Two-laser dynamic nuclear polarization with semiconductor electrons: Feedback, suppressed fluctuations, and bistability near two-photon resonance

Feedback control is a powerful tool to stabilize systems for which precision control is difficult to impose directly, such as the environment of an open quantum system. Reduction of noise from the environment is a major challenge on the road to harnessing delicate quantum effects such as superposition and entanglement. In particular, spin states of defects and quantum dots in semiconductors display promising coherence properties for future applications, often being limited by disturbance from disordered nuclear spins in their environment. Here we show how optical coherent population trapping (CPT) of the spin of localized semiconductor electrons stabilizes the surrounding nuclear spins via feedback control. We find distinct control regimes for different signs of laser detuning and examine the transition from an unpolarized, narrowed state to a polarized state possessing a bistability. The narrowing of the state protects the electron spin against dephasing and yields self-improving CPT. Our analysis is relevant for a variety of solid-state systems where hyperfine-induced dephasing is a limitation for using electron spin coherence.