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Interaction between light and matter generates optical nonlinearities, which are particularly pronounced in the quantum strong coupling regime. When a single bosonic mode couples to a single fermionic mode, a Jaynes-Cummings (JC) ladder is formed, which we realize here using cavity photons and quantum dot excitons. We measure and model 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. This is achieved using coherent nonlinear spectroscopy, specifically four-wave mixing, where the coherence between the ground state and the first (second) rung of the JC ladder can be interrogated for positive (negative) delays. With increasing excitation intensity and thus rising average number of injected photons, we observe spectral signatures of the quantum-to-classical crossover of the strong coupling regime.
Fascinating pictures that can be interpreted as showing molecular orbitals have been obtained with various imaging techniques. Among these, angle resolved photoemission spectroscopy (ARPES) has emerged as a particularly powerful method. Orbital images have been used to underline the physical credibility of the molecular orbital concept. However, from the theory of the photoemission process it is evident that imaging experiments do not show molecular orbitals, but Dyson orbitals. The latter are not eigenstates of a single-particle Hamiltonian and thus do not fit into the usual simple interpretation of electronic structure in terms of molecular orbitals. In a combined theoretical and experimental study we thus check whether a Dyson-orbital and a molecular-orbital based interpretation of ARPES lead to differences that are relevant on the experimentally observable scale. We discuss a scheme that allows for approximately calculating Dyson orbitals with moderate computational effort. Electronic relaxation is taken into account explicitly. The comparison reveals that while molecular orbitals are frequently good approximations to Dyson orbitals, a detailed understanding of photoemission intensities may require one to go beyond the molecular orbital picture. In particular we clearly observe signatures of the Dyson-orbital character for an adsorbed semiconductor molecule in ARPES spectra when these are recorded over a larger momentum range than in earlier experiments.