  Deep cooling of electron and nuclear spins is equivalent to achieving
polarization degrees close to 100% and is a key requirement in solid state
quantum information technologies. While polarization of individual nuclear
spins in diamond and SiC reaches 99% and beyond, it has been limited to 60-65%
for the nuclei in quantum dots. Theoretical models have attributed this limit
to formation of coherent "dark" nuclear spin states but experimental
verification is lacking, especially due to the poor accuracy of polarization
degree measurements. Here we measure the nuclear polarization in GaAs/AlGaAs
quantum dots with high accuracy using a new approach enabled by manipulation of
the nuclear spin states with radiofrequency pulses. Polarizations up to 80% are
observed - the highest reported so far for optical cooling in quantum dots.
This value is still not limited by nuclear coherence effects. Instead we find
that optically cooled nuclei are well described within a classical spin
temperature framework. Our findings unlock a route for further progress towards
quantum dot electron spin qubits where deep cooling of the mesoscopic nuclear
spin ensemble is used to achieve long qubit coherence. Moreover, GaAs hyperfine
material constants are measured here experimentally for the first time.
