Decoherence of 31P Donor Spins in Silicon

Abstract

Spin coherence is important for the fields of electron spin resonance (ESR), nuclear magnetic resonance (NMR), magnetic resonance imaging (MRI), and quantum devices. For donor spins in silicon, coherence both quantifies their potential as qubits and measures environmental processes. By understanding those processes, we can construct experiments which remove them to obtain longer coherence times. Silicon crystals are uniquely suited to this task, benefiting from decades of advancements in purification.

The two most well-known decoherence mechanisms for donors in silicon are 29Si atoms and the donor spins themselves. Although well studied for electron spins, these mechanisms are less understood for nuclear spins. Using crystals with controlled concentrations of 29Si and 31P donors, I evaluate the limitations imposed on 31P nuclear spins.

I find that nuclear spin echo decay times vary linearly with 29Si concentration. The non-exponential decays shown here establish a range of 29Si flip-flop rates, with some being fast compared to experiment timescales and others being slow. Furthermore, when compared to measurements of ionized nuclear spins, the echo decays here imply a "frozen core" picture where the donor electron spin protects the nuclear spin by detuning neighboring 29Si atoms.

In studying spin coherence relative to 31P concentration, I find that nuclear spin echo experiments can measure donor electron spin flip-flop rates. A stochastic model reproduces the experiments by fitting a local Zeeman frequency linewidth. However, experiments in more lightly doped crystals (<10^15 P/cm^3) suggest that coherence is not limited by flip-flops. The source of decoherence in these crystals is unknown, but the experiments serve as an upper bound on electric field noise.

Magnetic field fluctuations are known to obstruct spin coherence measurements. One popular method for removing that noise is dynamical decoupling via repeated pi rotations. However, these sequences also elongate echo decays for ensemble spins known to be decohered instead by instantaneous diffusion. This result suggested that cumulative rotation errors might artificially inflate decay times. After demonstrating that such effects were insignificant in practice, I find instead that pi rotation errors reduce the dipole-dipole coupling between spins.