  We present a quantum mechanical theory of optically induced dynamic nuclear
polarization 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 uniform hyperfine coupling strengths (box
model) for an arbitrary number of nuclear spins. This steady state is given by
a tractable expression that allows for an intuitive interpretation in terms of
spin-flip rates. Based on this result, we investigate the nuclear spin
behaviour for different experimental parameter regimes and find that our model
reproduces the flat-top and triangular absorption line shapes seen in various
experiments (line dragging) under the assumption of fast electron spin
dephasing due to phonons and co-tunneling. The mechanism responsible for line
dragging has been a matter of controversy so far; in contrast with previous
works, we show that the effect can be explained solely in terms of the contact
hyperfine interaction, without the need to introduce non-collinear terms or
other types of electron-nuclear interactions. Furthermore we predict a novel
nuclear spin polarization effect: under particular, experimentally realistic
conditions, the nuclear spin system tends to become sharply polarized in such a
way as to cancel the effect of the external magnetic field. This effect can
therefore suppress electron spin dephasing due to inhomogeneous broadening,
which could have important repercussions for quantum technological
applications.
