The Flux Mode and Charge Mode Regimes in Superconducting Weak Link Circuits

Abstract

In a series of papers [1–4] we have discussed the quantum mechanical description of superconducting weak link circuits in terms of the (integrated) electromagnetic field variables φ, the magnetic flux and Q, the electric flux. Here, it is understood that φ threads the inductive part of the circuit while Q pertains to the capactive part of the circuit, i.e. the region of the weak link. If C is taken as the effective (quantum mechanical) capacitance localised around the weak link then we can present the circuit variables as φ and Cφ(=Q). Thus we may write as the basis of our description [φ,Q] = iћ coupled with the uncertainty relation △φ. △Q ≽ ћ/2. Ultimately, it can be shown that these derive from the position-momentum duality in quantum mechanics [5] and, as such, is perfectly general, applying to both normal and superconducting quantum circuits.