= Solution
For a <double quantum dot>, write $(n_L,n_R)$ for occupation. Tune a bias window allowing the cycle $(0,1)\to(1,1)\to(0,2)\to(0,1)$. Two <electrons> in the same lowest orbital must form a <singlet state> by the <Pauli exclusion principle>. The $(0,2)$ triplet requires an excited orbital, with an <energy> cost $\Delta_{ST}$ above the accessible window. Approximately spin-conserving tunnelling transfers $S(1,1)$ into $S(0,2)$, but cannot transfer $T(1,1)$ into that singlet. Once a triplet loads, transport stops until <spin relaxation> or mixing occurs: this is <Pauli spin blockade>. The reverse bias can avoid trapping in this sequence, producing rectification. Coulomb charging sets the allowed occupancies, but the extra blockade is a spin-selection restriction, not merely an energetically forbidden charge state.
<magnetically driven spin-blockade lifting> uses <electron paramagnetic resonance>. A transverse oscillating <magnetic field> drives <spin> transitions at
$$
\boxed{hf=|g^*|\mu_B|B_0|.}
$$
Flipping one <spin> in $|\uparrow\uparrow\rangle$ gives $|\downarrow\uparrow\rangle=(|T_0\rangle-|S\rangle)/\sqrt2$, which has a singlet component and can resume charge transfer. A perfectly uniform simultaneous rotation of two identical <spins> preserves their triplet character; effective relative rotation needs unequal local <resonance> conditions or another singlet–triplet mixing mechanism. In a real GaAs double dot, inhomogeneous nuclear fields can supply that difference. Hyperfine mixing, spin-orbit effects, <cotunnelling> and ordinary relaxation also produce leakage and must be distinguished from driven <resonance>.
A demonstrated device used surface Ti/Au gates to define two dots in a GaAs/AlGaAs <electron> gas $90\,\mathrm{nm}$ below the surface. An insulated on-chip gold coplanar stripline supplied the oscillating <magnetic field>. With the dots biased in <spin> blockade, RF excitation produced current peaks at the two field polarities satisfying <resonance>. Peak positions varied linearly with <frequency>, giving $|g^*|=0.35\pm0.01$. RF applied to a side gate instead gave negligible response, testing magnetic rather than electric excitation. Gate pulses and RF bursts further produced coherent spin-rotation oscillations in the charge readout.<Driven coherent oscillations of a single electron spin in a quantum dot by F. H. L. Koppens and others>[author preprint, pp.3–5 and Figs.1–4: device, magnetic-control comparison, resonance slope and pulsed rotations]{ref}
An ideal isolated resonant <spin> has <Rabi oscillation> <probability> $P_{\rm flip}(t)=\sin^2(\Omega_Rt/2)$. For a linearly oscillating field of peak <amplitude> $B_{\rm ac}$, the rotating-wave convention is $\Omega_R=|g^*|\mu_BB_{\rm ac}/(2\hbar)$. Repeated initialization, isolated manipulation and blockade-sensitive readout can therefore map a damped oscillatory singlet yield into an average current. Nuclear fluctuations, readout rates and <dephasing> change the envelope and contrast; an ideal sine squared is not a reconstruction of experimental data. Compare RF on/off, <resonance> tracking with <frequency>, drive-amplitude dependence and detuning controls. Current enhancement alone does not prove coherent rotations; the pulse-duration oscillations provide the further time-domain test.
\Image[/past-exam-of-the-physics-of-nanoelectronic-systems-course-of-the-university-of-cambridge/2012/paper-1-spin-blockade.png]
{title=Spin blockade and magnetic resonance}
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