0198506961.pdf

204 Laser cooling and trapping

cooling limit in eqn 9.28. Thiscannotbe understood in terms of a simple

picture in which the scattering forces from each of the six laser beams

add independently. Sodium, and other alkalis, have Zeeman structure

in their ground states and this additional complexity, as compared to a

simple two-level atom, allows new processes to occur.

A particularly important mechanism by which atoms dissipate energy

as they move through a standing wave is theSisyphus effectthat was ex-

plained by Jean Dalibard and Claude Cohen-Tannoudji (1989), and this

section follows the description given in that seminal paper. Steven Chu

and co-workers also developed a model to explain sub-Doppler cooling

based on the transfer of population between the different sub-levels of

the ground configuration (optical pumping) as atoms move through the

light field. This transfer of populations takes place on a time-scaleτpump

that can be much longer than the spontaneous lifetime (τpump 1 /Γ).

This longer time-scale gives better energy resolution than in a two-level

atom and therefore allows cooling below the Doppler cooling limit, i.e.

kBT
/τpump<
Γ/2. A specific example of this general argument is

shown in Fig. 9.17, and the following section gives more details.

9.7.2 Detailed description of Sisyphus cooling

Consider an atom that has a lower level with angular momentumJ=1/ 2

and an upper level withJ′=3/2 that moves through a standing wave

formed by two counter-propagating laser beams with orthogonal linear

polarizations (e.g. alonĝexand̂ey). The resultant polarization depends

on the relative phase of the two laser beams and varies with position,

as shown in Fig. 9.18(b). This polarization gradient causes the periodic

modulation of the light shift of the states in the lower level. The strength

of the interaction with the light depends onMJ andMJ′in the lower

and upper levels, respectively. To understand this in detail, consider

Fig. 9.17The laser cooling mechanism
in a standing wave with a spatially-
varying polarization. The energy levels
of the atom are perturbed by the light
in a periodic way, so that the atoms
travel up and down hills and valleys
(maxima and minima) in the potential
energy. Kinetic energy is lost when the
atom absorbs laser light at the top of
a hill and emits a spontaneous photon
of higher frequency, so that it ends up
in a valley. This has been called the
Sisyphus effect and can be made more
probable than the reverse process, so
that there is strong laser cooling. Thus
atoms in a standing wave are cooled be-
low the Doppler cooling limit (the low-
est temperature achievable with scat-
tering force alone).

Ground state

Excited state