Magic recovery of spin coherence in an interacting quantum bath

The magic recovery of the spin coherence is a distinguished feature due to the quantum nature of the spin bath, which was first proposed from a pseudo-spin model. Here we proved without resorting to a specific bath model that this magic coherence recovery is general. Based on this proof and numerical simulations, we proposed the conditions under which the $\sqrt{2}\tau$ recovery would be experimentally observed. In particular, we explored the possibility of observing the phenomenon by measuring central nuclear spin coherence in solid state NMR experiments, where the coherence time $T_{2}$ and the inhomogeneous broadening time $T^{*}_{2}$ are of the same order.