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

Chapter 4
Data analysis
A correct data analysis is crucial to every experiment. In experiments on
cold atoms, the raw data is normally the density distribution of the atoms
acquired using absorption imaging techniques. Most often, the total
number of the atoms and the extent of the cloud in the two directions is
sufficient to interpret the data and can be achieved easily by performing
an appropriate fit on the atomic distribution. Here we want to focus
on a more advanced method of data analysis: firstly, the shape of the
cloud contains important information about the temperature of the cloud,
which can be extracted using appropriate fitting functions. Secondly,
the cloud we see on the computer screen is only a two dimensional
projection. Knowing that the original cloud has rotational symmetry, we
can reconstruct the three dimensional distribution of the atoms.
4.1 Determination of the temperature of a fermionic
gas
The temperature of a classical gas in a trap can be determined easily:
after a time-of-flight expansion, the momentum distribution of the gas
is known from which the temperature can be easily calculated. The
case of a bosonic gas is very different: once the gas has condensed
into a Bose-Einstein-Condensate, the fraction of the non-condensed
atoms is directly related to the temperature of the gas. At very low
temperatures, the condensate becomes nearly pure, and a temperature
measurement becomes a task that is difficult to accomplish. The case
of a fermionic gas is as tricky. At low temperatures, especially below
the Fermi temperature, the momentum distribution shows no changes
except that the smearing of the step in the Fermi distribution.
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