Laser cooling of atoms with broadband real Gaussian laser fields

We describe a theoretical approach to laser cooling with broadband real Gaussian laser fields that is based on adiabatic elimination methods and the Fokker-Planck equation for the Wigner function. This approach is used to model the recent broadband cooling experiment of Zhu, Oates, and Hall [Phys. Rev. Lett. 67, 46 (1991)] and gives correct order-of-magnitude results. The theory is then applied to J=0→J=1 and J=1→J=2 transitions in a ${\mathrm{\sigma }}_{+\mathrm{-}}$ ${\mathrm{\sigma }}_{\mathrm{-}}$ optical molasses configuration with correlated broadband laser fields. An instability in the cooling scheme at zero velocity is found for red laser detunings, and sub-Doppler-width velocity distributions are predicted for J=1→J=2 transitions with both red and blue laser detunings.