Nuclear-spin polaron formation: Anisotropy effects and quantum phase transition

We study theoretically the formation of nuclear-spin polaron state in semiconductor nanosystems within Lindblad equation approach. To this end, we derive a general for density operator that complies with symmetry system Hamiltonian and address localized charge carriers subject to an arbitrarily anisotropic hyperfine interaction when optically cooling nuclei. The steady-state solution matrix central spin model is presented as function electron nuclear bath temperature. Results electron-nuclear correlator well data distribution serve measure spin-entanglement. features both them clearly indicate at low temperatures where crossover regime coincides enhancement quantum fluctuations agrees mean-field prediction critical temperature line. can identify two distinct states dependent upon anisotropy which are separated by phase transition isotropic point. These reflected temporal auto-correlation functions accessible experiment via spin-noise measurements.