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We study theoretically the behavior of laser-cooled calcium monofluoride(CaF) molecules in an optical molasses and magneto-optical trap (MOT), andcompare our results to recent experiments. We use multi-level optical Blochequations to estimate the force and the diffusion constant, followed by aFokker-Planck-Kramers equation to calculate the time-evolution of the velocitydistribution. The calculations are done in three-dimensions, and we include allthe relevant energy levels of the molecule and all the relevant frequencycomponents of the light. Similar to simpler model systems, thevelocity-dependent force curve exhibits Doppler and polarization-gradientforces of opposite signs. We show that the temperature of the MOT is governedmainly by the balance of these two forces. Our calculated MOT temperatures andphoton scattering rates are in broad agreement with those measuredexperimentally over a wide range of parameters. In a blue-detuned molasses, thetemperature is determined by the balance of polarization gradient cooling, andheating due to momentum diffusion, with no significant contribution fromDoppler heating. In the molasses, we calculate a damping rate similar to themeasured one, and steady-state temperatures that have the same dependence onlaser intensity and applied magnetic field as measured experimentally, but areconsistently a few times smaller than measured. We attribute the highertemperatures in the experiments to fluctuations of the dipole force which arenot captured by our model. We show that the photon scattering rate is stronglyinfluenced by the presence of dark states in the system, but that thescattering rate does not go to zero even for stationary molecules because ofthe transient nature of the dark states.

Laser cooling and magneto-optical trapping of molecules analyzed using optical Bloch equations and the Fokker-Planck-Kramers equation