We experimentally demonstrate how coherent population trapping (CPT) for donor-bound electron spins in GaAs results in autonomous feedback that prepares stabilized states for the spin polarization of nuclei around the electrons. CPT was realized by excitation with two lasers to a bound-exciton state. Transmission studies of the spectral CPT feature on an ensemble of electrons directly reveal the statistical distribution of prepared nuclear spin states. Tuning the laser driving from blue to red detuned drives a transition from one to two stable states. Our results have importance for ongoing research on schemes for dynamic nuclear spin polarization, the central spin problem and control of spin coherence.PACS numbers: 03.65. Yz, 42.50.Ex, 76.30.Mi, 76.70.Hb, 78.47.jh Following the emergence of electron spins in quantum dots and solid state defects as candidates for spin qubits it has become a major goal to realize control over the nuclear spins in such nanostructures. In many experimental settings, interaction with disordered nuclear spins in the crystal environment is detrimental to the coherent evolution of carefully prepared electron spin states [1][2][3]. Preparation of nuclear spins in a state that has reduced spin fluctuations with respect to the thermal equilibrium state will help to overcome this problem [4]. Proposals to achieve this goal have been put forward for electron spin resonance (ESR) on one-or two-electron quantum dots [5,6], and for optical preparation techniques that either rely on a quantum measurement technique [7,8] or a stochastic approach [9][10][11]. Experimental advances have been made with ESR and optical techniques on single quantum dots [12][13][14][15][16][17][18] and nitrogen-vacancy centers [19], and on quantum dot ensembles [20,21].Several of these works [8-11, 15, 18, 19] make use of the optical response of the electronic system near the coherent-population-trapping resonance (CPT, explained below) because it is highly sensitive to perturbations from nuclear spins. Notably, these experiments so far have focussed on quantum dots where, due to the particular anisotropic confinement, hyperfine coupling with a hole-spin in the excited state is reported to dominate [15]. In recent work [22] we discussed how the interplay between electron-nuclear spin interaction and CPT influences the stochastics of the nuclear spin bath for a class of systems where hyperfine interaction with the groundstate electron spin dominates.Here we report experiments on this latter class of systems. We demonstrate an all-optical technique that stabilizes the nuclear spin bath around localized donor electrons in GaAs into a non-thermal state under conditions of two-laser optical pumping. We show that the nuclear spin system is directed either towards a single stable state or (probabilistically) towards one of two stable states, depending on laser detuning from the excited state. Our results show how feedback control arises from the interplay between CPT and dynamic nuclear spin polarization (DNP), and confi...