  The Zeeman-split spin-states of a single electron confined in a
self-assembled quantum dot provide an optically-accessible spin qubit. For
III-V materials the nuclear spins of the solid-state host provide an intrinsic
noise source, resulting in electron-spin dephasing times of few nanoseconds.
While a comprehensive study of electron-spin dynamics at low magnetic field has
recently been carried out, what limits the electron coherence in these systems
remains unclear, in part due to the dominant effect of measurement-induced
dynamic polarisation of the nuclear bath. We develop an all-optical method to
access the quantum dot spin-state without perturbing the nuclear environment.
We use this method to implement Hahn-echo decoupling and reach the intrinsic
limit to coherence set by inhomogeneous strain fields coupling to quadrupolar
moments of the nuclear bath. These results indicate that the extension of
electron spin coherence beyond this few-microsecond limit necessitates the
reduction of strain-induced quadrupolar broadening in these materials.
