Martin Teichmann Atomes de lithium-6 ultra froids dans la ... - TEL

5.1. MOMENTUM DISTRIBUTION
get na 3 = 3π/16x 2 0 , or ∆2 = 4¯h 4 k 3 F /3πm2 a. Then from (5.4) we see that
µ = −¯h 2 /2ma 2 . This is exactly the molecular binding energy per atom
that has been found in equation (2.25). Developing the summands in the
number equation (2.35) for small values of ∆/µ, in combination with the
result from this paragraph, leads to
nk = 4 3 1
(kFa)
3π (k2a2 + 1) 2
(5.6)
This result is interesting as it is the Fourier transform of a molecular
bound state. This means that the center of mass motion of the molecules
is condensed into p = 0 and only the relative motion of the atoms in
the molecule is relevant. This shows that in the BEC limit the BCS
wavefunction indeed describes a Bose-Einstein-Condensate of molecules.
5.1.4 Experiments
We measure the momentum distribution at three different magnetic
fields: at the unitarity limit at 83 mT, in the molecular regime and on
the BCS side of the Feshbach resonance.
We perform evaporative cooling as described in section 3.6. At the
end of this cooling stage we lower both trapping lasers to 10% of their
initial power, leading to transverse trapping frequencies of 2 kHz in both
the horizontal and vertical beam. The desired field is then ramped in
500 ms to the desired magnetic field.
At this point we would like to verify that we are indeed sufficiently
cold to be condensed into the superfluid state. The easiest way to achieve
that is to ramp the field to the BEC side of the resonance and let the
gas expand in the presence of the field. If the expanded gas is elliptic,
we know that the gas is Bose-Einstein condensed (we will go into more
details on this in section 5.3). But this will only happen if the trap is
non-isotropic in the observed plane, which is not the case. Therefore, we
recompress the horizontal beam in 200 ms to a trap frequency of 5,5 kHz.
Technically, it would not be necessary to recompress the horizontal
beam for the momentum distribution experiments, but as it does not
disturb the momentum distribution we prefer to keep the verified state
as is.
At the end, we switch off the trap, which takes about 5 µs. The gas
expands for 0,5 ms, after which we take an absorption image. In order
to reconstruct the three-dimensional distribution, we perform an inverse
Abel transform as described in section 4.2.
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