  Strongly coupled quantum dot-cavity systems provide a non-linear
configuration of hybridized light-matter states with promising quantum-optical
applications. Here, we investigate the coherent interaction between strong
laser pulses and quantum dot-cavity polaritons. Resonant excitation of
polaritonic states and their interaction with phonons allow us to observe
coherent Rabi oscillations and Ramsey fringes. Furthermore, we demonstrate
complete coherent control of a quantum dot-photonic crystal cavity based
quantum-bit. By controlling the excitation power and phase in a two-pulse
excitation scheme we achieve access to the full Bloch sphere. Quantum-optical
simulations are in good agreement with our experiments and provide insight into
the decoherence mechanisms.
