  Quantum degenerate molecules represent a new paradigm for fundamental studies
and practical applications. Association of already quantum degenerate atoms
into molecules provides a crucial shortcut around the difficulty of cooling
molecules to ultracold temperatures. Whereas association can be induced with
either laser or magnetic fields, photoassociation requires impractical laser
intensity to overcome poor overlap between the atom pair and molecular
wavefunctions, and experiments are currently restricted to magnetoassociation.
Here we model realistic production of a quantum degenerate gas of stable
molecules via two-photon photoassociation of Bose-condensed atoms. An adiabatic
change of the laser frequency converts the initial atomic condensate almost
entirely into stable molecular condensate, even for low-intensity lasers.
Results for dipolar LiNa provide an upper bound on the necessary
photoassociation laser intensity for alkali-metal atoms ~30 W/cm^2, indicating
a feasible path to quantum degenerate molecules beyond magnetoassociation.
