Photoassociation with chirped laser pulses: calculation of the absolute number of molecules per pulse

The total number of molecules produced in a pulsed photoassociation of ultracold atoms is a crucial link between theory and experiment. A calculation based on first principles can determine the experimental feasibility of a pulsed photoassociation scheme. The calculation method considers an initial thermal ensemble of atoms. This ensemble is first decomposed into a representation of partial spherical waves. The photoassociation dynamics is calculated by solving the multichannel time-dependent Schrodinger equation on a mapped grid. The molecules are primarily assembled in a finite region of internuclear distances, the 'photoassociation window'. The ensemble average was calculated by adding the contributions from initial scattering states confined to a finite volume. These states are Boltzmann averaged where the partition function is summed numerically. Convergence is obtained for a sufficiently large volume. The results are compared to a thermal averaging procedure based on scaling laws which leads to a single representative initial partial wave which is sufficient to represent the density in the 'photoassociation window'. For completeness a third high-temperature thermal averaging procedure is described which is based on random phase thermal Gaussian initial states. The absolute number of molecules in the two first calculation methods agree to within experimental error for photoassociation with picosecond pulses for a thermal ensemble of rubidium or caesium atoms in ultracold conditions.