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arXiv:cond-mat/0502010 · Journal of Physics B Atomic Molecular and Optical Physics

Diatomic molecules in ultracold Fermi gases—novel composite bosons

Dmitry S. Petrov, Ch Salomon, Gora V. Shlyapnikov

Published Apr 25, 2005• 97 citations
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Abstract

We give a brief overview of recent studies of weakly bound homonuclear molecules in ultracold two-component Fermi gases. It is emphasized that they represent novel composite bosons, which exhibit features of Fermi statistics at short intermolecular distances. In particular, the Pauli exclusion principle for identical fermionic atoms provides a strong suppression of collisional relaxation of such molecules into deep bound states. We then analyse heteronuclear molecules which are expected to be formed in mixtures of different fermionic atoms. We show how an increase in the mass ratio for the constituent atoms changes the physics of collisional stability of such molecules compared to homonuclear ones. We discuss Bose–Einstein condensation of these composite bosons and consider prospects for future studies.

DOI
10.1088/0953-4075/38/9/014

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We give a brief overview of recent studies of weakly bound homonuclear molecules in ultracold two-component Fermi gases. It is emphasized that they represent novel composite bosons, which exhibit features of Fermi statistics at short intermolecular distances. In particular, the Pauli exclusion principle for identical fermionic atoms provides a strong suppression of collisional relaxation of such molecules into deep bound states. We then analyse heteronuclear molecules which are expected to be formed in mixtures of different fermionic atoms. We show how an increase in the mass ratio for the constituent atoms changes the physics of collisional stability of such molecules compared to homonuclear ones. We discuss Bose–Einstein condensation of these composite bosons and consider prospects for future studies.
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.
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.
We consider weakly bound bosonic and fermionic heteronuclear molecules (dimers) in ultracold atomic gases, where the interspecies interaction is characterized by a large positive scattering length. We develop a new theoretical approach to solve the four-body scattering problem, which is valid when the mass ratio between the constituent atoms is sufficiently large. This approach is then used to study elastic and inelastic dimer- dimer scattering processes in the case that the light constituent atoms are fermions, while the heavy atoms can be either fermions or bosons. Due to the Fermi statistics of the light atoms, the heavy atoms experience a strong repulsion at large intermolecular distances. This leads to suppression of the collisional relaxation to universal trimer (Efimov) states and/or deeply bound molecular states. We present the formation rate of Efimov trimers as a function of the three-body parameter for several experimentally interesting systems. The competition between the formation of trimers and relaxation to deeply bound molecules is analyzed, and prospects for future studies of these systems are discussed.
We show that an ansatz based on independent composite bosons [Phys. Rep. 463, 215 (2008)] accurately describes the condensate fraction of molecular Bose-Einstein condensates in ultracold Fermi gases. The entanglement between the fermionic constituents of a single Feshbach molecule then governs the many-particle statistics of the condensate, from the limit of strong interaction to close to unitarity. This result strengthens the role of entanglement as the indispensable driver of composite-boson behavior. The condensate fraction of fermion pairs at zero temperature that we compute matches excellently previous results obtained by means of fixed-node diffusion Monte Carlo methods and the Bogoliubov depletion approximation. This paves the way towards the exploration of the BEC-BCS crossover physics in mixtures of cold Fermi gases with an arbitrary number of fermion pairs as well as the implementation of Hong-Ou-Mandel--like interference experiments proposed within coboson theory.