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

CHAPTER 5. EXPERIMENTAL RESULTS
F
E
=
¹
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0 1 2 3 4 5 6
¡ 1=
kFa
Figure 5.8: The chemical potential as a function of the inverse gas parameter
in the homogeneous case. The points are Monte-Carlo simulations from
reference [79], the solid line is the fit presented in reference [112], while
the dashed line is the prediction from mean-field BCS theory.
[110] experiments on collective excitations. The idea is to take the real
equation of state and calculate an effective polytropic exponent
γ = n ∂µ
µ ∂n
(5.12)
which coincides with the actual one for a polytropic equation of state. In
section 2.4 we calculated µ(n), which we could use to calculate γ, shown
in figure 5.9. Hu et al. [111] improved this approach by averaging over
the trap. Astrakharchik et al. [79] performed a quantum Monte Carlo
simulation to achieve a better approximation, and Manini et al. [112]
used an empiric fitting function to fit their data. The data and the fitted
function are presented in figure 5.8. We can use 5.12 to extract the
effective polytropic exponent, shown in figure 5.9.
The external potential Vext is the potential of the optical dipole trap. By
setting the partial derivatives with respect to time in the Euler equation
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