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Supplementary on-line information
Sample technology:
The micropillar fabrication is based on a microcavity structure grown by molecular beam
epitaxy (MBE). Figure 1 shows the design of the MBE layer sequence. The structure provides
strong optical confinement in the growth direction by Bragg reflector stacks composed of 20
and 23 periods of λ/4 GaAs and AlAs layers (69 nm /82 nm) in the top and bottom mirrors,
respectively. Here 
(quantum dots) in the cavity materials. The actual cavity is inserted between the Bragg
reflectors and has a thickness of 296 nm (single λ ). At the center of the GaAs cavity an
InGaAs QD layer is embedded. Due to the use of a single λ cavity the QDs are positioned at
the antinode of the fundamental mode in the growth direction.
The investigation of strong coupling effects for individual quantum dots in the micropillars
requires us to design the samples appropriately so that the cavity resonance for the pillar
diameter of interest is located in a spectral range in which clearly distinct single dot lines
occur. Therefore the samples are grown in such a way that in the planar structures the cavity
mode is located about 40 meV below the maximum of the dot emission band. The lateral
optical confinement in the 1.5 µm micropillars shifts the fundamental mode by about 25 meV
to higher energies into the spectral range of the onset of the dot emission band.
Dot linewidth:
The measured quantum dot linewidth is usually of the order of several tens of µeV. It is due to
inhomogeneous broadening e.g. by random charge fluctuations created by the nonresonant
excitation around the dot which modify the dot exciton energy during the long data recording
times (seconds to minutes). As strong coupling occurs via the emission and reabsorption of a
photon within the photon lifetime in the cavity (about 10 ps, much smaller than e.g.
recombination time scales) the influence of statistical charge fluctuations is negligible. For the
criterion for the onset of strong coupling the use of the homogeneous quantum dot exciton
linewidths is appropriate. At low temperatures this linewidths is on the order of a few to about
10 µeV and therefore much smaller than the cavity linewidth.
Control of in-plane dot position:
We would like to point out, that the in-plane dot position in the micropillar cannot be
controlled in the present epitaxial growth and patterning processes. Therefore the in-plane dot
location may not coincide with the antinode of the in-plane cavity field. For the estimate of
the oscillator strength of the dot this implies that we derive a lower limit.
Single dot identification:
We have chosen the relative spectral positions of the cavity mode and the quantum dot
emission band appropriately that the cavity is placed at the low energy side of the dot
emission. In this energy range only few dots emit, facilitating single dot studies. As can be
seen in Fig. 2b of the manuscript, there is typically one dot per meV in the energy range
around the cavity mode for a 1.5 µm diameter micropillar. In principle it is possible that there
are two dots interacting simultaneously with the cavity mode. However, when the dots are
tuned out of resonance with the cavity mode a two component spectrum would be expected as
long as the dots are separated by the spectral resolution of the set-up which approximately
coincides with the spectral resolution used in the experiments (both about 50 µeV). We
observe no indication for this in the strong or weak coupling cases investigated. The
probability to have two dots within an energy range of 50 µeV can be estimated to about a
few times 10-3. In addition, in order to obtain strong coupling both dots would have to be
located close to the antinode of the field, i.e. at the center of the cross section of the pillar
which reduces the probability further. Therefore it is very unlikely that we observe an
interaction of the cavity mode with more than one quantum dot exciton.
The oscillator strength of 50 estimated in the manuscript assuming a single quantum dot
exciton in the cavity showing strong coupling is also consistent with values observed for
studies on natural quantum dots in the literature. Guest et al. have obtained oscillator strength
values ranging from 45 to 180 for natural GaAs/AlGaAs quantum dots. Our estimate is at the
lower end of this range. This is consistent with the fact, that the dot is most likely not located
at the exact maximum of the field. Due to this our evaluation gives only a lower limit for the
oscillator strength.
Number of photons in a cavity at any given time:
We use a laser power of 2 µW for the strong coupling study. As a worst case model we
assume that the laser is entirely focussed on the micropillar and we neglect reflection at the
cryostat window and the sample surface. As we are using 532 nm excitation the main loss of
photons which has to be considered for the population of the cavity is absorption in the thick
upper Bragg reflector. Using an absorption coefficient of GaAs of 6x104/cm (M.D. Sturge,
Phys. Rev. 127, 768 (1962)) at 532 nm we obtain that only about 0.57 nW reach the cavity.
Using again a worst case estimate (i.e. giving us the highest number of photons) we assume
that all the photons reaching the cavity are absorbed there and the resulting carrier pairs all
reach the dot under consideration for the strong coupling, we obtain 1.5x109 excitons which
are created in that dot per second. The photon life time in the present cavities is about 10 ps.
As can be seen from the product of the number of excitons per time with the photon lifetime
the average population probability of the cavity by photons is 0.015. Therefore effects due to
the population of the cavity with more than one photon at a time are negligible.