  We study coherent photoassociation, phenomena analogous to coherent optical
transients in few-level systems, which may take place in photoassociation of an
atomic Bose-Einstein condensate but not in a nondegenerate gas. We develop a
second-quantized Hamiltonian to describe photoassociation, and apply the
Hamiltonian both in the momentum representation and in the position
representation (field theory). Solution of the two-mode problem including only
one mode each for the atomic and molecular condensates displays analogs of Rabi
oscillations and rapid adiabatic passage. A classical version of the field
theory for atoms and molecules is used to demonstrate that, in the presence of
photoassociating light, a joint-atom molecule is unstable against growth of
density fluctuations. Experimental complications, including spontaneous
emission and unwanted "rogue" photodissociation from a photoassociated molecule
are analyzed. A two-color Raman scheme is studied as a method to set up an
effective two-mode scheme with reduced spontaneous emission losses. We discuss
photoassociation rates and photoassociation Rabi frequencies for high-lying
vibrational states in alkalis both on the basis of molecular-structure
calculations, and by comparing with an experiment [Wynar et al., Science 287,
1016 (2000)].
