Feshbach resonances are the essential tool to control interaction between atoms in ultracold quantum gases. They have found numerous experimental applications, opening up way important breakthroughs. This review broadly covers phenomenon of gases and their main applications. includes theoretical background models for description resonances, methods find characterize a discussion properties various atomic species mixed systems, an overview key experiments with Bose-Einstein condensates,...

Photoassociation is the process in which two colliding atoms absorb a photon to form an excited molecule. The development of laser-cooling techniques for producing gases at ultracold $(<1\phantom{\rule{0.3em}{0ex}}\mathrm{mK})$ temperatures allows photoassociation spectroscopy be performed with very high spectral resolution. Of particular interest investigation molecular states whose properties can related, precision, their constituent ``complications'' chemical binding accounted by few...

This review article contains the 2018 self-consistent set of values constants and conversion factors physics chemistry recommended by Committee on Data for Science Technology (CODATA). The CODATA are based a least-squares adjustment that takes into account all data available up to end 2018. Details selection methodology described.

We study the magnetic-field dependence of cross sections for elastic and inelastic collisions pairs ultracold cesium atoms in a magnetic trap, calculated with coupled-channels method. pay special attention to f=3, ${\mathit{m}}_{\mathit{f}}$=-3 weak-field seeking state lower hyperfine manifold. The show pronounced resonance structure. discuss its origin, starting from pure bound singlet triplet rovibrational ${\mathrm{Cs}}_{2}$ states introducing perturbations due Zeeman interactions. also...

We report on the observation of Feshbach resonances in an ultracold mixture two fermionic species, $^{6}\mathrm{Li}$ and $^{40}\mathrm{K}$. The experimental data are interpreted using a simple asymptotic bound state model full coupled channels calculations. This unambiguously assigns observed terms various $s$- $p$-wave molecular states fully characterizes ground-state scattering properties any combination spin states.

We report the 2018 self-consistent values of constants and conversion factors physics chemistry recommended by Committee on Data International Science Council. The can also be found at physics.nist.gov/constants. are based a least-squares adjustment that takes into account all theoretical experimental data available through 31 December 2018. A discussion major improvements as well inconsistencies within is given. former include decrease in uncertainty dimensionless fine-structure constant...

The special least-squares adjustment of the values fundamental constants, carried out by Committee on Data for Science and Technology (CODATA) in summer 2017, is described detail. It based all relevant data available 1 July 2017. purpose this to determine numerical Planck constant h, elementary charge e, Boltzmann k, Avogadro NA revised SI expected be established 26th General Conference Weights Measures when it convenes 13–16 November 2018.

We report the 2022 self-consistent values of constants and conversion factors physics chemistry recommended by Committee on Data International Science Council (CODATA). The can also be found at physics.nist.gov/constants. are based a least-squares adjustment that takes into account all theoretical experimental data available through 31 December 2022. A discussion major improvements as well inconsistencies within is given.

We employ radio-frequency spectroscopy on weakly bound $^{6}\mathrm{Li}_{2}$ molecules to precisely determine the molecular binding energies and energy splittings between states for different magnetic fields. These measurements allow us extract interaction parameters of ultracold $^{6}\mathrm{Li}$ atoms based a multichannel quantum scattering model. singlet triplet lengths be ${a}_{s}=45.167(8){a}_{0}$ ${a}_{t}=\ensuremath{-}2140(18){a}_{0}$ ($1{a}_{0}=0.052\text{ }917\text{ }7\text{ }\text{...

We study conditions necessary for the observation of Bose-Einstein condensation in a magnetically trapped sample atomic Cs gas. These are associated with value elastic scattering length, rate events, and lifetime decay density due to both magnetic dipole relaxation two-body collisions, as well recombination ${\mathrm{Cs}}_{2}$ three-body collisions. find that, on basis these conditions, prospects observing favorable gas ground-state atoms highest state lowest hyperfine manifold. In all...

Feshbach resonances in lithium-6 were experimentally studied and theoretically analyzed. In addition to two previously known s-wave resonances, we found three p-wave resonances. Four of these are narrow yield a precise value the singlet scattering length, but do not allow us accurately predict location broad resonance near 83 mT. Its position was measured molecule-dissociation experiment for which we, here, discuss systematic shifts.

We have calculated the time-dependent dynamics of two ultracold Na atoms in an atom trap where a magnetic field $B(t)$ moves Feshbach resonance state across energy threshold for binary collision. Our coupled-channel scattering calculations, which reproduce observed properties such resonances sodium collisions, can be reduced to effective two-channel configuration-interaction model one bound and continuum. The is adapted describe induced by trapped either strongly confining single well...

We report a preliminary value for the zero magnetic field Na 2S(f = 1, m - 1) + scattering length, a1,-1. This parameter describes low-energy elastic two-body processes in dilute gas of composite bosons and determines, to large extent, macroscopic wavefunction Bose condensate trap. Our length is obtained from photoassociative spectroscopy with samples uncondensed atoms. The temperature atoms sufficiently low that contributions three lowest partial waves dominate spectrum. observed lineshapes...

We propose new experiments with high sensitivity to a possible variation of the electron-to-proton mass ratio $\ensuremath{\mu}\ensuremath{\equiv}{m}_{e}/{m}_{p}$. consider nearly degenerate pair molecular vibrational levels, each associated different electronic potential. With respect change in $\ensuremath{\mu}$, splitting between such levels can be large both on an absolute scale and relative splitting. demonstrate existence pairs states ${\mathrm{Cs}}_{2}$, where narrow spectral lines...

We have studied magnetic Feshbach resonances in an ultracold sample of Na prepared the absolute hyperfine ground state. report on observation three $s$-, eight $d$-, and $g$-wave resonances, including a more precise determination two known $s$-wave one resonance at field exceeding 200 mT. Using coupled-channels calculation we improved sodium ground-state potentials by taking into account these new experimental data derived values for scattering lengths. In addition, description molecular...

We consider the problem of cold atomic collisions in tight traps, where absolute scattering length may be larger than trap size. As long as size ground state is a characteristic van der Waals potential, energy eigenvalues can computed self-consistently from phase shift for untrapped atoms. By comparing with exact numerical trapping plus interatomic potentials, we verify that our model gives accurate up to milliKelvin energies single-channel s-wave ${}^{23}\mathrm{Na}$ atoms an isotropic...

We form ultracold Na2 molecules by single-photon photoassociation of a Bose-Einstein condensate, measuring the rate, linewidth, and light shift J = 1, v 135 vibrational level A1 Sigma (+)(u) molecular state. The rate constant increases linearly with intensity, even where it is predicted that many-body effects might limit rate. Our observations are in good agreement two-body theory having no free parameters.

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

We have observed and located more than 60 magnetic field-induced Feshbach resonances in ultracold collisions of ground-state $^{133}\mathrm{Cs}$ atoms. Multiple extremely weak associated with $g$-wave molecular states are detected through variations the radiative collision cross sections. The spectroscopy allows us to determine interactions between cesium atoms energy structure near dissociation continuum unprecedented precision. Our work not only represents a very successful collaboration...

We observe bound states just below the dissociation limit and shape Feshbach resonances between ground state hyperfine asymptotes by Raman spectroscopy on a molecular beam of sodium dimers. The rotational selectivity two-photon transition gives access to specific nuclear motion thus cold collision properties two colliding atoms. Modeling collisional resonance structures requires multichannel treatment dynamics that uses highly accurate $X{}^{1}{\ensuremath{\Sigma}}_{g}^{+}$...

We show that there are effective three- and higher-body interactions generated by the two-body collisions of atoms confined in lowest vibrational states a three-dimensional (3D) optical lattice. The collapse revival dynamics approximate coherent loaded into lattice particularly sensitive probe these interactions; visibility interference fringes depend on both two-, energy scales, produce an initial dephasing can help explain surprisingly rapid decay revivals seen experiments. If...

Condensates of spin-1 sodium display rich spin dynamics due to the antiferromagnetic nature interactions in this system. We use Faraday rotation spectroscopy make a continuous and minimally destructive measurement over multiple oscillations on single evolving condensate. This method provides sharp signature locate magnetically tuned separatrix phase space which depends net magnetization. also observe transition from two- three-component condensate at low but finite temperature using...