Theoretical study of ultra-cold Fermi gases in interaction: dynamical aspects and polarization effects
Description
Technical progress on ultra-cold Fermi gases experiments induced numerous studies for the last few years. Using these experimental setups, it is effectively possible to generate ultra-cold gases with selected properties, in particular through the Feshbach resonances phenomenon. This allows us to set the sign of the scattering length a using an external magnetic field. It is then possible to have an attractive interaction (a < 0) as well as a repulsive one (a > 0). The Feshbach resonance itself is defined for infinite values of a (positive or negative), which corresponds to a strongly interacting regime. Moreover, when a > 0, molecular bound states (bosonic because they are made with two fermionic atoms) can appear. Thus, below a critical temperature, a superfluid phase can emerge and a crossover can be observed (from the BEC to BCS superfluid states). Depending on the position on the phase diagram, frequency and damping of collective modes will be different. This is why the collective modes are good probes of the system phase. A precise extensive knowledge of their characteristics is thus very important. This thesis presents a complete study of some of these collective modes in the normal phase. This work mainly relies on the Boltzmann equation which will be solved in two different ways: firstly, with an improved (higher order) version of the so-called moments method; secondly with a numerical solution that has required to write a numerical code in order to take into account the in-medium effects (mean field potential and in-medium cross section). Particular attention has been paid to numerical simulations in order to reproduce as closely as possible the experimental conditions. Moreover, experimental procedures now allow to create spin unbalanced gases. We have shown in this work a study of these systems using the numerical resolution of the Boltzmann equation. Moreover, we have developed a theoretical approach in order to build the phase diagram of these polarized gases, which is not fully described yet. Finally, we have suggested a method to determine the in-medium effects, with the aim to solve the problem emerging with the usual method used in the balanced case. (author)
Abstract (French)
Les progres techniques realises dans le cadre des experiences sur les gaz de fermions ultrafroids ont engendre une emulation particulierement importante ces dernieres annees. En effet, ces dispositifs experimentaux permettent de produire des systemes gazeux 'a la carte', notamment grace au phenomene de resonances de Feshbach qui permet de controler le signe de la longueur de diffusion a par application d'un champ magnetique exterieur. Il est alors possible de generer aussi bien une interaction attractive (a < 0) que repulsive (a > 0). La resonance de Feshbach en elle-meme se trouve en a →±∞, cette limite correspondant a un regime de fortes correlations entre les particules. De plus, dans la region ou a est positive, des etats lies moleculaires (bosoniques car formes de deux fermions) peuvent se former. En-dessous d'une certaine temperature, une phase superfluide peut alors apparaitre, et une transition de phase continue entre l'etat bosonique et l'etat fermionique peut etre observee (BEC-BCS crossover). En fonction de la position dans le diagramme de phases, les modes collectifs possederont des caracteristiques (frequence, amortissement) differentes. En ce sens, ils constituent une sonde de l'etat de la matiere et une connaissance precise de ces modes est par consequent tres importante. Le travail presente dans cette these comporte une caracterisation detaillee de plusieurs modes collectifs dans la phase normale du systeme atomique. L'etude repose principalement sur l'equation de Boltzmann, que nous resolvons de deux facons differentes. La premiere consiste a utiliser une methode des moments 'amelioree' (c'est-a-dire d'ordre superieur). La seconde est numerique et a necessite l'ecriture d'un programme de simulation permettant l'incorporation de tous les effets de milieu (potentiel de champ moyen et section efficace). Une attention toute particuliere a ete apportee a la mise en place des simulations afin de reproduire le plus fidelement possible les conditions experimentales. Les techniques experimentales permettent egalement desormais la creation de gaz polarises. Nous presenterons donc dans ce travail une etude de ces gaz utilisant notre programme de simulation (mise en evidence des differents regimes de collision), puis une etude plus theorique ayant pour principal objectif d'etablir le diagramme de phase encore meconnu de ces gaz particuliers, et enfin de proposer une methode de calcul des effets de milieu, les techniques habituelles utilisees pour les gaz non polarises n'etant plus valables. (auteur)
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Additional details
Additional titles
- Original title (French)
- Etude theorique d'un gaz de fermions froids en interaction: aspects dynamiques et effets de polarisation
Publishing Information
- Imprint Pagination
- 147 p.
- Report number
- FRNC-TH--13834
INIS
- Country of Publication
- France
- Country of Input or Organization
- France
- INIS RN
- 54020348
- Subject category
- S71: CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS;
- Resource subtype / Literary indicator
- Thesis
- Descriptors DEI
- BOLTZMANN EQUATION; FERMI GAS; FERMIONS; NUMERICAL SOLUTION
- Descriptors DEC
- DIFFERENTIAL EQUATIONS; EQUATIONS; INTEGRO-DIFFERENTIAL EQUATIONS; KINETIC EQUATIONS; MATHEMATICAL SOLUTIONS; PARTIAL DIFFERENTIAL EQUATIONS
Optional Information
- Notes
- 89 refs.; Available from the INIS Liaison Officer for France, see the INIS website for current contact and E-mail addresses
- Secondary number(s)
- Lycen-T--2014-13