We investigate quantum nonlinear effects at a level of individual quanta in a double-tripod atom-light coupling scheme involving two atomic Rydberg states. In such a scheme the slow light coherently coupled to strongly interacting Rydberg states represents a two-component or spinor light. The scheme provides additional possibilities for the control and manipulation of light quanta. A distinctive feature of the proposed setup is that it combines the spin-orbit coupling for the spinor slow light with an interaction between the photons, enabling generation of the second probe beam even when two-photon detuning is zero. Furthermore, the interaction between the photons can become repulsive if the one-photon detunings have opposite signs. This is different from a single-ladder atom-light coupling scheme in which the interaction between the photons is attractive for both positive and negative detunings as long as the Rabi frequency of the control beam is not too high.
In this thesis, the properties of a strongly-coupled single-atom-cavity system are studied. Here, the atom predominantly interacts with only one mode of the electromagnetic field. Special attention was paid to the energy spectrum of the system, which consists of an anharmonic ladder of doublets. Developing a new laser cooling method for the preparation of the atom, it was possible for the first time to observe not only the first doublet, but also a state belonging to the second doublet in the optical spectrum. The quantization of light-matter interaction is confirmed by this observation, as the state can only be explained by a bonding of one atom to exactly two photons. Its excitation by a two-photon transition contains a nonlinearity at the level of single quanta. This leads to a dependency of the spectrum on the intensity of the impinging light.