Fig. 1: Electron and nuclear spins in a quantum dot.
a Schematic of an InAs quantum dot embedded in a n–i–Schottky diode structure. Electron spin is coupled to nuclei via hyperfine interaction (\({\hat{{\mathcal{H}}}}_{{\rm{hf}}}\)) and to phonons (\({\hat{{\mathcal{H}}}}_{{\rm{e}}-{\rm{ph}}}\)). Tunnel barrier thickness tB controls the cotunneling interaction (\({\hat{{\mathcal{H}}}}_{{\rm{cotun}}}\)). Quantum dot charge state is controlled with bias VS, which tunes the energies of one-electron (1e) and two-electron (2e) states with respect to Fermi energy EF. b Energy levels of an empty dot \(\left|0\right\rangle\), electron with spin up (\(\left|\uparrow \right\rangle\), sz = +1/2) or down (\(\left|\downarrow \right\rangle\), sz = −1/2), and a trion \(\left|\uparrow \downarrow \Uparrow \right\rangle\) with hole moment jz = +3/2, which has a small admixture β ≪ 1 of a trion \(\left|\uparrow \downarrow \Downarrow \right\rangle\) with opposite hole moment jz = −3/2. Arrow labels show the rates of radiative recombination γR, Auger recombination γA, recharging r, and electron spin flip ξ↑↓. Electron spin splitting is due to Zeeman effect (μBgeBz, where ge is electron g-factor and μB is Bohr magneton) and nuclear hyperfine shift Ehf ∝ AhfPN. c Timing diagram of a pump-delay-probe experiment where optical excitation is used to initialise and probe the spins of either the electron or nuclei. d Time-resolved resonance fluorescence (ResFl) in a pump-probe experiment. Resonance fluorescence pulses of intensities IResFl,Pump and IResFl,Probe indicate electron spin pumping and are used to calculate the residual (i.e. relative to initial) electron spin polarisation Pe = (IResFl,Pump − IResFl,Probe)/IResFl,Pump after time TDark. e Electron spin decay measured in Coulomb blockade regime as Pe(TDark) in diode sample structures with different tB (symbols). Lines show exponential (solid) or rate-equation (dashed) fitting. f Nuclear spin decay obtained by measuring hyperfine shift Ehf as a function of dark time TDark in a pump-delay-probe experiment. Lines show fitting with stretched exponential function.
