Tunnel-rate-selective spin readout

Map states with unequal escape rates ${\Gamma }_f\gg {\Gamma }_s$ onto distinct charge outcomes after an interval between their characteristic escape times. Both removal energies can lie above the reservoir chemical potential, so their splitting need not be thermally resolved. A useful rate difference must have a physical origin: a demonstrated single-dot example uses a two-electron singlet state and triplet state with different occupied orbitals. A bare single-electron Zeeman pair in the same orbital does not automatically provide the required rate contrast.^[ref]

For independent exponential escape, equal prior probabilities and no state relaxation, the mean classification error is $P_e(\tau )=[e^{-{\Gamma }_f\tau }+1-e^{-{\Gamma }_s\tau }]/2$. Setting its derivative to zero gives the displayed interval. The error increases both when the fast state is not given enough time to escape and when the slow state is given too much. Detector bandwidth, relaxation and reloading require an expanded measurement model.