Michal Tomza, Daniel Reich, Robert Moszynski, Christiane P. Koch
Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
Theoretische Physik, Universitat Kassel, Heinrich-Plett-Str. 40, 34132 Kassel, Germany
A theoretical proposal for the efficient formation of ultracoldmolecules with short picosecond laser pulses in a pump-dump scheme[1,2] has not yet been realized due to technical limitations ofpicosecond lasers. In contrast, pulse shaping techniques of femtosecondlasers are well developed. But femtosecond laser pulses have a largespectral width that overlaps with the atomic resonance and excitesatoms rather than molecular levels, depleting the trapped sample. Employing multi-photon instead of one-photon transitionscan be a remedy. In non-resonant multi-photon processes, a broadbandlaser drives a narrow transition utilizing optical interferencebetween different excitation pathways .
Here, we apply optimal control theory to ultracold multi-photon photoassociation. To this end we derive and test an optimizationfunctional that suppresses atomic excitation and maximizes theformation of molecules. We employ optimal control theory to maximizethe efficiency of non-resonant three-photon photoassociation ofultracold rubidium atoms when the initial state is the thermally populated continuum of scattering states in a MOT. Using a linearvariant of Krotov's method , we find that, at ultralowtemperatures, a pulse optimized for one initial scattering energyworks also for all other collision energies within the thermalensemble and for the lowest partial waves. Our study is the firstapplication of optimal control theory properly treating the initialthermal ensemble of scattering states in photoassociation.
 C. P. Koch, E. Luc-Koenig, F. Masnou-Seeuws, Phys. Rev. A 73, 033408 (2006).
 C. P. Koch, M. Shapiro, Chem. Rev. 212, 4928-4948 (2012).
 W. Salzmann, T. Mullins, J. Eng, M. Albert, R. Wester, M.Weidemuller, et al., Phys. Rev. Lett. 100, 233003 (2008).
 D. Meshulach, Y. Silberberg, Nature 396, 239 (1998).
 D. M. Reich, M. Ndong, C. P. Koch, J. Chem. Phys. 136, 104103 (2012).
Author entry (protected)