  A single atom in a cavity is the model system of cavity quantum
electrodynamics (CQED). The strong coupling regime between the atom and
cavity-confined photon corresponds to the reversible exchange of energy between
the two modes, and underpins a wide range of CQED phenomena with applications
in quantum information science, including for example as quantum logic gates
and as sources of entangled states. An important advance was achieved recently
when strong coupling between excitons and cavity photons was reported for the
first time for localized quantum dots (QDs) in micron-size solid state
cavities. This has significance in terms of scalability and integration with
other optical devices, and could lead to the emergence of "quantum optics on a
chip" technology. However the results presented so far for quantum dots are in
the linear regime, corresponding to coupling to the vacuum field (vacuum Rabi
splitting); they are not a true QED effect and can equally well be described by
classical physics as the coupling between two oscillators. In this paper, we
present evidence for a purely quantum phenomenon for the QD/cavity photon
system, namely the increase in splitting of the levels when the mean number of
photons in the cavity is increased. This corresponds to non-linearities on the
single-photon scale: the presence of a single excitation in the cavity changes
the level structure, affecting the emission energies for a second photon. Such
results are a first step in demonstrating the promise of quantum dots for CQED
applications.
