New effects in light scattering from cold atoms trapped by harmonic potentials

First, we study the scattering of light by a single ultracold, trapped atom initially in the ground state of the trapping harmonic potential. We find interesting features of the scattering in the regime where the atomic recoi l energy is much larger than the separation between oscillatory trap levels . Although we present the quantum mechanical expression for the scattering cross section, special attention is paid to the semiclassical analysis of t he process. We show that the major characteristics of the scattering might be deduced from two conservation laws: conservation of energy and momentum in absorption and emission of photon process separately. These conservation laws impose a strong correlation between scattered-light characteristics a nd the position of the trapped atom at the moment of photon emission. A det ailed analysis of the far-off resonance scattering of light from a single a tom trapped in an isotropic harmonic potential is also given. In this case, we are able to assume a more realistic, i.e., thermal, initial state of th e atomic center of mass. An exact closed-form expression for the differenti al scattering cross section is derived from a general S-matrix theory of sc attering. The possibility of measuring the density-density correlation func tions in light-scattering experiments is discussed.