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

TL;DR

This paper investigates the decoherence mechanisms of proximate nuclear spins near donor electrons in silicon, revealing potential for long-lived qubits and highlighting the roles of external spin baths and equivalent pairs within the frozen core.

Contribution

It introduces a comprehensive model of nuclear spin decoherence considering both external baths and equivalent pairs inside the frozen core, advancing understanding of silicon-based quantum memories.

Findings

Proximate nuclear spins can have coherence times around 1 second.

External spin baths and equivalent pairs significantly influence decoherence.

Proximate nuclei are promising candidates for long-lived quantum bits.

Abstract

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