In this paper, we systematically introduce the theoretical study of interaction of an ultracold atomic ensamble with a light wave in the frame of a vector quantum field theory. The many-body quantum correlation in the ultracold regime of atom optics is studied in terms of the vector quantum field theory. A general formalism of nonlinear atom optics for a coherent atomic beam is developed. Generation of squeezed light via spontaneous emission from a three-level cascade system. A theoretical investigation is made into the possibility of generating squeezed states of light in spontaneous emission from a three-level atom.
Spontaneous emission is known as a source of the noise which destroys coherence effects.
We find that rather than destroy squeezing, spontaneous emission from a three-level cascade system can actually create squeezing in an initially unsqueezed source field provided the atom is initially prepared in a suitable superposition of its states. The behaviour of a three level atom in a cascade configuration with the lower transition coherently driven and also coupled to a narrow bandwidth squeezed vacuum field is studied. A master equation treatment based on dressed atom states is used and expressions for probe absorption spectra obtained via linear response theory and the quantum regression theorem. The expressions obtained also apply to the broad bandwidth squeezed vacuum case. Numerical studies of the modifications caused by the finite squeezed vacuum bandwidth to the Mollow and Autler-Townes probe absorption spectra are made for the case where the squeezed vacuum field centre frequency and the driving laser frequency coincide and where upper transition relaxation terms are ignored.