SQUID Calculator

An asymmetric SQUID consists of two Josephson junctions with energies E_J1 ≥ E_J2 in a superconducting loop. The effective Josephson energy is tunable by an external flux.

Calculation direction: Individual junction energies → sweet spots Sweet spot energies → individual junctions

Josephson energy E_J1 (larger junction) [GHz]: Josephson energy E_J2 (smaller junction) [GHz]:

Formulas

Quantity	Formula
E_J^eff(Φ)	√(E_J1² + E_J2² + 2E_J1E_J2 cos(2πΦ/Φ₀)) = (E_J1+E_J2)√(cos²(πΦ/Φ₀) + d² sin²(πΦ/Φ₀))
Asymmetry d	d = (E_J1 − E_J2) / (E_J1 + E_J2) = E_J^lower / E_J^upper
Upper sweet spot (Φ = 0)	E_J^upper = E_J1 + E_J2
Lower sweet spot (Φ = Φ₀/2)	E_J^lower = \|E_J1 − E_J2\|
From sweet spots	E_J1 = (E_J^upper + E_J^lower)/2 E_J2 = (E_J^upper − E_J^lower)/2

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