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We describe the installation, commissioning, and characterization of the new injection kicker system in the Muon $g-2$ Experiment (E989) at Fermilab, which makes a precision measurement of the muon magnetic anomaly. Three Blumlein pulsers drive each of the 1.27-m-long non-ferric kicker magnets, which reside in a storage ring vacuum (SRV) that is subjected to a 1.45 T magnetic field. The new system has been redesigned relative to Muon $g-2$'s predecessor experiment, and we present those details in this manuscript.

An accurate knowledge of the scattering length is fundamental in ultracold quantum gas experiments and essential for the characterisation of the system as well as for a meaningful comparison to theoretical models. Here, we perform a careful characterisation of the s-wave scattering length $a_s$ for the four highest-abundance isotopes of erbium, in the magnetic field range from 0G to 5G. We report on cross-dimensional thermalization measurements and apply the Enskog equations of change to numerically simulate the thermalization process and to analytically extract an expression for the so-called number of collisions per re-thermalization (NCPR) to obtain $a_s$ from our experimental data. We benchmark the applied cross-dimensional thermalization technique with the experimentally more demanding lattice modulation spectroscopy and find good agreement for our parameter regime. Our experiments are compatible with a dependence of the NCPR with $a_s$, as theoretically expected in the case of strongly dipolar gases. Surprisingly, we experimentally observe a dependency of the NCPR on the density, which might arise due to deviations from an ideal harmonic trapping configuration. Finally, we apply a model for the dependency of the background scattering length with the isotope mass, allowing to estimate the number of bound states of erbium., Comment: 13 pages, 8 figures

We study the ground state properties of a system of $N$ harmonically trapped bosons of mass $m$ interacting with two-body contact interactions, from small to large scattering lengths. This is accomplished in a hyperspherical coordinate system that is flexible enough to describe both the overall scale of the gas and two-body correlations. By adapting the lowest-order constrained variational (LOCV) method, we are able to semi-quantitatively attain Bose-Einstein condensate ground state energies even for gases with infinite scattering length. In the large particle number limit, our method provides analytical estimates for the energy per particle $E_0/N \approx 2.5 N^{1/3} \hbar \omega$ and two-body contact $C_2/N \approx 16 N^{1/6}\sqrt{m\omega/\hbar}$ for a Bose gas on resonance, where $\omega$ is the trap frequency.

Experimental control of magnetic Fano-Feshbach resonances in ultracold $^{40}$K Fermi gases, using radio-frequency (RF) fields, is demonstrated. Spectroscopic measurements are made of three molecular levels within 50 MHz of the atomic continuum, along with their variation with magnetic field. Modifying the scattering properties by an RF field is shown by measuring the loss profile versus magnetic field. This work provides the high accuracy locations of ground molecular states near the s-wave Fano-Feshbach resonance, which can be used to study the crossover regime from a Bose-Einstein condensate to a Bardeen-Cooper-Schrieffer superfluid in presence of an RF field., 5 pages, 3 figures

We study the dynamics of a dilute Bose gas at zero temperature following a sudden quench of the scattering length from a noninteracting Bose condensate to unitarity (infinite scattering length). We apply three complementary approaches to understand the momentum distribution and loss rates. First, using a time-dependent variational ansatz for the many-body state, we calculate the dynamics of the momentum distribution. Second, we demonstrate that, at short times and large momenta compared to those set by the density, the physics can be well understood within a simple, analytic two-body model. We derive a quantitative prediction for the evolution of Tan's contact, which increases linearly at short times. We also study the three-body losses at finite densities. Consistent with experiments, we observe lifetimes which are long compared to the dynamics of large momentum modes., 4 pages, 3 figures

How does a chemical reaction proceed at ultralow temperatures? Can simple quantum mechanical rules such as quantum statistics, single scattering partial waves, and quantum threshold laws provide a clear understanding for the molecular reactivity under a vanishing collision energy? Starting with an optically trapped near quantum degenerate gas of polar $^{40}$K$^{87}$Rb molecules prepared in their absolute ground state, we report experimental evidence for exothermic atom-exchange chemical reactions. When these fermionic molecules are prepared in a single quantum state at a temperature of a few hundreds of nanoKelvins, we observe p-wave-dominated quantum threshold collisions arising from tunneling through an angular momentum barrier followed by a near-unity probability short-range chemical reaction. When these molecules are prepared in two different internal states or when molecules and atoms are brought together, the reaction rates are enhanced by a factor of 10 to 100 due to s-wave scattering, which does not have a centrifugal barrier. The measured rates agree with predicted universal loss rates related to the two-body van der Waals length.

We characterize zero-temperature dipolar Bose gases under external spherical confinement as a function of the dipole strength using the essentially exact many-body diffusion Monte Carlo (DMC) technique. We show that the DMC energies are reproduced accurately within a mean-field framework if the variation of the s-wave scattering length with the dipole strength is accounted for properly. Our calculations suggest stability diagrams and collapse mechanisms of dipolar Bose gases that differ significantly from those previously proposed in the literature.

Three magnetic-field induced heteronuclear Feshbach resonances were identified in collisions between bosonic 87Rb and fermionic 40K atoms in their absolute ground states. Strong inelastic loss from an optically trapped mixture was observed at the resonance positions of 492, 512, and 543 +/- 2 G. The magnetic-field locations of these resonances place a tight constraint on the triplet and singlet cross-species scattering lengths, yielding -281 +/- 15 Bohr and -54 +/- 12 Bohr, respectively. The width of the loss feature at 543 G is 3.7 +/- 1.5 G wide; this broad Feshbach resonance should enable experimental control of the interspecies interactions., Comment: revtex4 + 5 EPS figures

We have measured the intensity dependent rate and frequency shift of a photoassociation transition in a quantum degenerate gas of 7Li. The rate increases linearly with photoassociation laser intensity for low intensities, whereas saturation is observed at higher intensities. The measured rates and shifts agree reasonably well with theory within the estimated systematic uncertainties. Several theoretically predicted saturation mechanisms are discussed, but a theory in which saturation arises because of quantum mechanical unitarity agrees well with the data., Comment: 12 pages, 3 figures, to be published in PRL

We perform detailed close-coupling calculations for the rubidium isotopes 85Rb and 87Rb to ascertain the nature of their spinor Bose-Einstein condensates. These calculations predict that the spinor condensate for the spin-1 boson 87Rb has a ferromagnetic nature. The spinor condensates for the spin-2 bosons 85Rb and 87Rb, however, are both predicted to be polar. The nature of a spin-1 condensate hinges critically on the sign of the difference between the s-wave scattering lengths for total spin 0 and 2 while the nature of a spin-2 condensate depends on the values of the differences between s-wave scattering lengths for the total spin 0, 2 and 4. These scattering lengths were extracted previously and found to have overlapping uncertainties for all three cases, thus leaving the nature of the spinor condensates ambiguous. The present study exploits a refined uncertainty analysis of the scattering lengths based on recently improved result from experimental work by Roberts et al., which permits us to extract an unambiguous result for the nature of the ground state spinor condensates., Comment: 5 pages, 3 figures

We have measured independently both s-wave and p-wave cross-dimensional thermalization rates for ultracold potassium-40 atoms held in a magnetic trap. These measurements reveal that this fermionic isotope has a large positive s-wave triplet scattering length in addition to a low temperature p-wave shape resonance. We have observed directly the p-wave threshold law which, combined with the Fermi statistics, dramatically suppresses elastic collision rates at low temperatures. In addition, we present initial evaporative cooling results that make possible these collision measurements and are a precursor to achieving quantum degeneracy in this neutral, low-density Fermi system., 5 pages, 3 figures, 1 table