  The random magnetic field produced by nuclear spins has long been viewed as
the dominating source of decoherence in the quantum-dot based spins. Here we
obtain in both exact and analytical manner the dynamics of spin qubits coupled
to nuclear spin environments via the hyperfine interaction, going beyond the
weak system-bath interaction and Markovian approximation. We predict that the
detailed-balance breaking produced by chemical potential gradient in nuclear
baths leads to the rapid oscillations of populations, quantum coherence and
entanglement, which are absent in the conventional case (i.e., Overhauser
noise). This is attributed to the nonequilibrium feature of the system as shown
in the relation between the oscillation period and the chemical potential
imbalance. Our results reveal the essentiality of nonequilibriumness with
detailed-balance breaking for enhancing the dynamical coherence and
entanglement of spin qubits. Moreover, our exact solution explicitly
demonstrates that the non-Markovian bath comprised by nuclear spins can
preserve the collective quantum state, due to the recovery of coherence.
Finally, we propose an experiment using ultracold trapped ions to observe these
nonequilibrium and memory effects.
