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Contribution à la théorie des gaz de fermions ultrafroids fortement polarisés

Abstract : This thesis deals with the N+1 body problem in highly polarized Fermi gases. This is the situation where a single atom of one spin species is immersed in a Fermi sea of atoms of the other species.

The first part uses a Hamiltonian approach based on a general expansion for the wave function of the system with any number of particle-hole pairs. We show that the constructed series of successive approximations converges very rapidly and thus we get an essentially exact solution for the energy and the effective mass of the polaron. In one dimension, for two particular cases, this problem can be solved analytically. The excellent agreement with our series of approximations provides a further check of the reliability of this expansion. Finally, we consider more specifically various limiting cases, as well as the effect of the mass ratio between the two spin species.

In the second part, we use the Feynman diagrams formalism to describe both the polaron and the bound state. For the polaron, we develop a theory which is equivalent to the Hamiltonian approach. For the bound state, we get again a series of successive approximations whose fast convergence is perfectly understood. Therefore, this approach provides an essentially exact solution to the problem along the whole BEC-BCS crossover. Finally, by comparing the energies of the two quasi-particles, we study the position of the polaron to bound state transition.
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Contributor : Sébastien Giraud Connect in order to contact the contributor
Submitted on : Tuesday, June 15, 2010 - 4:31:09 PM
Last modification on : Wednesday, November 17, 2021 - 12:26:56 PM
Long-term archiving on: : Friday, October 19, 2012 - 2:11:03 PM

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  • HAL Id : tel-00492339, version 1

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Sébastien Giraud. Contribution à la théorie des gaz de fermions ultrafroids fortement polarisés. Matière Condensée [cond-mat]. Université Pierre et Marie Curie - Paris VI, 2010. Français. ⟨tel-00492339⟩

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