  Optimized light-matter coupling in semiconductor nanostructures is a key to
understand their optical properties and can be enabled by advanced fabrication
techniques. Using in-situ electron beam lithography combined with a
low-temperature cathodoluminescence imaging, we deterministically fabricate
microlenses above selected InAs quantum dots (QDs) achieving their efficient
coupling to the external light field. This enables to perform four-wave mixing
micro-spectroscopy of single QD excitons, revealing the exciton population and
coherence dynamics. We infer the temperature dependence of the dephasing in
order to address the impact of phonons on the decoherence of confined excitons.
The loss of the coherence over the first picoseconds is associated with the
emission of a phonon wave packet, also governing the phonon background in
photoluminescence (PL) spectra. Using theory based on the independent boson
model, we consistently explain the initial coherence decay, the zero-phonon
line fraction, and the lineshape of the phonon-assisted PL using realistic
quantum dot geometries.
