Exact Results in Quantum Theory

Milestone achievements in cavity quantum electrodynamics (cQED) have just been awarded with the Nobel prize in physics [1]. The underlying experiments were performed on individual atomic systems exploring light-matter interaction on a quantum level [2]. cQED effects can now be observed also in solid state systems, which owing to their intrinsicstability are better suited for a scalable technology and commercialization. When a single bosonic mode strongly couples to a single fermionic mode, a Jaynes-Cummings (JC) ladder is formed. This is realized here by combining photons confined in a micropillar cavity [3] with a single exciton (electron-hole pair bound by their electrostatic attraction), so as tocreate dressed states called polaritons.In this talk, I will present the measurements and modeling of the coherent anharmonic response of this strongly-coupled exciton-cavity system at resonance. Injecting two photons into the cavity, we demonstrate a \sqrt{2} larger polariton splitting with respect to the vacuum Rabi splitting [3]. This is achieved using coherent nonlinear spectroscopy, specif-ically four-wave mixing (FWM) [4], where the coherence between ground state and first (second) rung of the JC ladder can be interrogated for positive (negative) delays between laser pulses driving the FWM signal.As an outlook, I will highlight our recent spectroscopic studies of a multiexciton-cavity system, enabling pioneering investigations of its Tavis-Cummings physics [5] and thus paving the way towards long-range radiative coupling in a solid.[1] S. Haroche and D. J. Wineland[2] M. Brune et al Phys. Rev. Lett. 76 1800 (1996)[3] J. Kasprzak et al. Nature Mater. 9, 304 (2010).[4] W. Langbein and B. Patton Opt. Lett. 31, 1738 (2006)[5] F. Albert et al. Nature Comm. (2013)