In the wake of successful experiments in Fermi condensates, experimental attention is broadening to study resonant interactions in degenerate Bose-Fermi mixtures. Here, we consider the properties and stability of the fermionic molecules that can be created in such a mixture near a Feshbach resonance. To do this, we consider the two-body scattering matrix in the many-body environment, and assess its complex poles. The stability properties of these molecules strongly depend on their center-of-mass motion, because they must satisfy Fermi statistics. At low center-of-mass momenta the molecules are more stable than in the absence of the environment (due to Pauli-blocking effects), while at high center-of-mass momenta nontrivial many-body effects render them somewhat less stable.
In the wake of successful experiments in Fermi condensates, experimental attention is broadening to study resonant interactions in degenerate Bose-Fermi mixtures. Here, we consider the properties and stability of the fermionic molecules that can be created in such a mixture near a Feshbach resonance. To do this, we consider the two-body scattering matrix in the many-body environment, and assess its complex poles. The stability properties of these molecules strongly depend on their center-of-mass motion, because they must satisfy Fermi statistics. At low center-of-mass momenta the molecules are more stable than in the absence of the environment (due to Pauli-blocking effects), while at high center-of-mass momenta nontrivial many-body effects render them somewhat less stable.
In the wake of successful experiments in Fermi condensates, experimental attention is broadening to include resonant interactions in degenerate Bose-Fermi mixtures. In this thesis we wish to study the equilibrium properties of the fermionic molecules that can be created in such a mixture. To this end, we first discuss the two body properties of the system, and introduce the model Hamiltonian we use to describe the resonant physics, highlighting its virtues, as well as its limitations. We then proceed by analyzing the mean field solution of this model, by studying both the equilibrium problem, and the non-equilibrium equations of motion, thus developing a powerful language to discuss the system. We then highlight the limitations of the mean-field approach, and develop a numerically tractable generalized version of this theory, which is able to correctly describe the two-body properties of the system in the low-density limit. Finally, we study the properties of the system using this generalized mean-field theory, by first analyzing the two-body scattering matrix in the many-body environment, assessing its complex poles in order to understand the stability properties of the Feshbach molecules in the gas. Secondly we solve the equilibrium equations self-consistently, to study the molecular populations and density distributions at equilibrium, as a function of external bias magnetic field.
Using a Feshbach resonance, we create ultracold fermionic molecules starting from a Bose-Fermi atom gas mixture. The resulting mixture of atoms and weakly bound molecules provides a rich system for studying few-body collisions because of the variety of atomic collision partners for molecules; either bosonic, fermionic, or distinguishable atoms. Inelastic loss of the molecules near the Feshbach resonance is dramatically affected by the quantum statistics of the colliding particles and the scattering length. In particular, we observe a molecule lifetime as long as 100 ms near the Feshbach resonance.
We investigate the mechanical stability of Bose-Fermi mixtures at zero temperature in the presence of a tunable Feshbach resonance, which induces a competition between boson condensation and boson-fermion pairing when the boson density is smaller than the fermion density. Using a many-body diagrammatic approach validated by fixed-node Quantum Monte Carlo calculations and supported by recent experimental observations, we determine the minimal amount of boson-boson repulsion required to guarantee the stability of the mixture across the entire range of boson-fermion interactions from weak to strong coupling. Our stability phase diagrams indicate that mixtures with boson-to-fermion mass ratios near two, such as the ^{87} 87 Rb- ^{40} 40 K system, exhibit optimal stability conditions. Moreover, by applying our results to a recent experiment with a ^{23} 23 Na- ^{40} 40 K mixture, we find that the boson-boson repulsion was insufficient to ensure stability, suggesting that the experimental timescale was short enough to avoid mechanical collapse. On the other hand, we also show that even in the absence of boson-boson repulsion, Bose-Fermi mixtures become intrinsically stable beyond a certain coupling strength, preceding the quantum phase transition associated with the vanishing of the bosonic condensate. We thus propose an experimental protocol for observing this quantum phase transition in a mechanically stable configuration.
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 study a dilute mixture of degenerate bosons and fermions across a Feshbach resonance of the Fermi-Fermi scattering length aF. This scattering length is renormalized by the boson-induced interaction between fermions and its value is crucial to determine the phase diagram of the system. For the mixture in a box and a positive Bose-Fermi scattering length, we show that there are three possibilities: A single uniform mixed phase, a purely fermionic phase coexisting with a mixed phase, and a purely fermionic phase coexisting with a purely bosonic one. As 1∕aF is increased from a negative value to the Feshbach resonance (1∕aF=0), the region of pure separation increases and the other two regions are strongly reduced. Above the Feshbach resonance (1∕aF>0), pairs of Fermi atoms become Bose-condensed molecules. We find that these molecules are fully spatially separated from the bosonic atoms when 1∕aF exceeds a critical value. For a negative Bose-Fermi scattering length we deduce the condition for collapse, which coincides with the onset of dynamical instability of the fully mixed phase. We consider also the mixture in a harmonic trap and determine the conditions for partial demixing, full demixing, and collapse. The experimental implications of our results are investigated by analyzing mixtures of $^{6}\mathrm{Li}\text{\ensuremath{-}}^{23}\mathrm{Na}$ and $^{40}\mathrm{K}\text{\ensuremath{-}}^{87}\mathrm{Rb}$ atoms.
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.