The effect of long-range collisions between atoms on laser cooling

Andrew M. Smith II, Keith R. Burnett

A theory to describe collisions between pairs of atoms that are being cooled by a laser field is presented. The derivation uses the Heisenberg picture and results in a set of coupled optical Bloch equations and associated equations for the translational motion. By defining a correlation variable between the two atoms, we obtain a system of linear equations that may be solved numerically. If the interaction is ignored, the usual cooling curve is obtained: In the full simulation it is found that long-range collisions (0.1ƛ → 10ƛ) can significantly alter the atomic velocities. Depending on how the atoms approach each other, there are various effects: jumps in velocity at the center of the collision, interruptions of the cooling cycle, and signs of collective effects for long-range collisions. If the atom density is sufficiently large and the atoms are moving slowly, these collisional mechanisms may prevent any further cooling.

Paul S. Julienne, Andrew M. Smith II, Keith R. Burnett

Andrew M. Smith II, Keith R. Burnett

An analytical description of the collisions between atoms in a laser cooling field is developed. The results confirm predictions made in our recent numerical simulations for the same model. The effect of the collision can be separated analytically, to first order in a perturbation expansion in collision strength, into two parts. The first of these parts comes from the interruption of the laser cooling cycle in each atom, and the second from the direct force resulting from a photon exchange between the atoms.

Thad G Walker

Ghosh, Pradip N

Andrew M. Smith II, Keith R. Burnett

An extension to a previous model [ J. Opt. Soc. Am. B8, 1594 ( 1991)], which described the collision between two atoms in a cooling laser field, is made, which allows diffusive effects to be analyzed. A method similar to that used in Monte Carlo studies is developed, except that the diffusion is now determined exactly at all times. This approach relies directly on making a local classical path approximation for the atoms’ trajectories. For the simple case of a single two-level atom in the cooling field, the energy of the atom reaches equilibrium at the Doppler limit, as one would expect. In the full collisional situation we make the assumption that each atom undergoes a series of binary collisions. For sufficiently high atomic densities these collisions provide a limit on the lowest temperature that may be achieved by the cooling process.