Numerical study of non-linear spectroscopy and four-wave-mixing in two and multi-level atoms

Abstract

In this research, we undertake a numerical study of the interaction between laser beams and two as well as multi-level atoms. The main aim of this research is to obtain a deeper understanding of laser-atom interactions and non-linear processes such as optical four-wave mixing. This work will supplement experiments to be conducted by other members of the group, who are involved in generating entangled photons via four-wave mixing in cold rubidium atoms. We begin by performing a basic study of the interaction between laser beams and two-level atoms as an aid to gain knowledge of numerical techniques, as well as an understanding of the physics behind light-atom interactions. We make use of a semi-classical approach to describe the system where the atoms are treated quantum mechanically and the laser beams are treated classically. We study the interaction between atoms and laser beams using the density matrix operator and Maxwell's equations respectively. By solving the optical Bloch equations for two-level atoms we examine the atomic populations and coherences and present plots of the density matrix elements as a function of time. The e ects of various parameters such as laser intensity, detuning and laser modulation have been tested. The behaviour of the laser beam as it propagates through the atomic sample is also studied. This is determined by Maxwell's equation where the atomic polarization is estimated from the coherence terms of the density matrix elements.