Bose-Einstein condensation (BEC) has been observed in a dilute gas of sodium atoms. A Bose-Einstein condensate consists of a macroscopic population of the ground state of the system, and is a coherent state of matter. In an ideal gas, this phase transition is purely quantum-statistical. The study of BEC in weakly interacting systems which can be controlled and observed with precision holds the promise of revealing new macroscopic quantum phenomena that can be understood from first principles.

Bose-Einstein condensation in a gas of sodium atoms

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.

Feshbach resonances in ultracold gases

Feshbach Resonances in Ultracold Gases

This paper presents a review of the current state of the art in the research field of cold and ultracold molecules. It serves as an introduction to the focus issue of New Journal of Physics on Cold and Ultracold Molecules and describes new prospects for fundamental research and technological development. Cold and ultracold molecules may revolutionize physical chemistry and few-body physics, provide techniques for probing new states of quantum matter, allow for precision measurements of both fundamental and applied interest, and enable quantum simulations of condensed-matter phenomena. Ultracold molecules offer promising applications such as new platforms for quantum computing, precise control of molecular dynamics, nanolithography and Bose-enhanced chemistry. The discussion is based on recent experimental and theoretical work and concludes with a summary of anticipated future directions and open questions in this rapidly expanding research field.

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Cold and ultracold molecules: science, technology and applications

The realization of superfluidity in a dilute gas of fermionic atoms, analogous to superconductivity in metals, represents a long-standing goal of ultracold gas research. In such a fermionic superfluid, it should be possible to adjust the interaction strength and tune the system continuously between two limits: a Bardeen–Cooper–Schrieffer (BCS)-type superfluid (involving correlated atom pairs in momentum space) and a Bose–Einstein condensate (BEC), in which spatially local pairs of atoms are bound together. This crossover between BCS-type superfluidity and the BEC limit has long been of theoretical interest, motivated in part by the discovery of high-temperature superconductors. In atomic Fermi gas experiments superfluidity has not yet been demonstrated; however, long-lived molecules consisting of locally paired fermions have been reversibly created. Here we report the direct observation of a molecular Bose–Einstein condensate created solely by adjusting the interaction strength in an ultracold Fermi gas of atoms. This state of matter represents one extreme of the predicted BCS–BEC continuum.

Emergence of a molecular Bose-Einstein condensate from a Fermi gas

We compute ab initio cross sections for cold collisions of Rb atoms with OH radicals. We predict collision rate constants of order ${10}^{\ensuremath{-}11}\text{ }\text{ }{\mathrm{cm}}^{3}/\mathrm{s}$ at temperatures in the range 10--100 mK at which molecules have already been produced. However, we also find that in these collisions the molecules have a strong propensity for changing their internal state, which could make sympathetic cooling of OH in a Rb buffer gas problematic in magnetostatic or electrostatic traps.

/pdf/ultracold-rb-oh-collisions-and-prospects-for-sympathetic-44t309nfzu.pdf

Ultracold Rb-OH Collisions and Prospects for Sympathetic Cooling

We have developed a new potential energy surface for spin-polarized K($^2$S) + K$_{2}(^3\Sigma^+_u)$ collisions and carried out quantum dynamical calculations of vibrational quenching at low and ultralow collision energies for both bosons $^{39}$K and $^{41}$K and fermions $^{40}$K. At collision energies above about 0.1 mK the quenching rates are well described by a classical Langevin model, but at lower energies a fully quantal treatment is essential. We find that for the low initial vibrational state considered here ($v=1$), the ultracold quenching rates are {\it not} substantially suppressed for fermionic atoms. For both bosons and fermions, vibrational quenching is much faster than elastic scattering in the ultralow-temperature regime. This contrasts with the situation found experimentally for molecules formed via Feshbach resonances in very high vibrational states.

https://arxiv.org/pdf/cond-mat/0411158.pdf

Ultracold quantum dynamics: Spin-polarized K+ K 2 collisions with three identical bosons or fermions

We have calculated elastic and state-resolved inelastic cross sections for cold and ultracold collisions in the $\mathrm{Rb}(^{1}S)+\mathrm{O}\mathrm{H}(^{2}\ensuremath{\Pi}_{3∕2})$ system, including fine-structure and hyperfine effects. We have developed a set of five potential energy surfaces for $\mathrm{Rb}\text{\ensuremath{-}}\mathrm{O}\mathrm{H}(^{2}\ensuremath{\Pi})$ from high-level ab initio electronic structure calculations, which exhibit conical intersections between covalent and ion-pair states. The surfaces are transformed to a quasidiabatic representation. The collision problem is expanded in a set of channels suitable for handling the system in the presence of electric and/or magnetic fields, although we consider the zero-field limit in this work. Because of the large number of scattering channels involved, we propose and make use of suitable approximations. To account for the hyperfine structure of both collision partners in the short-range region we develop a frame-transformation procedure which includes most of the hyperfine Hamiltonian. Scattering cross sections on the order of ${10}^{\ensuremath{-}13}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{2}$ are predicted for temperatures typical of Stark decelerators. We conclude that spin orientation of the partners is completely disrupted during the collision. Implications for both sympathetic cooling of OH molecules in an environment of ultracold Rb atoms and experimental observability of the collisions are discussed.

https://arxiv.org/pdf/physics/0608200.pdf

Daniel E. Potter

Papers

Ultracold Rb-OH Collisions and Prospects for Sympathetic Cooling

Ultracold quantum dynamics: Spin-polarized K+ K 2 collisions with three identical bosons or fermions

Cold collisions between OH and Rb: The field-free case