a Study of the Quantum Nature of Light: Macroscopic Quantum Jumps from a Two-Atom System, Photon Statistics, and Light Propagation

In my dissertation, first, I show that when a pair of two-level atoms are confined in a region whose linear dimension is much smaller than the resonant wavelength, the intensity fluorescence exhibits dark and bright periods. The time scale for these "macroscopic quantum jumps" is the order of the lifetime of the metastable state. The creation of this metastable state is a direct consequence of the cooperative interaction between the atoms. My analysis is based on the study of quasi-steady-state populations and frequency resolved delay functions, an extension of a concept introduced by S. Reynaud, J. Dalibard, and C. Cohen-Tannoudji (IEEE J. Quant. Elec. 24, 1395 (1988)). I also show that these concepts simplify both calculations and interpretations in many problems involving macroscopic quantum jumps. Second, I study the quantum statistical properties of the fluorescence from one two-level and two two-level atoms. The generation of sub-Poissonian light, in which the intensity fluctuations are smaller than the classical limit, is investigated. I show that the two systems considered are capable of generating sub-Poissonian light under certain conditions. My analysis is based on the frequency resolved delay functions and branching functions developed in Chapter I. My method is found to be simpler than the conventional approach which is based on second order correlation functions of the field. Third, I study pulse propagation through a nonlinear medium. The field representing the pulse is quantized and the medium is made up of randomly distributed identical two-level atoms. I show that operator versions of the Maxwell-Bloch equations with added Langevin fluctuating terms and a c-number source term correctly describe the propagation of the pulse. I solve these equations in the weak field regime and show that many results predicted by a semiclassical theory of this problem are reproduced, and that no quantum property of the field plays an important role in this regime. I also solve the same equations in the strong field regime and show that quantum noise, which is the direct manifestation of the quantized nature of the field, is created and subsequently amplified as the pulse propagates through the medium.