This is the energy-level view of the same double-quantum-dot Pauli spin blockade readout as the 3D geometric simulator: instead of watching electrons hop between two physical dots, you watch their energy levels move as the interdot detuning ε is pulsed.
|S⟩ = (|↑↓⟩ − |↓↑⟩)/√2 (antisymmetric spin)
|T₀⟩ = (|↑↓⟩ + |↓↑⟩)/√2 (symmetric spin)
|T₊⟩ = |↑↑⟩ , |T₋⟩ = |↓↓⟩
The singlet channel is a genuine two-level system: the diabatic S(1,1) and S(0,2) charge-orbital energies cross as ε sweeps, but the tunnel coupling tc hybridizes them into an avoided crossing (upper/lower branches E± = (E11+E02)/2 ∓ √((ΔE/2)² + tc²), gap = 2tc at degeneracy) — the marker glides smoothly from the (1,1) branch onto the (0,2) branch. Every triplet has no orbital partner to hybridize with in this manifold, so its diabatic line stays flat and simply crosses through — it is Pauli-blocked and cannot follow the singlet down to (0,2).
The tunnelling itself is still the same rate process as the geometric version, driving identical statistics:
Γ_S = (t_c / t_ref)² / τ_ref
P_tunnel(S) = 1 − exp(−Γ_S · τ)
P_tunnel(T) = P_tunnel(S) × leakage_fraction
A charge sensor reads dot B's electron count as before. The leakage slider now visibly shakes the triplet lines up and down — a direct stand-in for spin-orbit/hyperfine mixing with the nuclear-spin bath, which is what lets a triplet occasionally sneak through the blockade and caps real single-shot readout fidelity below 100%.
- S / T₀ / T₊ / T₋ — prepare the two-electron spin state before the pulse.
- tc, τ — set the anticrossing gap size and how long the readout point is held; both raise the singlet tunnelling probability.
- Leakage — the blockade-breaking probability from spin-orbit/hyperfine mixing, also drawn as triplet-line jitter.
- Run Readout Pulse — sweeps ε across the diagram, samples one projective readout shot, and updates the running fidelity statistics.