Semiclassical model for the dephasing of a two-electron spin qubit coupled to a coherently evolving nuclear spin bath

We study electron spin decoherence in a two-electron double quantum dot due to the hyperfine interaction, under spin-echo conditions as studied in recent experiments. We develop a semiclassical model for the interaction between the electron and nuclear spins, in which the time-dependent Overhauser fields induced by the nuclear spins are treated as classical vector variables. Comparison of the model with experimentally obtained echo signals allows us to quantify the contributions to the nuclear spin evolution of various processes such as coherent Larmor precession and spin diffusion.