0198506961.pdf

200 Laser cooling and trapping

there are two important criteria in the design of dipole-force traps: (a)

the trap must be deep enough to confine the atoms at a certain temper-

ature (that depends on the method of cooling); and (b) the scattering

rate must be low to reduce heating.

Example 9.2 Dipole trapping of sodium atoms

The wavelength of the laser light used for a dipole-force trap depends

(^43) Whereas for scattering-force tech- mainly on practical considerations. (^43) It is convenient to use a high-
niques the frequency of the laser must
be tunable, so that it can be adjusted
to within several line widths from an
atomic transition frequency.
power solid-state laser such as a Neodymium:YAG laser that produces
continuous-wave radiation at a fixed infra-red wavelength ofλ=1. 06 μm.
The frequency detuning of this laser radiation from the sodium resonance
atλ 0 = 589 nm is
δ
Γ

=

2 π

Γ

{

c

λ 0

−

c

λ

}

=2. 3 × 107 , (9.48)

(^44) This frequency detuningδ∼ 21 ω 0 ,so in units of Γ, where 1/Γ=τ=16ns. (^44) Solid-state lasers can produce
that the rotating-wave approximation
is not very good.
powers of many tens of watts, but in this example we use a conservative
value ofP= 1 W. When focused to a waist ofw 0 =10μmthislaser
beam has an intensity ofI=2P/(πw^20 )=6. 4 × 109 Wm−^2 ≡ 1 × 108 Isat.
Equation 9.46 gives
Udipole=

Γ

2

× 1 .1 = 260μK. (9.49)

Thus atoms cooled below the Doppler cooling limit
Γ/2 can be trapped.

For this laser intensity and frequency detuning, eqn 9.47 gives

Rscatt=2. 4 × 10 −^8 Γ=2s−^1. (9.50)

A sodium atom only scatters a few photons per second which gives a low

(^45) If atoms gain twice the recoil energy heating rate. (^45) The scattering force is negligible for these conditions, 46
per scattering event, as in eqn 9.24, it
takes many seconds before the atoms
boil out of the trap. The fluctuations
in the dipole force itself can cause heat-
ing andFdipole+δFdipoleshould be in-
cluded in eqn 9.20. The fluctuations
δFdipolegive comparatively small heat-
ing in a dipole-force trap with a large
frequency detuning; however, there are
circumstances where δFdipole is the
dominant cause of heating, e.g. for the
Sisyphus effect described in Section 9.7.
(^46) Writing eqn 9.50 as
Rscatt=5× 10 −^8 (Γ/2),
where Γ/2isthemaximumofRscatt,
shows thatFscattis 5× 10 −^8 times its
maximum value.
i.e. the force pushing in the direction of the light is weaker than the
dipole force pulling the atom towards the high-intensity focus. The
condition that the laser light has a frequency detuning far from the
atomic resonance is not restrictive, and calculations along the same lines
as that given here for sodium show that a laser with the above properties
can be used for the dipole-force trapping of any alkali metal atom.
A force derived from a potential is conservative, i.e. the total energy
remains constant during motion. Thus an atom that enters a dipole trap
gains kinetic energy as it moves towards the bottom of the potential well
and then it rides up the other side of the trap and escapes, because no
energy is lost. To load a dipole trap there must be either some dissipa-
tion of energy by spontaneous emission (as in the MOT), or the atoms
must be placed gently in the bottom of the trap. In the first exper-
imental demonstration of a dipole trap for atoms the laser beam was
focused into a cloud of atoms that were cooled by the optical molasses
technique, see Fig. 9.14 (Chuet al. 1986). The trapped atoms were
observed as a bright spot in the region of more diffuse fluorescence from