  We study the competition of hole capture between an In(Ga)As quantum dot and
a directly adjacent ionized impurity in view of spin-photon interfaces. The
Kerr rotation noise spectroscopy at 4.2 K shows that the hole-capture
probability of the In(Ga)As quantum dot is about one order of magnitude higher
compared to the hole-capture probability of the ionized impurity and suggests
that a simultaneous occupation of quantum dot and impurity by a hole is
efficiently suppressed due to Coulomb interaction. A theoretical model of
interconnected spin and charge noise allows the quantitative specification of
all relevant time scales.
