  Photoassociation with short laser pulses has been proposed as a technique to
create ultracold ground state molecules. A broad-band excitation seems the
natural choice to drive the series of excitation and deexcitation steps
required to form a molecule in its vibronic ground state from two scattering
atoms. First attempts at femtosecond photoassociation were, however, hampered
by the requirement to eliminate the atomic excitation leading to trap
depletion. On the other hand, molecular levels very close to the atomic
transition are to be excited. The broad bandwidth of a femtosecond laser then
appears to be rather an obstacle. To overcome the ostensible conflict of
driving a narrow transition by a broad-band laser, we suggest a two-photon
photoassociation scheme. In the weak-field regime, a spectral phase pattern can
be employed to eliminate the atomic line. When the excitation is carried out by
more than one photon, different pathways in the field can be interfered
constructively or destructively. In the strong-field regime, a temporal phase
can be applied to control dynamic Stark shifts. The atomic transition is
suppressed by choosing a phase which keeps the levels out of resonance. We
derive analytical solutions for atomic two-photon dark states in both the
weak-field and strong-field regime. Two-photon excitation may thus pave the way
toward coherent control of photoassociation. Ultimately, the success of such a
scheme will depend on the details of the excited electronic states and
transition dipole moments. We explore the possibility of two-photon femtosecond
photoassociation for alkali and alkaline-earth metal dimers and present a
detailed study for the example of calcium.
