  It is shown that the momentum diffusion of free-space laser cooling has a
natural correspondence in optical cavities when the internal state of the atom
is treated as a harmonic oscillator. We derive a general expression for the
momentum diffusion which is valid for most configurations of interest: The atom
or the cavity or both can be probed by lasers, with or without the presence of
traps inducing local atomic frequency shifts. It is shown that, albeit the
(possibly strong) coupling between atom and cavity, it is sufficient for
deriving the momentum diffusion to consider that the atom couples to a mean
cavity field, which gives a first contribution, and that the cavity mode
couples to a mean atomic dipole, giving a second contribution. Both
contributions have an intuitive form and present a clear symmetry. The total
diffusion is the sum of these two contributions plus the diffusion originating
from the fluctuations of the forces due to the coupling to the vacuum modes
other than the cavity mode (the so called spontaneous emission term). Examples
are given that help to evaluate the heating rates induced by an optical cavity
for experiments operating at low atomic saturation. We also point out
intriguing situations where the atom is heated although it cannot scatter
light.
