Josephson Effect - The Effect

The Effect

The basic equations governing the dynamics of the Josephson effect are

(superconducting phase evolution equation)

(Josephson or weak-link current-phase relation)

where U(t) and I(t) are the voltage and current across the Josephson junction, 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 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 voltage-to-frequency 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 frequency-to-voltage converter.