0198506961.pdf

202 Laser cooling and trapping

Fig. 9.15The evanescent wave, cre-
ated when a laser beam is totally in-
ternally reflected, forms a mirror for
atoms. For a light with a blue detun-
ing (ω>ω 0 ) the dipole force repels
atoms from the region of high inten-
sity close to the vacuum–glass interface.
(The same principle applies if the sur-
face is curved (e.g. concave) and such
an arrangement can be used to focus
the matter waves.)

Slow atom

Glass

Vacuum

Evanescent

wave

Laser beam

The dipole potential associated with this force depends on the in-

tensity of the light (cf. eqn 9.46 for a large frequency detuning). Two

counter-propagating beams of linearly-polarized light produce an electric

field given by

E=E 0 {cos (ωt−kz)+cos(ωt+kz)}̂ex

=2E 0 cos (kz)cos(ωt)̂ex. (9.51)

(^51) This form is only true for large de- This standing wave gives a dipole potential of the form 51
tunings,δ Γ,Ω. If this inequality is
satisfied then there is also little sponta-
neous scattering from the atoms.
Udipole=U 0 cos^2 (kz). (9.52)
HereU 0 is the light shift at the anti-nodes—these maxima have an inten-
sity four times that of the individual beams. For a frequency detuning
to the red, a standing wave of light traps atoms at the anti-nodes and
gives confinement in the radial direction as in a single beam. This reg-
ular array of microscopic dipole traps is called anoptical lattice.With
more laser beams the interference between them can create a regular
array of potential wells in three dimensions, e.g. the same configuration
of six beams in the optical molasses technique shown in Fig. 9.5 (along
±̂ex,±̂eyand±̂ez) can create a regular cubic lattice of potential wells
for suitable polarizations and a large frequency detuning.^52 The poten-
(^52) Interference will generally lead to
a periodic arrangement of positions
where atoms become localised (at in-
tensity maxima for a frequency detun-
ing to the red) in a three-dimensional
standing wave of light, but the creation
of a particular configuration of the op-
tical lattice requires control of the po-
larization (and relative phase). tial wells in this optical lattice have a spacing ofλ/2, and so one atom
per lattice site corresponds to a density of 8/λ^3  7 × 1013 cm−^3 for
λ=1. 06 μm. Therefore the sites will be sparsely populated when the
atoms are loaded into the lattice after cooling by the optical molasses
technique. (A typical number density in the optical molasses technique
is a few times 10^10 cm−^3 ≡ 0 .01 atomsμm−^3 .)
Experiments that load more than one atom in each potential well have
been carried out by adiabatically turning on the light that creates an
optical lattice in a region containing a sample of atoms that are in a
Bose–Einstein condensate (see Chapter 10).^53 Moreover, these atoms go
(^53) The phase-space density at which
BEC occurs is approximately equal to
that at which there is one atom per well
in the ground state of an optical lattice.
into the lowest vibrational level in each of the potential wells. The use of
one-dimensional standing waves as diffraction gratings for matter waves
is discussed in Chapter 11.^54
(^54) As atoms pass through a standing
wave of light they accumulate a phase
shift of orderφ U 0 t/
for an inter-
action timet. Light with either sign of
frequency detuning can be used to give
φ∼±π, and so create a phase grating
with significant amplitude in the dif-
fraction orders.