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

<br/>Spins in solid state defects represent promising building blocks for quantum information applications. For these purposes, maintaining the desired quantum state of these spins is crucial, however it is generally not straightforward, 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 [1,2] 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 [3]. In this work, we discuss extending this generalized CCE method to capture the spin dynamics of two qubit spins coupled with a common bath of nuclear spins [4]. Using this framework, we evaluate the spin dynamics in a variety of defect qubit candidate systems, where we also consider different defect pair separations, magnetic field strengths, and pulse sequence schemes. We study the interplay of the two qubits and the role of the hyperfine spin bath and highlight particularly important quantum-dynamical processes involved in these various regimes.<br/><br/>1. Yang and Liu, PRB, 78, 085315 (2008)<br/>2. Yang and Liu, PRB, 79, 115320 (2009)<br/>3. Yang et al, Annals of Physics, 413, 168063 (2020)<br/>4. Ciccarino and Narang, in preparation.