  In a multi-electron atom, an excited electron can decay by emitting a photon.
Typically, the leftover electrons are in their ground state. In a radiative
Auger process, the leftover electrons are in an excited state and a redshifted
photon is created. In a semiconductor quantum dot, radiative Auger is predicted
for charged excitons. Here we report the observation of radiative Auger on
trions in single quantum dots. For a trion, a photon is created on
electron-hole recombination, leaving behind a single electron. The radiative
Auger process promotes this additional (Auger) electron to a higher shell of
the quantum dot. We show that the radiative Auger effect is a powerful probe of
this single electron: the energy separations between the resonance fluorescence
and the radiative Auger emission directly measure the single-particle
splittings of the electronic states in the quantum dot with high precision. In
semiconductors, these single-particle splittings are otherwise hard to access
by optical means as particles are excited typically in pairs, as excitons.
After the radiative Auger emission, the Auger carrier relaxes back to the
lowest shell. Going beyond the original theoretical proposals, we show how
applying quantum optics techniques to the radiative Auger photons gives access
to the single-electron dynamics, notably relaxation and tunneling. This is also
hard to access by optical means: even for quasi-resonant $p$-shell excitation,
electron relaxation takes place in the presence of a hole, complicating the
relaxation dynamics. The radiative Auger effect can be exploited in other
semiconductor nanostructures and quantum emitters in the solid state to
determine the energy levels and the dynamics of a single carrier.
