Flux Qubit — RF-SQUID Double-Well Potential

The RF-SQUID flux qubit is described by U(φ) = E_L(φ−2πf)²/2 − E_J·cos(φ), where φ is the loop flux and f=Φ_ext/Φ₀. At f=0.5, the potential is symmetric with a double well; tunneling through the barrier creates the qubit states |0⟩ and |1⟩ with an avoided crossing (tunnel splitting Δ).

RF-SQUID potential U(φ) = E_L(φ-2πf)²/2 - E_J·cos(φ). Energy levels shown as horizontal lines.
Energy levels E₀,E₁ vs external flux f=Φ/Φ₀. Avoided crossing at f=0.5.
Symmetry:
Barrier height ΔU:
Tunnel splitting Δ:
ω_01/2π:
β_L = 2πE_J/E_L·(2π):
Ground |ψ₀|² (purple) and first excited |ψ₁|² (green) wavefunctions.
Zoom: avoided crossing E₀,E₁ near f=0.5.