Figure 2. Effects of different orders of many-body correlations on central spin decoherence under dynamical decoupling.

(a) Schematics of various CPMG and UDD pulse sequences. (b) Comparisons of the P-donor electron spin decoherence in a natural abundance ²⁹Si nuclear spin bath calculated by the numerically exact CCE method (lines) and those by the LCE approximation (symbols) to determine the many-body correlations that contribute significantly to the spin decoherence under various CPMG and UDD controls. Here, LCE-V₂ (crosses) represents the leading-order pairwise flip-flop processes in the nuclear spin bath which dominate for sequences with an odd number of π pulses, while LCE-V_4z (squares) represents the diagonal interaction renormalized pairwise flip-flop processes which dominate for the even-numbered sequences where LCE-V₂ is zero (see Fig. 1b). The magnetic field was set as B=0.3 T applied along the [110] lattice direction.