Observation of Fano-suppression in scattering resonances of bosonic erbium atoms

Abstract

The collisional properties of lanthanides exhibit remarkable complexity due to their many valence electrons, leading to an extraordinarily dense Feshbach spectrum showing signs of quantum chaos. Here we explore the situation of bosonic spin mixtures of erbium, adding the additional spin degree of freedom to the problem. We detect several inter- and intra-spin scattering resonances, exhibiting a peculiar asymmetric shape with a pronounced loss minimum. By developing a simplified multi-channel model we are able to recreate this characteristic behavior and to trace its origin to destructive interference between multiple pathways as predicted by Fano. We additionally observe a series of Fano-Feshbach resonances across multiple spin channels connected to the same molecular state, again confirmed by our theory. Our work opens the door for a detailed investigation to study multi-spin strongly-coupled scattering phenomena.

Figures (7)

• Figure 1: Spin-manifold and detection. a) Illustration of spin mixtures. Here we exemplary show a 50:50 mixture of ${m_J^1=-6}$ and ${m_J^2=-5}$ (${m_J^\text{tot}=-11}$) and a pure ${m_J^1=m_J^2=-5}$ sample (${m_J^\text{tot}=-10}$). b) Exemplary absorption image of the spin mixture with ${m_J^1=-6}$, ${m_J^2=-5}$ (${m_J^\text{tot}=-11}$).
• Figure 2: Observation of Fano-suppression in the $m_J^1=m_J^2=-5$ scattering channel. a) Atom number loss spectra as a function of $B$ for $m_J^1=m_J^2=-5$ ($m_J^\text{tot}=-10$) spin-polarized atoms for a hold time of $t_h=20\,$ms. b) Zoom-in on the data in a) around the Fano-shaped feature at $0.65$G. The solid line depicts a generic Fano-profile fit to the experimental data which coincides with the theory results. c) Time-resolved atom decay at three magnetic fields $B=[0.63,0.65,0.7]\,$G (triangles, squares, diamonds) across the Fano profile. The solid lines are two-body decay fits to the data, giving decay rates $L_2=[4.3(2),0.34(2),1.41(11)]\times10^{-12}\,$cm$^3$s$^{-1}$. Errorbars denote the standard error of the mean of 3-5 experimental repetitions.
• Figure 3: Square-well toy model. a) Model potentials in the case of three scattering channels (closed, entrance, loss) indicating two scattering paths: Path $1$ directly coupling the entrance and loss channel via $C_{12}$ and Path $2$ coupling the entrance and loss channel via a bound state in the closed channel with coupling strengths $C_{13}$ and $C_{32}$. b) Cross-sections $\sigma_{21}$ (inelastic, solid line) and $\sigma_{11}$ (elastic, dashed-dotted line) as a function of $\Delta E$. Markers denote the experimental $\sigma_{12}$ derived either directly from the lifetime measurements of Fig. \ref{['fig:fig2']}c (circles) or indirectly from the measured atom number of Fig. \ref{['fig:fig2']}b (squares).
• Figure 4: Molecular state crossing: (a) Loss spectra of successive spin combinations obtained in the experiment. The plots show the remaining $N_{m_J}$ after $t_h=20\,$ms from $m_J^\text{tot}=[-6, ..., -10]$ normalized to the initial atom number. Solid lines denote a fit to the experimental data. The diamonds mark the resonance position from the fits. b) Total Zeeman energy $E_{m_J^\text{tot}}$ of the scattering thresholds with the detected resonance positions for experimental (diamonds) and theory data (circles). Solid lines depict the Zeeman energy of the inferred molecular state with a magnetic moment of $\mu_\text{mol} = -2.70(4)\,\mu_B$ (experiment) and $\mu_\text{mol} = -2.328\,\mu_B$ (theory). c) Scaling of the resonance strength $\Gamma_\text{res}$ as a function of $m_J^\text{tot}$ for experimental (diamonds) and theory data (circles). The solid line shows an exponential fit through the experimental data. d) Predicted loss spectra from our toy model, see main text.
• Figure S1: Analysis of the decay processes in atom number (top) and temperature (bottom). Fits with only one-body (dashed line), two-body (solid line), and three-body (dashed-dotted line) decay according to Equ. \ref{['equ:lossorder']}. A two-body fit without temperature dependence (dotted line) is also shown for reference.