Long-time noise characteristics of an isotopically-enriched silicon nuclear spin bath

Electron spin qubits in silicon are known to have long coherence times, especially in isotopically-enriched materials with few nuclear spins. As a variety of silicon qubit devices are explored experimentally, it is useful to have a theoretical understanding of noise characteristics as induced by nuclear spins to know when other noise sources should be suspected. We present a quantitative study of nuclear spin dynamics for moderately-sized baths over a range of timescales. We approximate the quantum dynamics by adapting the cluster-correlation expansion (CCE) technique to calculate bath “flip-flop” probabilities, improving the accuracy of simulations for longer timescales by introducing random, projective measurements throughout the time evolution as a semiclassical approximation. In this way, we are able to estimate the spectral density of noise induced by a nuclear spin bath for a wide range of frequencies and study the variation for different instances of nuclear spin samples. We present results of our modified CCE technique, comparing it to exact analytical and numerical solutions. SAND2019-12116A