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

CHAPTER 1. INTRODUCTION
crossover from weak to strong interactions, but instead, looking at it
from a mean-field standpoint, we have weak attractive interactions in the
BCS limit, and weak repulsive interactions between the strongly bound
pairs, which we call molecules. This is important, because this enables us
to condense the molecules into a BEC, it would implode if the interactions
were attractive. In between these two weakly interacting limits lies a
zone where the interactions are sufficiently strong to form stable pairs,
but not yet strongly bound enough to be considered particles on their
own. This region has drawn large attention to theorists, because the
approximations usually used in many-body theory do not hold anymore,
as the parameters around which the approximations are performed are
not small.
At the 10 th International Conference on Recent Progress in Many-
Body Theories [11], a challenge was posed by George Bertsch:
What are the ground state properties of the many-body system
composed of spin-1/2-fermions interacting via a zero-range,
infinite scattering-length contact interaction.
What was thought of as a toy model to describe the behavior of neutron
stars, started a large discussion in the field. Furthermore, as a rare
exception for neutron star theorists, an experimental realization was
possible [12]. In the very center of the crossover that we just described,
the fermionic atoms fulfill, at least as a very good approximation, the
conditions of this challenge. This means that the crossover forms a link
between different parts of physics.
It is this transition, from a bosonic to a fermionic gas, that this thesis
is devoted to. As this transition is smooth, it is known in the literature
as the BEC-BCS crossover.
The pioneering work in the field of fermionic gases started around
1997. The group at JILA had reached quantum degeneracy of 40 K [13]
in 1998, while the groups at Rice [14] and our group [15] used 6 Li and
reached quantum degeneracy in 2001, followed by the groups at MIT [16]
with 6 Li and Florence [17] with 40 K. The most important tool to manipulate
the atoms, the Feshbach resonance, was found and characterized [18,19].
The next important step was the creation of weakly bound molecules
in such a resonance [20]. Our group showed that these molecules are
surprisingly long-lived in 6 Li [21]. Together with an exact calculation of
the scattering length between molecules [22], this laid the foundations
for the creation of molecular Bose-Einstein condensate at Innsbruck
[23], JILA [24], MIT [25] and our group (see the article in appendix A.1).
The condensation of fermion pairs on the BCS side has been shown at
10