Decoherence of nuclear spins in the 'frozen core' of an electron spin

摘要

Hybrid qubit systems combining electronic spins with nearby ("proximate")nuclear spin registers offer a promising avenue towards quantum informationprocessing, with even multi-spin error correction protocols recentlydemonstrated in diamond. However, for the important platform offered by spinsof donor atoms in cryogenically-cooled silicon,decoherence mechanisms of$^{29}$Si proximate nuclear spins are not yet well understood.The reason ispartly because proximate spins lie within a so-called "frozen core" regionwhere the donor electronic hyperfine interaction strongly suppresses nucleardynamics. We investigate the decoherence of a central proximate nuclear qubitarising from quantum spin baths outside, as well as inside, the frozen corearound the donor electron. We consider the effect of a very large nuclear spinbath comprising many ($\gtrsim 10^8$) weakly contributing pairs outside thefrozen core. We also propose that there may be an important contribution from afew (of order $100$) symmetrically sited nuclear spin pairs ("equivalentpairs"), which were not previously considered as their effect is negligibleoutside the frozen core. If equivalent pairs represent a measurable source ofdecoherence, nuclear coherence decays could provide sensitive probes of thesymmetries of electronic wavefunctions. For the phosphorus donor system, weobtain $T_{2n}$ values of order 1 second for both the "far bath" and"equivalent pair" models, confirming the suitability of proximate nuclei insilicon as very long-lived spin qubits.