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Optical response of an active medium can substantially be modified when coherent superpositions of states are excited, that is, when systems display quantum coherence and interference. This has led to fascinating applications in atomic and molecular systems. Examples include coherent population trapping, lasing without inversion, electromagnetically induced transparency, cooperative spontaneous emission, and quantum entanglement. We study quantum coherence effects in several quantum optical systems and find interesting applications. We show that quantum coherence can lead to transient Raman lasing and lasing without inversion in short wavelength spectral regions--extreme ultraviolet and x-ray--without the requirement of incoherent pumping. For example, we demonstrate transient Raman lasing at 58.4 nm in Helium atom and transient lasing without inversion at 6.1 nm in Helium-like Boron (triply-ionized Boron). We also investigate dynamical properties of a collective superradiant state prepared by absorption of a single photon when the size of the sample is larger than the radiation wavelength. We show that for large number of atoms such a state, to a good approximation, decays exponentially with a rate proportional to the number of atoms. We also find that the collective frequency shift resulting from repeated emission and reabsorption of short-lived virtual photons is proportional to the number of species in the sample. Furthermore, we examine how a position-dependent excitation phase affects the evolution of entanglement between two dipole-coupled qubits. It turns out that the coherence induced by position-dependent excitation phase slows down the otherwise fast decay of the two-qubit entanglement. We also show that it is possible to entangle two spatially separated and uncoupled qubits via interaction with correlated photons in a cavity quantum electrodynamics setup. Finally, we analyze how quantum coherence can be used to generate continuous-variable entanglement in quantum-beat lasers in steady state and propose possible implementation in quantum lithography.

This thesis presents a joint experimental and theoretical study of a bimolecular collision between OH(A) and H₂ diatoms. The study focuses on the relationship between the initial, <b><i>j</i></b>, and final rotational angular momentum, <b><i>j'</i></b>. This relationship is explored from both a scalar point of view by measuring rotational energy transfer (RET), and a vectorial viewpoint by considering the collisional depolarisation. The experimental technique used in this investigation, Zeeman quantum beat spectroscopy, is first demonstrated by applying it to the determination of the lab-frame orientation of OH(X) photofragments following the photolysis of H₂O₂. The H₂O₂ is photolysed by circularly-polarised light at 248 nm, and Zeeman quantum beat spectroscopy probes the angular momentum orientation as a function of the photofragment spin-rotation level. The results of this experiment are compared with orientation parameters predicted by a simulation that couples the rotation of the parent molecule to the torsional motion during bond cleavage. The calculations from the model agree qualitatively with those from the experiment. The Zeeman quantum beat spectroscopy technique is then used to monitor the evolution of angular momentum polarisation of OH(A) radicals during collisions with H₂. The technique allows for the determination of depolarisation cross sections for oriented and aligned distributions, as a result of collisions with H₂. Alongside this, cross sections for collisional quenching to non-reactive OH(X)+H₂ and reactive H₂O+H products are determined. By resolving the fuorescence with a monochromator the contributions to depolarisation from elastic collisions (the elastic depolarisation cross sections) are measured alongside cross sections for RET. Cross sections for total depolarisation and rotational energy transfer demonstrate only weak dependence on the rotational quantum number of the OH(A) radical, <i>N</i>_OH. Competing quenching processes that fall with <i>N</i>_OH are likely a considerable cause of this weak dependence. Furthermore, the polarisation of the angular momentum of OH(A) is randomised following RET. The elastic depolarisation cross sections make only a small contribution to the depolarisation and fall with increasing <i>N</i>_OH. Collectively these trends have not been seen previously in similar studies on OH(A) collisions with atomic colliders. For the theoretical calculations, a four-atom quasi-classical trajectory (QCT) method has been developed, utilising Lagrangian multipliers to fix the OH(A) and H₂ bonds. The calculations demonstrate that collisions involving the formation of complexes that survive for several rotational periods are prevalent in this collision system, and that these lead to large amounts of depolarisation. The calculations also demonstrate that RET in the H₂ diatom supports higher levels of RET in OH(A) than seen in previous triatomic systems. Additionally, when one diatom is depolarised the accompanying diatom is typically also depolarised. These trends, at least in part, are owed to the highly attractive and anisotropic potential energy surface (PES) describing the interaction. The QCT calculations overestimate the experimentally-measured cross sections by more than a factor of 2. The calculations are adiabatic and do not account for the non-adiabatic activity associated with this collision system, and this is likely one cause of the discrepancies. In an attempt to further account for this overestimation, alternative angular momentum binning approaches for the QCT calculations are developed, but with limited success. Further exploration of the topology of the PES used in the calculations suggests that inadequacies in this surface are a major contributor to the discrepancies.