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

The authors review progress in understanding the nature of atomic collisions occurring at temperatures ranging from the millidegrees Kelvin to the nanodegrees Kelvin regime. The review includes advances in experiments with atom beams, light traps, and purely magnetic traps. Semiclassical and fully quantal theories are described and their appropriate applicability assessed. The review divides the subject into two principal categories: collisions in the presence of one or more light fields and ground-state collisions in the dark.

Experiments and theory in cold and ultracold collisions

The recent creation of a Bose–Einstein condensate of atomic hydrogen has added a new system to this exciting field. The differences between hydrogen and the alkali metal atoms require other techniques for the initial trapping and cooling of the atoms and the subsequent detection of the condensate. The use of a cryogenic loading technique results in a larger number of trapped atoms. Spectroscopic detection is well suited to measuring the temperature and density of the sample in situ. The transition was observed at a temperature of 50 μK and a density of 2×1014 cm-3. The number of condensed atoms is about 109 at a condensate fraction of a few percent. A peak condensate density of 4.8×1015 cm-3 has been observed.

http://ultracold.rice.edu/publications/HBEC_vol81_num18.pdf

Bose-Einstein Condensation of Atomic Hydrogen

We present a novel formulation for SQUID operation, which enables us to evaluate and compare the sensitivity and applicability of different devices. SQUID magnetometers for low-frequency applications are analyzed, taking into account the coupling circuits and electronics. We discuss nonhysteretic and hysteretic single-junction rf SQUIDs, but the main emphasis is on the dynamics, sensitivity, and coupling considerations of dc-SQUID magnetometers. A short review of current ideas on thin-film, dc-SQUID design presents the problems in coupling and the basic limits of sensitivity. The fabrication technology of tunnel-junction devices is discussed with emphasis on how it limits critical current densities, specific capacitances of junctions, minimum linewidths, conductor separations, etc. Properties of high-temperature superconductors are evaluated on the basis of recently published results on increased flux creep, low density of current carriers, and problems in fabricating reliable junctions. The optimization of electronics for different types of SQUIDs is presented. Finally, the most important low-frequency applications of SQUIDs in biomagnetism, metrology, geomagnetism, and some physics experiments demonstrate the various possibilities that state-of-the-art SQUIDs can provide.

SQUID magnetometers for low-frequency applications

We have studied the time and temperature dependence of trapped magnetic fields in ceramic tubes of the high-${T}_{c}$ superconductor ${\mathrm{Y}}_{1}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{x}$. The maximum field in a particular tube is largely a function of temperature, although decays of the form ${t}^{\ensuremath{-}\ensuremath{\alpha}}$ occur for fields at the maximum values. For fields away from the critical values, limits on the decay rates give $\ensuremath{\rho}\ensuremath{\le}{10}^{\ensuremath{-}16}$ \ensuremath{\Omega} cm. These results are consistent with the superconductor being in a spin-glass-like state.

Current persistence and magnetic shielding properties of Y 1 Ba 2 Cu 3 O x tubes

We report on the design and initial testing of a new type of hydrogen maser, operated at dilution refrigerator temperatures, in which H atoms circulate back and forth between a microwave-pumped state selector and the maser cavity. Other novel design features include liquid-/sup 4/He-coated walls, He-cooled electronics, and the use of microscopic magnetic particles to relax the two lowest hyperfine levels in the state selector. Stabilities at least as good as that of a Rb clock and a high-stability quartz oscillator are observed for measuring times between 1 and 300 s.

Recirculating cryogenic hydrogen maser.

Conventional hydrogen masers are the most stable of all atomic clocks with stabilities Δf/f of better than 10-15 for measuring times τ of 103 sec. A new generation of cryogenic hydrogen masers has the potential to improve this figure by 2 to 3 orders of magnitude. Here we describe how research on spin-polarized atomic hydrogen led to the construction at the University of British Columbia of a uniquely cryogenic hydrogen maser. In this maser, which operates at 0.5K and uses liquid helium coated walls throughout, H atoms circulate back and forth between a microwave pumped state selector and the maser cavity. The measurement of the frequency stability is presently limited by the frequency stability of the available references, but values of Δf/f<10-13 for τ=1 sec have been recently established. The successful development of rather different cryogenic masers at other institutions will also be discussed.

Application of Atomic Hydrogen at Low Temperatures: The Recirculating Cryogenic Hydrogen Maser

We have studied spin-polarized deuterium, Darrow-down, in the temperature range 0.3 to 0.7 K in a field of 40 kG using electron-spin resonance at 114 GHz. The intrinsic rates for recombination of two D atoms to form D/sub 2/ on the surface of l-/sup 4/He have been measured for both the ortho and para channels. The two rates are approximately equal and when extrapolated to zero field are 1600 times greater than the rates for H/sub 2/ formation. Doubly spin-polarized deuterium, Darrow-downX, has been observed for the first time, with nuclear-spin purities >0.98 and sample lifetimes as long as 1 h.

Observation of doubly spin-polarized deuterium by electron-spin resonance.

Measurements of the two-body recombination of spin-polarized atomic hydrogen in a magnetic field of 40 kG have been extended to temperatures above 0.5/sup 0/K. The rate constant for the formation of parahydrogen shows an unexpected increase with temperature, which is explained by inverse predissociation into the v = 14,J = 4 level of H/sub 2/. Data indicate the level is bound by 0.7 +- 0.1/sup 0/K.

R. W. Cline

Papers

Current persistence and magnetic shielding properties of Y 1 Ba 2 Cu 3 O x tubes

Recirculating cryogenic hydrogen maser.

Application of Atomic Hydrogen at Low Temperatures: The Recirculating Cryogenic Hydrogen Maser

Observation of doubly spin-polarized deuterium by electron-spin resonance.

Observation of inverse predissociation of spin-polarized atomic hydrogen at low temperatures