  This thesis is devoted to the study of quantum mechanical effects that arise
in systems of reduced dimensionality. Specifically, we investigate coherence
and correlation effects in quantum transport models. In the first part, we
present a theory of Markovian and non- Markovian current correlations in
nanoscopic conductors. The theory is applied to obtain the spectrum of quantum
noise and high-order current correlations at finite frequencies in quantum-dot
systems. One of the main conclusions is that only the non-Markovian approach
contains the physics of vacuum fluctuations. In the second part, we study the
coupling of superconducting qubits to optical atomic systems and to cavity
resonators. We propose a hybrid quantum system consisting of a flux qubit
coupled to NV centers in diamond. We also demonstrate the existence of the
so-called Bloch-Siegert shift in the ultra-strong coupling regime between a
flux qubit and a LC resonator. Throughout the thesis, we make special emphasis
on the study of decoherence effects produced by the distinct dissipative baths
to which the various types of qubits presented in this thesis are inevitably
coupled.
