Quantum communication networks enable secure transmission of information between remote sites. However, at present, photon losses in the optical fiber limit communication distances to less than 150 kilometers. The quantum repeater idea allows extension of these distances. In practice, it involves the ability to store quantum information for a long time in atomic systems and coherently transfer quantum states between matter and light. Previously known schemes involved atomic Raman transitions in the UV or near-infrared and suffered from severe loss in optical fiber that precluded long-distance quantum communication.

In this thesis, we investigate the quantum mechanical interaction of light with matter in the form of a gas of ultracold atoms: the atomic ensemble. We present a theoretical analysis of two problems, which involve the interaction of quantized electromagnetic fields (called signal and idler) with the atomic ensemble (i) cascade two-photon emission in an atomic ladder configuration, and (ii) photon frequency conversion in an atomic diamond configuration. The motivation of these studies comes from potential applications in long-distance quantum communication where it is desirable to generate quantum correlations between telecommunication wavelength light fields and ground level atomic coherences. In the two systems of interest, the light field produced in the upper arm of an atomic Rb level scheme is chosen to lie in the telecom window. The other field, resonant on a ground level transition, is in the near-infrared region of the spectrum. Telecom light is useful as it minimizes losses in the optical fiber transmission links of any two long-distance quantum communication device. We develop a theory of correlated signal-idler pair correlation. The analysis is complicated by the possible generation of multiple excitations in the atomic ensemble. An analytical treatment is given in the limit of a single excitation assuming adiabatic laser excitations. The analysis predicts superradiant timescales in the idler emission in agreement with experimental observation. To relax the restriction of a single excitation, we develop a different theory of cascade emission, which is solved by numerical simulation of classical stochastic differential equation using the theory of open quantum systems. The simulations are in good qualitative agreement with the analytical theory of superradiant timescales. We further analyze the feasibility of this two-photn source to realize the DLCZ protocol of the quantum repeater communication system. We provide a quantum theory of near-infrared to telecom wavelength conversion in the diamond configuration. The system provides a crucial part of a quantum-repeater memory element, which enables a "stored" near-infrared photon to be converted to a telecom wavelength for transmission without the destruction of light-atom quantum correlation. We calculate the theoretical conversion efficiency, analyzing the role of optical depth of the ensemble, pulse length, and quantum fluctuations on the process.

The deterministic generation and manipulation of quantum states has attracted much interest ever since the rise of quantum mechanics. Large-scale, distributed quantum states are the basis for novel applications such as quantum communication, quantum remote sensing, distributed quantum computing or quantum voting protocols. The necessary infrastructure will be provided by distributed quantum networks, allowing for quantum bit processing and storage at single nodes. Quantum states of light then allow for inter-node transmission of quantum information. Transmission losses in optical fibers may be overcome by quantum repeaters, the quantum equivalent of classical signal amplifiers. The fragility of quantum superposition states makes building such networks very challenging. Hybrid solutions combine the strengths of different physical systems: Efficient quantum memories can be realized using alkali atoms such as rubidium. Leading in the deterministic generation of single photons and polarization entangled photon pairs are semiconductor InAs/GaAs quantum dots grown by the Stranski-Krastanov method. Despite remarkable progress in the last twenty years, complex quantum optical protocols could not be realized due to low degree of entanglement, low brightness and broad wavelength distribution. In this work, an emerging family of epitaxially grown GaAs/AlGaAs quantum dots obtained by droplet etching and nanohole infilling is studied. Under pulsed resonant two-photon excitation, they emit single pairs of entangled photons with high purity and unprecedented degree of entanglement. Entanglement fidelities up to f = 0.94 are observed, which are only limited by the optical setup or a residual exciton fine structure. The samples exhibit a very narrow wavelength distribution at rubidium memory transitions. Strain tuning is applied via piezoelectric actuators to allow for reversible fine-tuning of the emission frequency. In a next step, active feedback is employed to stabilize the frequency of single photons emitted by two separate quantum dots to an atomic rubidium standard. The transmission of a rubidium-based Faraday filter serves as the error signal for frequency stabilization. A residual frequency deviation of < 30MHz is achieved, which is less than 1.5% of the quantum dot linewidth. Long-term stability is demonstrated by Hong-Ou-Mandel interference between photons from the two quantum dots. Their internal dephasing limits the expected visibility to V = 40%. For frequency-stabilized dots, V = (41 ± 5)% is observed as opposed to V = (31 ± 7)% for free-running emission. This technique reaches the maximally expected visibility for the given system and therefore facilitates quantum networks with indistinguishable photons from distributed sources. Based on the presented techniques and improved emission quality, pivotal quantum communication protocols can now be implemented with quantum dots, such as transferring entanglement between photon pairs. Embedding quantum dots in a dielectric antenna ensures a bright emission. For the first time, entanglement swapping between two pairs of photons emitted by a single quantum dot is realized. A joint Bell measurement heralds the successful generation of the Bell state Ψ+ with a fidelity of up to (0.81 ± 0.04). The state's nonlocal nature is confirmed by violating the CHSH-Bell inequality with S = (2.28 ± 0.13). The photon source is tuned into resonance with rubidium transitions, facilitating implementation of hybrid quantum repeaters. This work thus represents a major step forward for the application of semiconductor based entangled photon sources in real-world scenarios.