Light and matter are mostly considered as separate phenomena. First works exploring mixed states of light and matter are due to Hopfield, who 50 years ago considered quantized Eigenstates of matter coupled to light, to explain optical properties of the solid state. In the medium the electromagnetic wave is accompanied by a polarization wave, and a polariton, a coupled state of matter and light, develops. The topic of these mixed states has gained considerable interest due to recent experimental developments. In atomic gases, aided by dark resonances, optical group velocities with magnitudes down to a few meters per second can be observed, eight orders of magnitude below the speed of light in vacuum. A central role here plays the concept of dark polaritons, i.e. long lived mixed states of matter and light. A further fascinating development in the area of mixed states of light and matter are exciton Bose-Einstein condensates. These constitute macroscopic quantum states of half matter and half light.

It is the aim of this seminar to highlight present frontier research of mixed states of light and matter in different areas of physics, ranging from atomic and molecular systems up to solid state physics ensembles.