A Josephson junction has critical current and sits in a circuit with total shunting…

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Quantum Information and Technology, Ch Superconducting qubits and circuit QED

Problem

A Josephson junction has critical current Ic=30 nAI_c = 30\,\mathrm{nA} and sits in a circuit with total shunting capacitance CΣ=90 fFC_\Sigma = 90\,\mathrm{fF}. Using Φ0=2.068×10−15 Wb\Phi_0 = 2.068\times10^{-15}\,\mathrm{Wb}, find: ((a)) the Josephson energy EJ/hE_J/h; ((b)) the Josephson inductance LJ=Φ0/2πIcL_J = \Phi_0/2\pi I_c; ((c)) the charging energy EC/h=e2/2CΣhE_C/h = e^2/2C_\Sigma h.

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