Units Energy-scale converter

µeV · GHz · K · T · Φ₀ · EC · EJ

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Energy scale

Edit any field; the others follow.

CODATA 2022

Zeeman splitting ΔE = g μB B. Flux Φ = B·A through a loop of area A, in units of Φ₀ = h/2e. Wavenumber ν̃ = f/c.

Charging energy

EC = e²/2C

EC

Josephson energy

EJ = ħIc/2e = Φ₀Ic/2π

EJ
Bulk Tc:

Ambegaokar–Baratoff: IcRn = (πΔ/2e) tanh(Δ/2kBT) for an SIS tunnel junction with identical electrodes; Δ(T) from the weak-coupling BCS gap equation. Presets use bulk Tc; thin films differ.

Transmon

From the EC and EJ cards

EJ/EC

E₀₁ ≈ √(8EJEC) − EC, α ≈ −EC: leading terms of the expansion in √(EC/EJ) (Koch et al. 2007).

Units · conventions

Energy scale

All rows represent one energy E: f = E/h, T = E/kB, ν̃ = E/hc. The field row is the Zeeman splitting E = g μB B of a two-level system with g-factor g (free electron g ≈ 2.0023; default 2). The flux row is Φ/Φ₀ = BA/Φ₀ for the field B of the previous row threading a loop of area A, with Φ₀ = h/2e. Changing g or A keeps the last-edited quantity fixed.

Charging energy

EC = e²/2C is the single-electron charging energy (transmon convention of Koch et al.). The Cooper-pair charging energy is 4EC = (2e)²/2C.

Josephson energy

EJ = ħIc/2e = Φ₀Ic/2π. From the normal-state resistance, the Ambegaokar–Baratoff relation for an SIS tunnel junction with identical BCS electrodes gives IcRn = (πΔ(T)/2e) tanh(Δ(T)/2kBT); at T = 0 this is EJ = RKΔ₀/8Rn with RK = h/e². Δ(T) solves the weak-coupling BCS gap equation ln(Δ₀/Δ) = 2∫₀∞dξ f(E)/E, E = √(ξ² + Δ²), with Δ₀ = πe−γkBTc ≈ 1.764 kBTc. Strong-coupling materials (Nb, Pb) have larger Δ₀/kBTc; enter the measured Δ₀ directly in that case.

Transmon

E₀₁ ≈ √(8EJEC) − EC and anharmonicity α = E₁₂ − E₀₁ ≈ −EC are the leading terms of the asymptotic expansion for EJ/EC ≫ 1; charge dispersion is neglected. The card warns below EJ/EC = 20.

References

V. Ambegaokar and A. Baratoff, Phys. Rev. Lett. 10, 486 (1963); J. Koch et al., Phys. Rev. A 76, 042319 (2007); CODATA 2022 recommended values (NIST).