Numerical Modeling of Two-Defect Spin Dynamics in a Hyperfine Field

Spins in solid state defects represent promising building blocks for quantum information applications. For these purposes, maintaining coherent spin states is crucial; however, long coherence is generally not straightforward to achieve, as spins can interact with various degrees-of-freedom of the solid state host. In many cases, hyperfine interactions between the electronic spin of the defect and the nuclear spins of the host lattice dominate decoherence. In these scenarios, the cluster-correlation expansion (CCE) method has proven to be a useful numerical tool in qualitatively and quantitatively capturing the effective spin coherence of the combined spin-bath system, and more recent generalizations have included population dynamics as well. In this work, we extend this generalized CCE method to capture the spin dynamics of two qubit spins coupled with a common bath of nuclear spins. Using this framework, we evaluate the spin dynamics in a variety of defect qubit candidate systems as a function of different defect pair separations, magnetic field strengths, and pulse sequence schemes. More broadly, our method can be used to systematically study the dynamical interactions of complex defect clusters and their coupling to the hyperfine spin bath.