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The random magnetic field produced by nuclear spins has long been viewed asthe dominating source of decoherence in the quantum-dot based spins. Here weobtain in both exact and analytical manner the dynamics of spin qubits coupledto nuclear spin environments via the hyperfine interaction, going beyond theweak system-bath interaction and Markovian approximation. We predict that thedetailed-balance breaking produced by chemical potential gradient in nuclearbaths leads to the rapid oscillations of populations, quantum coherence andentanglement, which are absent in the conventional case (i.e., Overhausernoise). This is attributed to the nonequilibrium feature of the system as shownin the relation between the oscillation period and the chemical potentialimbalance. Our results reveal the essentiality of nonequilibriumness withdetailed-balance breaking for enhancing the dynamical coherence andentanglement of spin qubits. Moreover, our exact solution explicitlydemonstrates that the non-Markovian bath comprised by nuclear spins canpreserve the collective quantum state, due to the recovery of coherence.Finally, we propose an experiment using ultracold trapped ions to observe thesenonequilibrium and memory effects.

Nonequilibrium-induced enhancement of dynamical quantum coherence and entanglement of spin arrays