Emergence of Chaotic Scattering in Ultracold Er and Dy

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.

Quantum chaos in ultracold collisions betweenYb(1S0)andYb(3P2)

“…Following recent practice in the coldmatter literature [1,2,41], we interpolate between the Poisson and Wigner-Dyson cases using the Brody ansatz P [42]. We note that other methods of interpolating between the Poisson and Wigner-Dyson nearest-neighbor distributions exist, including rigorous semiclassical expressions [43].…”

“…Physically, the anisotropy is due to the 6p valence electron of [Xe]4f 14 6s6pYb( 3 P). As a result, the anisotropy in this system is much larger than in the Er+Er and Dy+Dy systems, which involve f-shell electrons submerged beneath a closed 6s shell [1,2]. We extrapolate the potentials at long range with the dispersion form −C 6 /R 6 [30], using calculated dispersion coefficients of 2999 and 2649 E h a 6 0 [31] for the 3 Σ g and 3 Π g states respectively.…”

“…The Wigner-Dyson distribution exhibits strong level repulsion, i.e., vanishingly small probabilities of finding levels that coincide. The Feshbach resonance spectra for Er+Er and Dy+Dy show statistics that indicate a considerable degree of chaos [1,2,14], which for Dy increases steadily with magnetic field [2].…”

“…Ultracold collisions involving the lanthanides Er and Dy in magnetic fields exhibit dense Feshbach resonance spectra that show strong signatures of quantum chaos [1][2][3]. The density of the spectra results from large reduced masses that produce a large number of bound levels.…”

An Arrested Implosion

“…Our investigations are aimed at probing strongly dipolar Bose gases of 164 Dy, which are characterized by a dipolar length a dd ¼ μ 0 μ 2 m=12πℏ 2 ≃ 131a 0 , where a 0 is the Bohr radius with μ ¼ 9.93μ B Dy's magnetic dipole moment in units of the Bohr magneton μ B , ℏ the reduced Planck constant, and m the atomic mass. The additional short-range interaction of 164 Dy, characterized by the scattering length a has been the focus of several papers [8][9][10][11], and the background scattering length was measured to be a bg ¼ 92ð8Þa 0 , modulated by many Feshbach resonances. Thus, away from Feshbach resonances at the mean-field level the dipolar interaction dominates with ε dd;bg ¼ a dd =a bg ≃ 1.45.…”