Mediated interactions between ions in quantum degenerate gases

Abstract

We explore the interaction between two trapped ions mediated by a surrounding quantum degenerate Bose or Fermi gas. Using perturbation theory valid for weak atom-ion interaction, we show analytically that the interaction mediated by a Bose gas has a power-law behaviour for large distances whereas it has a Yukawa form for intermediate distances. For a Fermi gas, the mediated interaction is given by a power-law for large density and by a Ruderman-Kittel-Kasuya-Yosida form for low density. For strong atom-ion interactions, we use a diagrammatic theory to demonstrate that the mediated interaction can be a significant addition to the bare Coulomb interaction between the ions, when an atom-ion bound state is close to threshold. Finally, we show that the induced interaction leads to substantial and observable shifts in the ion phonon frequencies.

main text: 5 pages, 4 figures. Supplemental materials: 6 pages, 5 figures

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• Collective excitations of a Bose-Einstein condensate of hard-core bosons and their mediated interactions: from two-body bound states to mediated superfluidity
• Ion solvation in atomic baths: from snowballs to polarons
• Modified mean field ansatz for charged polarons in a Bose-Einstein condensate
• Exact results for heavy unitary Bose polarons
• Fermi polaron in atom-ion hybrid systems
• Mediated Interactions and Damping Effects in Superfluid Mixtures of Bose and Fermi Gases
• Cooling dynamics of a free ion in a Bose-Einstein condensate
• Tunable Fujita-Miyazawa-Type Three-Body Force in Ultracold Atoms
• Phonon-mediated quantum gates in trapped ions coupled to an ultracold atomic gas
• Polaronic dressing of bound states
• Probing spatially resolved spin density correlations with trapped excitons
• Universality in Ionic Three-body Systems Near an Ion-atom Feshbach Resonance