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Transmon qubit

Select two independent parameter groups to solve the single-junction transmon in the usual large E_J/E_C approximation.

Circuit

\hat{H}_{\rm T}=4E_C\left(\hat{n}-n_g\right)^2-E_J\cos\hat{\varphi}

\phi_0=\frac{\hbar}{2e}=3.29106\times10^{-16}\,{\rm Wb}

\Delta_{\rm Al}=180\,\mu{\rm eV}

E_J=\phi_0 I_c=\frac{\phi_0^2}{L_J}

I_cR_n=\frac{\pi\Delta_{\rm Al}}{2e}=282.743\,\mu{\rm V}

E_C=\frac{e^2}{2C}

E_m\simeq-E_J+\sqrt{8E_CE_J}\left(m+\frac{1}{2}\right)-\frac{E_C}{12}\left(6m^2+6m+3\right)

\hbar\omega_{ge}\simeq\sqrt{8E_CE_J}-E_C

\alpha\simeq-E_C

Uses the Al/AlOx/Al Ambegaokar-Baratoff conversion from Scientific Reports 13, 6772 (2023) and Δ_Al = 180 µeV from Nature Communications 13, 7196 (2022).

Parameter	Value	Numerical	Unit

Parameter	Value	Numerical	Unit

ω₀₁ num

α num

ε₀₁