Josephson effect

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The Josephson effect is a term given to the phenomenon of current flow across two superconductors separated by a very thin insulating barrier. This arrangement—two superconductors linked by a non-conducting oxide barrier—is known as a Josephson junction; the current that crosses the barrier is the Josephson current. The terms are named eponymously after British physicist Brian David Josephson, who predicted the existence of the effect in 1962<ref name=Joe> Josephson BD. Phys. Letters 1962. 1:251</ref>. It has important applications in quantum-mechanical circuits.

1 The effect
2 The device
3 See also
4 References

[edit]

The effect

The basic equations<ref name=barone>Barone A, Paterno G. Physics and Applications of the Josephson Effect. New York: John Wiley & Sons; 1982.</ref> governing the dynamics of the Josephson effect are

<math>U(t) = \frac{\hbar}{2 e} \frac{\partial \phi}{\partial t}, \ \ \ I(t) = I_c \sin (\phi (t))</math>

where <math>U(t</math>) and <math>I(t)</math> are the voltage and current across the Josephson junction, <math>\phi (t)</math> is the phase difference between the wave functions in the two superconductors comprising the junction, and <math>I_c</math> 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, <math>\begin{matrix} \frac{h}{2 e} \end{matrix}</math> 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 <math>-I_c</math> and <math>I_c</math>.
The AC Josephson effect. With a fixed voltage <math>U_{DC}</math> across the junctions, the phase will vary linear with time and the current will be an AC current with amplitude <math>I_c</math> and frequency <math>\begin{matrix} \frac{2 e}{h} \end{matrix}</math><math>U_{DC}</math>. 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 <math>\phi (t) = \phi_0 + n \omega t + a \sin( \omega t)</math>, the voltage and current will be
<math>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)</math>
The DC components will then be
<math>U_{DC} = n \frac{\hbar}{2 e} \omega, \ \ \ I(t) = I_c J_{-n} (a) \sin \phi_0</math> <p>Hence, for distinct DC voltages, the junction may carry a DC current and the junction acts like a perfect frequency-to-voltage converter.

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The device

The Josephson junction finds numerous important applications. Its properties are exploited in SQUIDs used to measure magnetic flux at the quantum level. This finds application in medicine for measurement of small currents in the brain and the heart. A version using different superfluids can be used as a quantum gyroscope. Josephson junctions are also used in Rapid Single Flux Quantum integrated circuits, and some other of their properties can be exploited to build photon or particle detectors. Josephson junctions are used as microwave detectors in the giga- and terahertz range. When assembled in two dimensional arrays, "testboards" for the physical realization of mathematical model systems are created. When assembled in linear arrays (connected in series) the inverse Josephon effect is used as a representation of the SI unit volt. It is also speculated that Josephson junctions may allow the realisation of qubits, the key elements of a future quantum computer.

Image:Josephson junction IV.jpg

There are two general types of Josephson junctions: overdamped and underdamped. In overdamped junctions, the barrier is conducting (ie. it is a normal metal or superconductor bridge). The effects of the junction's internal electrical resistance will be large compared to its small capacitance. An overdamped junction will quickly reach a unique equilibrium state for any given set of conditions.

The barrier of an underdamped junction is an insulator. The effects of the junction's internal resistance will be minimal. Underdamped junctions do not have unique equilibrium states, but are hysteretic.

A Josephson junction can be transformed into the so-called Giaever tunneling junction by the application of a small, well defined magnetic field. In such a situation, the new device is called a superconducting tunneling junction (STJ)<ref name=ESA>European Space Agency. Payload and Advanced Concepts: Superconducting Tunnel Junction (STJ). © 2000—2006 [Last updated February 17 2005; accessed February 23 2006].</ref> and is used as a very sensitive photon detector throughout a wide range of the spectrum, from infrared to hard x-ray. Each photon breaks up a number of Cooper pairs. This number depends on the ratio of the photon energy to approximately twice the value of the gap parameter of the material of the junction. The detector can be operated as a photon-counting spectrometer, with a spectral resolution limited by the statistical fluctuations in the number of released charges. The detector has to be cooled to extremely low temperature, typically below 1 Kelvin, to distinguish the signals generated by the detector from the thermal noise. Small arrays of STJs have demonstrated their potential as spectro-photometers and could further be used in astronomy<ref name=ESA />. They are also used to perform energy dispersive X-ray spectroscopy and in principle they could be used as elements in infrared imaging devices as well. <ref name=Enss>Enss C (ed). Cryogenic Particle Detection. Topics in Applied Physics Vol. 99. Springer; 2005. ISBN 3-540-20113-0</ref>