This theoretical thesis consists of two parts which concern rather different topics
belonging to the field of quantum optics.

Part I:
A mechanical oscillator can serve as an efficient link between electromagnetic modes of different frequencies. We find that such a transducer can be characterized by two key parameters, the signal transfer efficiency and added noise temperature. In terms of these, we may evaluate its performance in various tasks ranging from classical signal detection to quantum state conversion between, e.g., superconducting circuitry and traveling optical signals. Having established the requirements for efficient performance, we turn to the question of optimization. We address this by developing a unifying equivalent-circuit formalism for electro-optomechanical transducers. This approach accommodates arbitrary linear circuits and integrates the novel optomechanical transduction functionality into the well-established framework of electrical engineering, thereby facilitating its implementation in potential applications such as nuclear magnetic resonance imaging and radio astronomy. We consider such optomechanical sensing of weak electrical signals and discuss how the equivalent circuit formalism can be used to optimize the electrical circuit design. We also discuss the parameter requirements for transducing microwave photons in the quantum regime.

Part II:
Effective photon-photon interactions can be engineered by combining long-range Rydberg interactions between atoms in a cold, optically dense cloud with light fields propagating under the condition of electromagnetically induced transparency (EIT). This can lead to strong and non-linear dissipative dynamics at the quantum level that prevent slow-light polaritons from coexisting within a blockade radius of one another. We introduce a new approach to analyzing this challenging many-body problem in the limit of large optical depth per blockade radius. The idea is to separate the single-polariton EIT physics from the Rydberg-Rydberg interactions in a serialized manner while using a hard-sphere model for the latter, thus capturing the dualistic particle-wave nature of light as it manifests itself in dissipative Rydberg-EIT media. Using this approach, we analyze the saturation behavior of the transmission through one-dimensional Rydberg-EIT media in the regime of non-perturbative single-polariton EIT-decay relevant to present-day experiments. Our model is found to be compatible with experimental data. Next, we analyze a scheme for generating regular trains of single photons from continuous-wave input and derive its scaling behavior in the limit of perturbative single-polariton EIT-decay