Role of off-resonant excitation in cold collisions in a strong laser field K.-A. Suominen Theoretical Physics Division, Department of Physics, University of Helsinki, PL 9, FIN-00014 Helsingin yliopisto, Finland K. Burnett* and P. S. Julienne Atomic Physics Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-0001 ~Received 22 November 1995! We have studied how the presence of a strongly coupled off-resonant molecular potential affects cold collisions in a laser field. To do this, we have performed a fully quantal time-dependent three-state calculation that includes both spontaneous emission and laser-driven dynamics of the collision complex. Our results show that although the presence of the off-resonant state has an effect on the collision process, two-state calculations will be valid unless the Rabi coupling greatly exceeds the detuning. We have investigated how this physics impinges on trap loss and optical shielding in a magneto-optical trap. Our results indicate that the experimen- tally observed saturation of optical shielding cannot be explained adequately by off-resonant effects. PACS number~s!: 32.80.Pj, 42.50.Vk, 42.50.Lc Laser cooling and trapping now produce atomic cloud densities for which the cold binary collisions between the atoms have a significant effect on the conditions ~density and temperature! that can be reached. The presence of the laser field can make these collisions highly inelastic, if the light is detuned below ~i.e., to the red! the atomic transition @1–4#. Cold collisions then lead to a loss of atoms from a magneto- optical trap ~MOT! either via a fine-structure change mecha- nism, or via radiative escape. On the other hand, cold colli- sions can be inelastic even in the absence of laser fields due to, e.g., transitions between ground-state hyperfine levels ~Rb collisions @5#! or Penning ionization ~He * @6#, Kr * @7#, Xe * @8# collisions! at short interatomic distances. These pro- cesses can, however, be suppressed using optical shielding, where the colliding atoms are reflected at large interatomic distances by using a blue-detuned laser field @9#. In theoretical studies the cold collisions are most often described by regarding the colliding atoms as a quasimole- cule. In the Born-Oppenheimer approximation one obtains potential surfaces, which depend parametrically on the inter- atomic distance R . The quasimolecule states are coupled by the laser field, and may be excited resonantly at a Condon point R C . Such resonant excitation is usually taken to domi- nate any off-resonant processes @3,4,9#. At the laser detun- ings typically used in laser cooling and trapping the dipole- dipole interaction is the dominant interaction near R C . The excited-state potential is then given by U e 6 ~ R ! 5E ‘ 6 C 3 R 3 , ~1! where E ‘ is the asymptotic energy of the excited quasimol- ecule state. In Fig. 1 we present the potential surface and laser field configurations used in our study. For simplicity we consider only the s -wave processes but our results can be generalized to higher partial waves ~for a discussion of the partial wave method in cold inelastic collisions see, e.g., Refs. @2,3,8#!. The R dependence of the potentials couples the laser- induced excitation of the quasimolecule to the relative mo- tion of the atoms. At the low temperatures we consider, the collision is so slow that spontaneous emission from the quasimolecule excited state during the collision cannot be ignored ~this is not strictly true for optical shielding at large detunings, as we shall show later!. The appropriate theoreti- cal approach to the problem is therefore wave packet dynam- ics with spontaneous emission treated using the Monte Carlo wave function ~MCWF! method @10,11#. In this approach the spontaneous emission is described in terms of random quan- tum jumps, which correspond to the detection of the emitted photons. The time evolution of the collision complex is ob- tained by solving the corresponding time-dependent Schro ¨- dinger equation for a three-component state vector ~the wave-packet amplitudes!. For each time step, we determine using a random number if a quantum jump has occurred. By *Permanent address: Clarendon Laboratory, Department of Phys- ics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom. FIG. 1. Dipole-dipole interaction potentials. In the trap loss case ~a! the laser has a red detuning and therefore U g and U e 2 are reso- nantly coupled at the Condon point. In the shielding case ~b! the detuning is blue and now U e 1 has the Condon point with U g . PHYSICAL REVIEW A MARCH 1996 VOLUME 53, NUMBER 3 53 1050-2947/96/53~3!/1220~4!/$10.00 R1220 © 1996 The American Physical Society