Measuring central-spin interaction with a spin bath by pulsed ENDOR: Towards suppression of spin diffusion decoherence

We present pulsed electron-nuclear double resonance (ENDOR) experiments which enable us to characterize the coupling between bismuth donor spin qubits in Si and the surrounding spin bath of ${}^{29}\text{Si}$ impurities which provides the dominant decoherence mechanism (nuclear spin diffusion) at low temperatures ($<$16 K). Decoupling from the spin bath is predicted and cluster correlation expansion simulations show near-complete suppression of spin diffusion, at optimal working points. The suppression takes the form of sharply peaked divergences of the spin diffusion coherence time, in contrast with previously identified broader regions of insensitivity to classical fluctuations. ENDOR data suggest that anisotropic contributions are comparatively weak, so the form of the divergences is largely independent of crystal orientation.

Figure 1

Pulsed ENDOR measured for bismuth-doped silicon with frequency 9.8 GHz at which ten EPR lines are observed, the resonance peaks due to interactions of the donor with ${}^{29}\text{Si}$ nuclei at inequivalent lattice sites. The isotropic superhyperfine couplings were extracted from the spectrum at the highest magnetic field. As the field is varied, the smooth lines follow the resonance positions according to Eq. (9). Solid and dotted lines distinguish between the two peaks observed for each coupling, each corresponding to one of the two donor levels involved in the EPR transition. Only the peaks labeled $X_1$ and $X_2$, in addition to a third pair not resolved here, were found to show anisotropy from performing ENDOR as a function of crystal orientation.

Figure 2

Suppression of Bi-${}^{29}\text{Si}$ spin bath decoherence for the $|12\rangle \to |9\rangle$ EPR transition. (a) Simulated ENDOR and nuclear spin diffusion coherence times $T_{\text{SD}}$ as a function of magnetic field $B$, showing collapse of the superhyperfine couplings and a sharp increase in $T_{\text{SD}}$ as the field approaches the $B=188.0$ mT optimal working point (OWP). The dashed line is a fit. (b) Simulated ENDOR at the $B=188.0$ mT OWP (upper panel) and experimental spectrum at 9.755 GHz (lower panel). (c) Calculated donor Hahn spin echo decays from which coherence times in Fig. 2a were extracted.