  Understanding fully the dynamics of coupled electron-nuclear spin systems,
which are important for the development of long-lived qubits based on
solid-state systems, remains a challenge. We show that in a singly charged
semiconductor quantum dot with inhomogeneous hyperfine coupling, the nuclear
spins relatively strongly coupled to the electron spin form a polarized core
during the dynamical polarization process. The polarized core provides a
protection effect against the electron spin relaxation, reducing the decay rate
by a factor of $N_1$, the number of the nuclear spins in the polarized core, at
a relatively small total polarization. This protection effect may occur in
quantum dots and solid-state spin systems defect centers, such as NV centers in
diamonds, and could be harnessed to fabricate in a relatively simple way
long-lived qubits and quantum memories.
