238 Magnetic trapping, evaporative cooling and Bose–Einstein condensation
the strength of the interactions, whereasTCdoes not. In this example
the condensate has a density about a factor of 5 greater than the thermal(^42) The repulsive interactions prevent cloud at the phase transition, (^42) but the gas remains dilute because the
the much greater increase in the density
that would occur if atoms congregated
in a region of volumea^3 ho.
average distance between atoms in the condensate is larger than the
scattering length, that isna^3 1 (for the data in the tablen 0 a^3 =
4 × 10 −^6 ). Equation 10.40, and the similar equation forRz,givethe
ratio of sizes asRz/Rx=ωx/ωz=16(andRy=Rx), so in this trap
the condensate has the shape of a long, thin cigar.
Fig. 10.13Cross-sections of the images
similar to those shown in Fig. 10.12, but
for different temperatures and a time
of 12 ms after release from the mag-
netic trap. (a) Just below the critical
temperature (0. 99 TC) a small central
peak appears on the Gaussian distribu-
tion of thermal atoms. (b) At 0. 82 TC
most of the atoms are in the condensate
with some thermal atoms in the wings.
(c) At 0. 63 TConly a small thermal
cloud remains. This narrowing of the
distribution and change from a Gaus-
sian to an inverted-parabolic shape oc-
curs over a small range of temperatures
which is a behaviour characteristic of a
phase transition. From Hechenblaikner
(2002), for a trap withωx =ωy=
2 π×126 Hz andωz =2π×356 Hz.
The fraction of atoms in the conden-
sate (N 0 /N) differs from that predicted
by eqn F.16 because of interactions (see
Marag`oet al. 2001).
0 100 200 300 400 500
0.0
0.4
0.8
1.2
0.0
0.4
0.8
1.2
0.0
0.4
0.8
1.2
Optical depth
Distance ( m)μ
(a)
(b)
(c)