weakly superconducting. The screening effect produces a spatial variation of the transport current, and the critical current goes through a series of maxima and minima as the field is increased.

Josephson junctions, and instruments incorporating Josephson junctions, are used in applications for metrology at dc and microwave frequencies, frequency metrology, magnetometry, measurement of absolute temperatures below about 1 K, detection and amplification of electromagnetic signals, and other superconducting electronics such as high-speed analog-to-digital converters and computers. A Josephson junction, like a vacuum tube or a transistor, is capable of switching signals from one circuit to another; a Josephson tunnel junction is the fastest switch known. Josephson junction circuits are capable of storing information. Finally, because a Josephson junction is a superconducting device, its power dissipation is extremely small, so that Josephson junction circuits can be packed together as tightly as fabrication techniques permit. All the basic circuit elements required for a Josephson junction computer have been developed. See also Low-temperature thermometry; Superconducting devices; Superconductivity.

Britannica Concise Encyclopedia: Josephson effect

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Flow of electric current between two pieces of superconducting material (see superconductivity) separated by a thin layer of insulating material. This flow was predicted by the British physicist Brian Josephson in 1962, based on the BCS theory (see John Bardeen). According to Josephson, pairs of electrons can move from one superconductor to the other across the insulating layer (tunneling). The locus of this action is called a Josephson junction. The Josephson current flows only if no battery is connected across the two conductors. A major application of this discovery is in superfast switching devices used in computers, which can be 100 times faster than ordinary semiconducting circuits.

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Wikipedia: Josephson effect

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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, who predicted the existence of the effect in 1962.^[1] It has important applications in quantum-mechanical circuits, such as SQUIDs.

1 The effect
2 Applications
3 See also
4 References

The effect

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

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

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

where $\displaystyle U(t)$ and $\displaystyle I(t)$ are the voltage and current across the Josephson junction, $\displaystyle\phi (t)$ 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.

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 $\frac{2 e}{h}\cdot U_{DC}$ . The complete expression for the current drive $I ext$ becomes $I_\text{ext} = C_J \frac{dv}{dt} + I_J \sin \phi + \frac{V}{R}$ . 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 $\displaystyle \phi (t) = \phi_0 + n \omega t + a \sin( \omega t)$ , 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 [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].

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^[4].

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.

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. doi:10.1103/PhysRevLett.63.1307.
^ V. Bouchiat, D. Vion, P. Joyez, D. Esteve and M.H. Devoret, Quantum coherence with a single Cooper pair, Physica Scripta T76 165 (1998).

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		Dictionary. The American Heritage® Dictionary of the English Language, Fourth Edition Copyright © 2007, 2000 by Houghton Mifflin Company. Updated in 2007. Published by Houghton Mifflin Company. All rights reserved. Read more
		Sci-Tech Encyclopedia. McGraw-Hill Encyclopedia of Science and Technology. Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved. Read more
		Britannica Concise Encyclopedia. Britannica Concise Encyclopedia. © 2006 Encyclopædia Britannica, Inc. All rights reserved. Read more
		Wikipedia. This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Josephson effect". Read more

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Josephson effect

Contents

The effect

Applications

See also

References