Theory of nuclear induced spectral diffusion: Spin decoherence of phosphorus donors in Si and GaAs quantum dots

TL;DR

This paper develops a theoretical model for nuclear-induced spectral diffusion affecting spin decoherence in semiconductors, providing estimates for decoherence times in silicon and GaAs quantum dots, with implications for quantum computing.

Contribution

The paper introduces a new model for spectral diffusion due to nuclear spins, calculating decoherence times and analyzing motional narrowing effects in semiconductors.

Findings

Decoherence time for Si:P is approximately 0.64 ms, longer than experimental measurements.

Spectral diffusion in P-31 nuclear spins is in the motional narrowing regime.

Decoherence times in GaAs quantum dots range from 10 to 50 microseconds, depending on size.

Abstract

We propose a model for spectral diffusion of localized spins in semiconductors due to the dipolar fluctuations of lattice nuclear spins. Each nuclear spin flip-flop is assumed to be independent, the rate for this process being calculated by a method of moments. Our calculated spin decoherence time $T_{M}=0.64$ ms for donor electron spins in Si:P is a factor of two longer than spin echo decay measurements. For $^{31}$P nuclear spins we show that spectral diffusion is well into the motional narrowing regime. The calculation for GaAs quantum dots gives $T_{M}=10-50$ $\mu$s depending on the quantum dot size. Our theory indicates that nuclear induced spectral diffusion should not be a serious problem in developing spin-based semiconductor quantum computer architectures.