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.