Main Equations Describing The SIS Junction
The Josephson equation relates the superconducting current (usually called the supercurrent) through the tunnel junction to the phase difference ,
- (Josephson current-phase relationship)
Here is the critical current of the tunnel junction, determined by the area and thickness of the tunnel barrier in the junction, and by the properties of the superconductors on either side of the barrier. For a junction with identical superconductors on either side of the barrier, the critical current is related to the superconducting gap and the normal state resistance of the tunnel junction by the Ambegaokar-Baratoff formula
- (Ambegaokar-Baratoff formula)
The Gor'kov phase evolution equation gives the rate of change of the phase (the velocity of the phase) as a linear function of the voltage as
- (Gor'kov-Josephson phase evolution equation)
This equation is a generalization of the Schrödinger equation for the phase of the BCS wavefunction (see BCS theory). The generalization was carried out by Gor'kov in 1958.
Read more about this topic: Phase Qubit
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