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. 2014 Sep 10;5:4822. doi: 10.1038/ncomms5822

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(a) Schematics of bifurcated pseudospin evolutions conditioned on the central spin state under CPMG-2 (or UDD-2) control. The conjugate pseudospins (corresponding to the central spin in the state |±›) describe the dynamics of two-spin correlations. The more the trajectories are separated, the greater the central spin decoherence. The conjugate pseudospins exchange their pseudofields at time t=τ, 3τ when the central spin is flipped by a π-pulse. Without the diagonal interaction renormalization, the conjugate trajectories are symmetric and coincide at time T in the leading order of the evolution time, leading to cancellation of decoherence. (b) Histogram of the number of nuclear spin clusters (with inter-nuclei distances <1 nm) in 200 different bath configurations. (c) Decomposition of the LCE-V_4z term into three-body and four-body correlations (see Fig. 1a) for CPMG-2 (or UDD-2) control of the central spin. The magnetic field was B=0.3 T applied along the [110] lattice direction.

Inline graphic — (a) Schematics of bifurcated pseudospin evolutions conditioned on the central spin state under CPMG-2 (or UDD-2) control. The conjugate pseudospins (corresponding to the central spin in the state |±›) describe the dynamics of two-spin correlations. The more the trajectories are separated, the greater the central spin decoherence. The conjugate pseudospins exchange their pseudofields at time t=τ, 3τ when the central spin is flipped by a π-pulse. Without the diagonal interaction renormalization, the conjugate trajectories are symmetric and coincide at time T in the leading order of the evolution time, leading to cancellation of decoherence. (b) Histogram of the number of nuclear spin clusters (with inter-nuclei distances <1 nm) in 200 different bath configurations. (c) Decomposition of the LCE-V_4z term into three-body and four-body correlations (see Fig. 1a) for CPMG-2 (or UDD-2) control of the central spin. The magnetic field was B=0.3 T applied along the [110] lattice direction.