Molecular regimes in ultracold Fermi gases

The use of Feshbach resonances for tuning the interparticle interaction in ultracold Fermi gases has led to remarkable developments, in particular to the creation and Bose-Einstein condensation of weakly bound diatomic molecules of fermionic atoms. These are the largest diatomic molecules obtained so far, with a size of the order of thousands of angstroms. They represent novel composite bosons, which exhibit features of Fermi statistics at short intermolecular distances. Being highly excited, these molecules are remarkably stable with respect to collisional relaxation, which is a consequence of the Pauli exclusion principle for identical fermionic atoms. The purpose of this review is to introduce theoretical approaches and describe the physics of molecular regimes in two-component Fermi gases and Fermi-Fermi mixtures, focusing attention on quantum statistical effects.Comment: Chapter of the book: "Cold Molecules: Theory, Experiment, Applications" edited by R. V. Krems, B. Friedrich and W. C. Stwalley (publication expected in March 2009

Three-body problem in Fermi gases with short-range interparticle interaction

We discuss 3-body processes in ultracold two-component Fermi gases with short-range intercomponent interaction characterized by a large and positive scattering length $a$. It is found that in most cases the probability of 3-body recombination is a universal function of the mass ratio and $a$, and is independent of short-range physics. We also calculate the scattering length corresponding to the atom-dimer interaction.Comment: 4 pages, 2 figure

Efimov physics from the functional renormalization group

Few-body physics related to the Efimov effect is discussed using the functional renormalization group method. After a short review of renormalization in its modern formulation we apply this formalism to the description of scattering and bound states in few-body systems of identical bosons and distinguishable fermions with two and three components. The Efimov effect leads to a limit cycle in the renormalization group flow. Recently measured three-body loss rates in an ultracold Fermi gas $^6$Li atoms are explained within this framework. We also discuss briefly the relation to the many-body physics of the BCS-BEC crossover for two-component fermions and the formation of a trion phase for the case of three species.Comment: 28 pages, 13 figures, invited contribution to a special issue of "Few-Body Systems" devoted to Efimov physics, published versio

On Parity-Violating Three-Nucleon Interactions and the Predictive Power of Few-Nucleon EFT at Very Low Energies

We address the typical strengths of hadronic parity-violating three-nucleon interactions in "pion-less" Effective Field Theory in the nucleon-deuteron (iso-doublet) system. By analysing the superficial degree of divergence of loop diagrams, we conclude that no such interactions are needed at leading order. The only two linearly independent parity-violating three-nucleon structures with one derivative mix two-S and two-P-half waves with iso-spin transitions Delta I = 0 or 1. Due to their structure, they cannot absorb any divergence ostensibly appearing at next-to-leading order. This observation is based on the approximate realisation of Wigner's combined SU(4) spin-isospin symmetry in the two-nucleon system, even when effective-range corrections are included. Parity-violating three-nucleon interactions thus only appear beyond next-to-leading order. This guarantees renormalisability of the theory to that order without introducing new, unknown coupling constants and allows the direct extraction of parity-violating two-nucleon interactions from three-nucleon experiments.Comment: 20 pages LaTeX2e, including 9 figures as .eps file embedded with includegraphicx. Minor modifications and stylistic corrections. Version accepted for publication in Eur. Phys. J.

Low-Energy Universality in Atomic and Nuclear Physics

An effective field theory developed for systems interacting through short-range interactions can be applied to systems of cold atoms with a large scattering length and to nucleons at low energies. It is therefore the ideal tool to analyze the universal properties associated with the Efimov effect in three- and four-body systems. In this "progress report", we will discuss recent results obtained within this framework and report on progress regarding the inclusion of higher order corrections associated with the finite range of the underlying interaction.Comment: Commissioned article for Few-Body Systems, 47 pp, 16 fig

More on the infrared renormalization group limit cycle in QCD

We present a detailed study of the recently conjectured infrared renormalization group limit cycle in QCD using chiral effective field theory. It was conjectured that small increases in the up and down quark masses can move QCD to the critical trajectory for an infrared limit cycle in the three-nucleon system. At the critical quark masses, the binding energies of the deuteron and its spin-singlet partner are tuned to zero and the triton has infinitely many excited states with an accumulation point at the three-nucleon threshold. We exemplify three parameter sets where this effect occurs at next-to-leading order in the chiral counting. For one of them, we study the structure of the three-nucleon system in detail using both chiral and contact effective field theories. Furthermore, we investigate the matching of the chiral and contact theories in the critical region and calculate the influence of the limit cycle on three-nucleon scattering observables.Comment: 17 pages, 7 figures, discussion improved, results unchanged, version to appear in EPJ

The Unitary Gas and its Symmetry Properties

The physics of atomic quantum gases is currently taking advantage of a powerful tool, the possibility to fully adjust the interaction strength between atoms using a magnetically controlled Feshbach resonance. For fermions with two internal states, formally two opposite spin states, this allows to prepare long lived strongly interacting three-dimensional gases and to study the BEC-BCS crossover. Of particular interest along the BEC-BCS crossover is the so-called unitary gas, where the atomic interaction potential between the opposite spin states has virtually an infinite scattering length and a zero range. This unitary gas is the main subject of the present chapter: It has fascinating symmetry properties, from a simple scaling invariance, to a more subtle dynamical symmetry in an isotropic harmonic trap, which is linked to a separability of the N-body problem in hyperspherical coordinates. Other analytical results, valid over the whole BEC-BCS crossover, are presented, establishing a connection between three recently measured quantities, the tail of the momentum distribution, the short range part of the pair distribution function and the mean number of closed channel molecules.Comment: 63 pages, 8 figures. Contribution to the Springer Lecture Notes in Physics "BEC-BCS Crossover and the Unitary Fermi gas" edited by Wilhelm Zwerger. Revised version correcting a few typo