Abstract
We show that for ultracold magnetic lanthanide atoms chaotic scattering emerges due to a combination of anisotropic interaction potentials and Zeeman coupling under an external magnetic field. This scattering is studied in a collaborative experimental and theoretical effort for both dysprosium and erbium. We present extensive atom-loss measurements of their dense magnetic Feshbach-resonance spectra, analyze their statistical properties, and compare to predictions from a random-matrix-theory-inspired model. Furthermore, theoretical coupled-channels simulations of the anisotropic molecular Hamiltonian at zero magnetic field show that weakly bound, near threshold diatomic levels form overlapping, uncoupled chaotic series that when combined are randomly distributed. The Zeeman interaction shifts and couples these levels, leading to a Feshbach spectrum of zero-energy bound states with nearest-neighbor spacings that changes from randomly to chaotically distributed for increasing magnetic field. Finally, we show that the extreme temperature sensitivity of a small, but sizable fraction of the resonances in the Dy and Er atom-loss spectra is due to resonant nonzero partial-wave collisions. Our threshold analysis for these resonances indicates a large collision-energy dependence of the three-body recombination rate.
Highlights
Anisotropic interactions are a central and modern tool for engineering quantum few- and many-body processes [1]
We show that for ultracold magnetic lanthanide atoms chaotic scattering emerges due to a combination of anisotropic interaction potentials and Zeeman coupling under an external magnetic field
The magnetic field is ramped up over a few milliseconds to a magnetic-field value B, where the atoms are held in the optical dipole trap (ODT) for 500 ms for Dy, 400 ms for 168Er, and 100 ms for 167Er
Summary
Anisotropic interactions are a central and modern tool for engineering quantum few- and many-body processes [1]. For magnetic lanthanides, which include the successfully laser-cooled elements Ho [19] and Tm [20], the orbital anisotropy is a consequence of a partially filled submerged 4f electron shell that underlies a closed outer 6s shell. This leads to an electronic ground state with a total atomic angular momentum ~| with j ≫ 1. We present a RMT-inspired model to gain insight into their statistical properties as well as theoretical evidence based on coupled-channels calculations with a microscopic Hamiltonian that chaotic scattering requires both strong molecular anisotropy and Zeeman mixing to fully develop. We present experimental data and a comparison to a resonant trimer model to show that our increase in resonance density with temperature is a consequence of the strong collision-energy dependence of transitions from entrance d-wave channels of three free atoms to resonant trimer states
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