Direct observation of photon bound states using a single artificial atom

The interaction between photons and a single two-level atom constitutes a fundamental paradigm in quantum physics. The nonlinearity provided by the atom means that the light-matter interaction depends strongly on the number of photons interacting with the two-level system within its emission lifetime. This nonlinearity results in the unveiling of strongly correlated quasi-particles known as photon bound states, giving rise to key physical processes such as stimulated emission and soliton propagation. While signatures consistent with the existence of photon bound states have been measured in strongly interacting Rydberg gases, their hallmark excitation-number-dependent dispersion and propagation velocity have not yet been observed. Here, we report the direct observation of a photon-number-dependent time delay in the scattering off a single semiconductor quantum dot coupled to an optical cavity. By scattering a weak coherent pulse off the cavity-QED system and measuring the time-dependent output power and correlation functions, we show that single photons, and two- and three-photon bound states incur different time delays of 144.02\,ps, 66.45\,ps and 45.51\,ps respectively. The reduced time delay of the two-photon bound state is a fingerprint of the celebrated example of stimulated emission, where the arrival of two photons within the lifetime of an emitter causes one photon to stimulate the emission of the other from the atom.