A solvable quantum model of dynamic nuclear polarization in quantum dots*

Dynamic nuclear polarization (DNP) in quantum dots has given rise to a variety of unexpected and potentially useful effects, yet a consistent theoretical description with predictive power is still lacking. We present a quantum mechanical theory of optically induced DNP applicable to quantum dots and other interacting spin systems. The exact steady state of the optically driven coupled electron-nuclear system is calculated under the assumption of constant hyperfine coupling strengths (box model) for an arbitrary number of nuclear spins. Based on this analytical result we investigate the nuclear spin behaviour for different experimental parameter regimes and find that our model reproduces the flat-top and triangular absorption lineshapes (linedragging) seen in various experiments. Furthermore we predict a novel DNP effect. Under particular and achievable experimental conditions the nuclear spin system tends to polarize in such a way as to cancel the effect of the external magnetic field. The predicted sharply peaked nuclear spin polarization probability distributions centered at the value corresponding to degenerate electronic transitions would be of great significance for quantum technological applications.