1. Introduction 2. Quantum Dynamics in Hilbert Space 3. The Density Operator and Quantum Dynamics in Liouville Space 4. Quantum Electrodynamics, Optical Polarization, and Nonlinear Spectroscopy 5. Nonlinear Response Functions and Optical Susceptibilities 6. The Optical Response Functions of a Multilevel System with Relaxation 7. Semiclassical Simulation of the Optical Response Functions 8. The Cumulant Expansion and the Multimode Brownian Oscillator Model 9. Fluorescence, Spontaneous-Raman and Coherent-Raman Spectroscopy 10. Selective Elimination of Inhomogeneous Broadening Photon Echoes 11. Resonant Gratings, Pump-Probe, and Hole Burning Spectroscopy 12. Wavepacket Dynamics in Liouville Space The Wigner Representation 13. Wavepacket Analysis of Nonimpulsive Measurements 14. Off-Resonance Raman Scattering 15. Polarization Spectroscopy Birefringence and Dichroism 16. Nonlinear Response of Molecular Assemblies The Local-Field Approximation 17. Many Body and Cooperative Effects in the Nonlinear Response
We introduce a tomography approach to describe the optical response of a cavity quantum electrodynamics device, beyond the semiclassical image of polarization rotation, by analyzing the polarization density matrix of the reflected photons in the Poincaré sphere. Applying this approach to an electrically-controlled quantum dot-cavity device, we show that a single resonantly-excited quantum dot induces a large optical polarization rotation by
20∘ in latitude and longitude in the Poincaré sphere, with a polarization purity remaining above
84%. The quantum dot resonance fluorescence is shown to contribute to the polarization rotation via its coherent part, whereas its incoherent part contributes to degrading the polarization purity.
Summary form only given. The ultrafast nonlinear optical response of semiconductor-microcavities (SMCs) in the nonperturbative regime is attracting growing interest for exploring fundamental light-matter interactions in many-particle quantum systems, as well as for the future implementations of ultrafast photonic devices. In spite of many investigations, the coherent dynamics of excitonic nonlinear-response in the nonperturbative regime has not been fully understood. Open questions are how strong exciton-cavity coupling affects exciton-exciton (X-X) interactions, and how in turn the X-X correlation influences the nonlinear response of SmCs. We investigate these open questions and show that the nonperturbative regime provides an unprecedented tool for investigating four-particle correlations.We start from the equations for the third order exciton polarization and cavity field describing quantum optical effects and coherent nonlinear optics in SMCs, perform the semiclassical factorization and include multiple scattering processes.