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 eponymously 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.

[edit] 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, \displaystyle\phi (t) is the phase difference between the wave functions in 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:

  1. 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.
  2. 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}. This means a Josephson junction can act as a perfect voltage-to-frequency converter.
  3. 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

    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.

[edit] See also

[edit] References

  1. ^ B. D. Josephson. The discovery of tunnelling supercurrents. Rev. Mod. Phys. 1974; 46(2): 251-254.
  2. ^ Barone A, Paterno G. Physics and Applications of the Josephson Effect. New York: John Wiley & Sons; 1982.
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