Nuclear State Preparation via Landau-Zener-Stückelberg Transitions in Double Quantum Dots

We theoretically model a nuclear-state preparation scheme that increases the coherence time of a two-spin qubit in a double quantum dot. The two-electron system is tuned repeatedly across a singlet-triplet level anticrossing with alternating slow and rapid sweeps of an external bias voltage. Using a Landau-Zener-Stückelberg model, we find that in addition to a small nuclear polarization that weakly affects the electron spin coherence, the slow sweeps are only partially adiabatic and lead to a weak nuclear spin measurement and a nuclear-state narrowing which prolongs the electron spin coherence. This resolves some open problems brought up by a recent experiment [D. J. Reilly et al., Science 321, 817 (2008).]. Based on our description of the weak measurement, we simulate a system with up to $n=200$ nuclear spins per dot. Scaling in $n$ indicates a stronger effect for larger $n$.

Figure 1

(a) Energy diagram for the relevant states of the double QD as a function of the bias $\epsilon$. (b) The hyperfine interaction allows for flip-flop processes that open a gap ${\Delta }_{\mathrm{HF}}$ at the $\mathrm{S}\mathrm{\text{−}}{\mathrm{T}}_{+}$ crossing. Driving the system slowly from S(2,0) can result either in an adiabatic (b) or a nonadiabatic (c) transition. Driving the system back very fast results in a nonadiabatic passage to two distinguishable charge states.

Figure 2

(a) Averaged Overhauser field fluctuations ${\sigma }^{(z)}$ and electron spin decoherence $T_2^{*}=\hslash /{\sigma }^{(z)}$ (upper inset) as a function of the number of performed cycles. (b) Singlet return probability $P_S$ as a function of the number of performed cycles. Error bars are smaller than line thickness. (c) Initial (black) and final (orange) averaged probability distribution of the nuclear spin eigenstates of $\delta h^z$. Repeated cycles narrow the distribution, showing a reduction of ${\sigma }^{(z)}$.