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

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 observed Feshbach resonances in collisions between ultracold $^{52}\mathrm{Cr}$ atoms. This is the first observation of collisional Feshbach resonances in an atomic species with more than one valence electron. The zero nuclear spin of $^{52}\mathrm{Cr}$ and thus the absence of a Fermi-contact interaction leads to regularly spaced resonance sequences. By comparing resonance positions with multichannel scattering calculations we determine the $s$-wave scattering length of the lowest $^{2S+1}\ensuremath{\Sigma}_{g}^{+}$ potentials to be $112(14)\text{ }\text{ }{a}_{0}$, $58(6)\text{ }\text{ }{a}_{0}$, and $\ensuremath{-}7(20)\text{ }\text{ }{a}_{0}$ for $S=6$, 4, and 2, respectively, where ${a}_{0}=0.0529\text{ }\text{ }\mathrm{nm}$.

https://arxiv.org/pdf/cond-mat/0412049.pdf

Observation of Feshbach resonances in an ultracold gas of 52Cr.

Microwave study of the critical state in high-Tc superconductors

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 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.

Atomic-deuterium gas has been studied at temperatures just above 1 K. A short rf discharge was used to dissociate solid D2 on the surface of a sealed pyrex bulb lined with a saturated helium film. Pulsed magnetic resonance on the β-δ transition at its minimum frequency (309 MHz in a magnetic field of 3.9 mT) was used to observe the resulting D. The free induction decays were shortened by spin-exchange collisions with impurity H atoms present in the sample. The H density, inferred using calculated spin-exchange cross sections, was typically higher than the D density. In addition, the samples of D were short-lived, decaying exponentially in time with a strongly temperature-dependent lifetime. We were able to show that recombination with the H impurity was not the cause of the sample decay, and we propose that the decay is due to the thermally activated process wherein D atoms penetrate the liquid helium film that coats the cell walls. Analysis of the lifetime data yields the value 13.6 (6) K for the rest energy of a D atom dissolved in liquid helium, the first measurement of this quantity for any hydrogen isotope.

Hyperfine resonance of atomic deuterium at 1 K

In sufficiently large magnetic fields, the weakly bound levels of H2 acquire finite lifetimes owing to hyperfine predissociation and become manifest as scattering resonances in spin-polarized atomic hydrogen (H↓). In this work we investigate in detail the contribution to the reaction kinetics in H↓ due to the resonance, denoted , arising from the predissociation of the (v,J) = (14,4) level of H2. To characterize the formation and disintegration of , we calculate the predissociation as a function of both the applied magnetic field and the dissociation energy, D, of the level. Recombination occurs when is stabilized in collisions that cause transitions to lower molecular levels. For low H↓, densities, collisions with atoms of the saturated 4He vapour dominate; we calculate the cross section in the distorted wave Born approximation and also use a coupled-channels approach. At higher densities, stabilization occurs in collisions with H↓ as well; the effect of proton exchange between the atom and the molecule ...

Resonance recombination of spin-polarized atomic hydrogen at low temperatures

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.

M. W. Reynolds

Papers

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

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

Hyperfine resonance of atomic deuterium at 1 K

Resonance recombination of spin-polarized atomic hydrogen at low temperatures

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