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Theoretical study of imbalanced Fermi gases

par Frédéric Chevy - 21 mars 2008

Clogston-Chandrasekhar criterion

According to the BCS scenario, fermionic superfluidity is a consequence of the pairing between opposite spin electrons at the Fermi surface. When one tries to polarize the sample, there is a competition between Cooper pairing that tends to keep the pairs as a whole, hence keeping equal spin populations, and the magnetic field that aims at poalrizing all electrons in the same spin state.

Clogston and Chandrasekhar have demonstrated that, the superfluid was robust to magnetic fields lower than the binding energy of a Cooper pair, in which case the population of the two spin species would stay the same. However, when the threshold is reached, the electron spin start to align along the magnetic field and the superfluid phases turns into new exotic phases whose nature is not yet fully elucidated. Depending on the model considered, one would expect inhomogeneous superfluid phases (FFLO phases, named after their discoverers Fulde, Ferrell, Larkin and Ovshinikov), or the Sarma phase in which pairing tkes place in the bulk of the Fermi sea (hence the name of Inner gap superfluid sometimes given to this phase).

Rice and MIT experiments

In a series of complemetary experiments, the Rice and MIT teams have obtained partially polarized unitary cloudds of Lithium 6. In these two experiments, the atoms form a shell structure, the innermost correponding to a superfluid core where the densitites of the two spin species are perfectly balanced. Despite this similarity, the rim of the cloud shows striking differences whose origin is not yet clarified.

- In Rice, there is a single outer shell, containing only particle of the majority spin state.

- At MIT, the outermot shell is just like in Rice constituted of majority species atoms. However, there is a third intermediate phase, where both spin species coexist with different populations.

The N+1 body problem

We have tried to understand these experimental data using results as exactas possible (and in particular avoiding the use of the mean-field approximation that only gives access to qualitative feautures of the problem). Although the origin of the disagreement is still unclear, we have demonstrated that

- Rice experiment : we have used the knowledge of the equation of state of a unitary superfluid to describe the density profile of the cloud. We obtain an excellent agrrement between theory and experiment, without any adjustable parameter.

- MIT experiment : we have demonstrated that the stability of an intermediate phase was related to the N+1 body problem of an impurity immersed in a Fermi sea, the analog of a polaron in condensed matter. In collaboration with the groups of R. Combescot at Laboratoire de physique statistique de l’ENS and C. Lobo and A. Reccatti in Trento, we have shown that most physical properties of the intermediate phase could be understood by describing the polaron as a bare impurity dressed by a single particle-hole pair.

- The study of the polaron shows a divergence of the effective mass for k_F a\sim 1. This singularity in the model can be interpreted as a transition between a fermionic (the polaron) and a a bosonic (dimer) behavior of the impurity. With C. Mora at Laboratoire Pierre Aigrain, we have extended the variational space of the polaron to take into account this new molecular branch of the phase diagram. We have shown that, in agreement with Monte-Carlo simulations, the impurity behaves as a point-like boson immersed in a Fermi Sea with which it interacts through a mean-field interaction.

Read more

Ground state of a tightly bound composite dimer immersed in a Fermi Sea  : C. Mora et F. Chevy, PRA 80 033607 (2009), arXiv:0908.0608v2

Unitary polarized Fermi gases : F. Chevy, to be published in the proceedings of the 2006 Enrico Fermi summer school on Fermi gases, arXiv:cond-mat/0701350

Normal State of Highly Polarized Fermi Gases : Simple Many-Body Approaches : R. Combescot, A. Recati, C. Lobo, and F. Chevy, Phys. Rev. Lett. 98, 180402 (2007), arXiv:cond-mat/0702314.

Universal phase diagram of a strongly interacting Fermi gas with unbalanced spin populations : F. Chevy, Phys. Rev. A 74, 063628 (2006), cond-mat/0605751.

Phase separation in a strongly interacting Fermi gas with unbalanced populations : F. Chevy, Phys. Rev. Lett. 96, 130401 (2006), cond-mat/0601122.

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