It is well known that the optical properties of multi-level atomic and molecular system can be controlled and manipulated efficiently using quantum coherence and interference, which has led to many new effects in quantum optics for e.g. lasing action without population inversion, ultraslow light, high resolution nonlinear spectroscopy etc. Recent experimental and theoretical studies have also provided support for the hypothesis that biological systems uses quantum coherence. Nearly perfect excitation energy transfer in photosynthesis is an excellent example of this. In this dissertation we studied quantum coherence and interference effects in the transient and the continuous-wave regimes. This study led to (i) the first experimental demonstration of carrier-envelope phase effects on bound-bound atomic excitation in multi-cycle regime (~15 cycles), (ii) a unique possibility for standoff detection of trace gases using their rotational and vibrational spectroscopic signals and from herein called Coherent Raman Umklappscattering, (iii) several possibilities for frequency up-conversion and generation of short-wavelength radiation using quantum coherence (iv) the measurement of spontaneous emission noise intensity in Yoked-superfluorescence scheme. Applications of the obtained results are development of XUV (X-Ray) lasers, con- trolled superfluorescent (superradiant) emission, carrier-envelope phase effects, coherent Raman scattering in the backward direction, enhancement of efficiency for generating radiation in XUV and X-Ray regime using quantum coherence with and without population inversion and to extend XUV and X-Ray lasing to ~4.023 nm in Helium-like carbon.

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.