210 Laser cooling and trapping
τpulse= 600μs selectively transfers atoms in a range of width ∆v
1mms−^1. Thisisaboutthirtytimeslessthanvrand equivalent to a
‘temperature’ ofTr/900 for the motion along the axis of the laser beams.
This velocity selection doesnotproduce any more cold atoms than at
the start—it just separates the cold atoms from the others—so it has a
different nature to the laser cooling processes described in the previous
sections.^70(^70) A useful comparison can be made
with the method of reducing the
Doppler broadening shown in Fig. 8.2,
in which a narrow slit is used to colli-
mate an atomic beam and so reduce the
spread of transverse velocities.
9.8.2 Raman cooling
The previous section showed that Raman transitions give the precision of
radio-frequency spectroscopy combined with a sensitivity to the Doppler
shift twice that of single-photon (optical) transitions. Raman cooling
exploits the extremely high velocity resolution of coherent Raman tran-
sitions to cool atoms below the recoil limit. The complete sequence of
operations in Raman cooling is too lengthy to describe here, but the
important principle can be understood by considering how atoms with
a velocity distribution that is already below the recoil limit are cooled
further. Figure 9.21 shows such an initial distribution in level 1 (the
lower hyperfine level in the ground configuration of the atom; level 2 is
the upper hyperfine level). Raman cooling uses the following steps.(a) Velocity selection by a Raman pulse that transfers atoms with ve-
locities in the range fromv−∆v/2tov+∆v/2uptolevel2,where
they have velocities centred aboutv− 2 vr. (The process of absorp-
tion and stimulated emission in the opposite direction changes the(^71) Equivalently, the atom’s momentum atom’s velocity by 2vr. (^71) )
changes byk 1 −k 2
2 k.(Here
ω 12 ω 1
ω 2 .) (b) Atoms in level 2 are excited to leveliby another laser beam and can
decay back to level 1 with velocities centred aroundv−vr(includ-
ing the change in velocity produced by absorption). Spontaneous
emission goes in all directions so that the atoms return to level 1
(^72) Some atoms fall back into level 2 and with velocities anywhere in the rangevtov− 2 vr. 72
are excited again until eventually they
end up in level 1. Atoms that un-
dergo more than one excitation receive
additional impulses from the absorbed
and emitted photons, which reduces the
cooling efficiency but does not affect
the principle.
It might appear that this cycle of a velocity-selective Raman pulse
followed by repumping has made things worse since the final spread
of velocities is comparable to, if not greater than the initial spread.
Crucially, however, some atoms fall back into level 1 with velocities
very close to zero so the number of very slow atoms has increased, and
increases further for each repetition of the cycle with different initial
(^73) For velocity selection of atoms with velocity. (^73) Precise control of the Raman pulses ensures that atoms with
v<0 the direction of the beams is
reversed so that these atoms are dis-
tributed into the rangevtov+2vr(that
includesv=0).
velocities in the narrow range−δv<v<δvare never excited, so that
after many cycles a significant fraction of the population accumulates in
this narrow velocity class withδvvr. In this Raman cooling process
the atomic velocity undergoes a random walk until either it falls into the
desired velocity class aroundv= 0, and remains there, or diffuses away
to higher velocities. The recoil limit is circumvented because atoms
withv0 do not interact with the light and this sub-recoil cooling
mechanism does not involve a radiation force (in contrast to the Doppler
and sub-Doppler cooling mechanisms described in previous sections).