Understanding and controlling interactions of ultracold molecules is a cornerstone of quantum chemistry. While the laboratory creation of degenerate molecular gases comprised of bosonic atoms has unlocked powerful platforms for quantum simulation, progress is limited by the absence of a robust theoretical framework for characterizing intermolecular interactions. This is in stark contrast to the situation for Fermi gases. In this Letter, we present such a framework providing universal expressions for these molecular scattering lengths as functions of experimentally measurable quantities. Our discoveries are crucial for understanding molecular condensate formation. Calculations of the compressibility reveal that a sign change in such molecular scattering lengths is directly correlated with the instability of these condensates. These results offer fresh insight with broad applications for atomic, molecular, and condensed matter physics, as well as quantum chemistry.
Understanding and controlling interactions of ultracold molecules is a cornerstone of quantum chemistry. While the laboratory creation of degenerate molecular gases comprised of bosonic atoms has unlocked powerful platforms for quantum simulation, progress is limited by the absence of a robust theoretical framework for characterizing intermolecular interactions. This is in stark contrast to the situation for Fermi gases. In this Letter, we present such a framework providing universal expressions for these molecular scattering lengths as functions of experimentally measurable quantities. Our discoveries are crucial for understanding molecular condensate formation. Calculations of the compressibility reveal that a sign change in such molecular scattering lengths is directly correlated with the instability of these condensates. These results offer fresh insight with broad applications for atomic, molecular, and condensed matter physics, as well as quantum chemistry.
Feshbach resonances are the essential tool to control the interaction between atoms in ultracold quantum gases. They have found numerous experimental applications, opening up the way to important breakthroughs. This review broadly covers the phenomenon of Feshbach resonances in ultracold gases and their main applications. This includes the theoretical background and models for the description of Feshbach resonances, the experimental methods to find and characterize the resonances, a discussion of the main properties of resonances in various atomic species and mixed atomic species systems, and an overview of key experiments with atomic Bose-Einstein condensates, degenerate Fermi gases, and ultracold molecules.
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.
In this thesis, we investigated the physics of two- and three-dimensional ultra cold Bose gases in the strongly interacting regime at zero temperature. This regime can be experimentally accessed using a Feshbach resonance. We applied a self-consistent diagrammatic approach to determine the chemical potential of three-dimensional Bose gases for a wide range of interaction values. We showed that such strongly interacting Bose gases become unstable towards the formation of molecules at a finite positive scattering length. In fact, the interaction between atoms becomes effectively attractive and the system looses its metastability before reaching the unitary limit. We also found that such systems are nearly fermionized close to the instability point. Near this critical point, the chemical potential reaches a maximum and the contribution to the system energy due to three-body forces is estimated to be only a few percent. We also studied the same system using a self-consistent renormalization group method. This approach confirms the existence of an instability point towards the formation of molecules as well as fermionization. We showed that the instability and accompanying maximum are precursors of the sign change of the effective two-body interaction strength from repulsive to attractive near resonance. In addition, we examined the physics of two-dimensional Bose gases near resonance using a similar self-consistent diagrammatic approach as the one introduced for three-dimensional Bose gases. We demonstrated that a competition between three-body attractive interactions and two-body repulsive forces results in the chemical potential of two-dimensional Bose gases to exhibit a maximum at a critical scattering length beyond which these quantum gases possess a negative compressibility. For larger scattering lengths, the increasingly prominent role played by three-body attractive interactions leads to an onset instability at a second critical value. The three-body effects studied for these systems are universal, fully characterized by the effective two-dimensional scattering length and are, in comparison to the three-dimensional case, independent of three-body ultraviolet physics.
We study ultracold gases of alkali-metal atoms in the quantum degenerate regime. The interatomic interactions in these type of systems can be tuned using resonances induced by magnetic or electric fields. The tunability of the interactions, together with the possibility of confining the atoms with several kinds of external potentials, allows for a completely novel approach to study basic problems in many-body physics, and moreover, allows to enter regimes which have never been accessible in condensed matter or nuclear physics. For example, this has led to the experimental demonstration of an intimate relation between two types of superfluidity: the crossover from Bose-Einstein condensation of tightly bound molecules to the superfluid behavior related to weakly bound BCS-like pairs. Another experimental landmark was reached when the existence of universal Efimov three-body bound states was proven in experiments with ultracold bosonic cesium atoms. In this thesis, we study several aspects of these strongly interacting and ultracold atomic gases. We develop an analytical model that encapsulates all of the relevant scattering physics in atomic systems where open-channel shape resonances and closedchannel Feshbach resonances give rise to complicated and non-trivial scattering properties. This model provides lots of physical insight and is shown to describe important quantities, such as the molecular energies and scattering phase shifts, with a high level of accuracy. The model is compared to full numerical coupled-channel calculations in two atomic systems: rubidium and lithium. We study the BCS-BEC crossover using a many-body description of the ultracold gas that includes the non-trivial energy dependence of the scattering model. We show that it gives rise to superfluid behavior associated with the formation of BCS-like pairs while the low-energy interactions are repulsive in character. The energy dependence of the interactions is crucial, as it gives rise to attractive interactions at the Fermi energy, necessary for the formation of Cooper pairs. We demonstrate new ways of controlling the interatomic interactions using a combination of magnetic and electric fields. This leads to experimental control of, for instance, the three-body parameter in the context of Efimov physics and of non-universal behavior in the BCS-BEC crossover in fermionic gases. Using a four-body method based on first principles, we solve the molecule-molecule scattering problem to calculate several important properties of bosonic and fermionic Summary 145 molecules that consist of light and heavy atoms. These type of molecules are of current experimental interest, and we predict several exciting relations between three- and four-body observables in these type of systems.
Quantum degenerate molecular gases are of interest for the unique level of control they offer over chemical interactions and processes. To reach the quantum degenerate regime, these molecular gases must be cooled to ultracold temperatures, typically on the order of 100 nanoKelvins. Unlike atoms, with a few-level system that facilitates cooling, molecules represent a many-level system, which makes these temperatures experimentally difficult to achieve. As a result, experiments have turned to photoassociation and Feshbach resonance as shortcuts to form ultracold molecules from already ultracold atoms. Photoassociation and Feshbach resonance have been utilized to successfully create stable quantum degenerate molecules, but not on a routine basis, and only for a small range of molecular species. The primary focus of this thesis will be to study photoassociation and Feshbach resonance, and investigate possible routes to more efficient long-lived quantum degenerate molecule formation. We will also investigate realistic limiting conditions to open the possibility to more routine molecules, and to molecular species that are currently inaccessible. Overall, we find combined photoassociation and Feshbach resonance are viable schemes for efficiently creating quantum degenerate molecules, under realistic restrictions such as low laser intensity, narrow Feshbach resonance, and strong elastic collisions. As the techniques to create quantum degenerate molecules become more robust and experimentally available, the creation of colder, larger, and more long-lived samples will facilitate study of these molecules, and spur development into new applications.