Universal van der Waals Force Between Heavy Polarons in Superfluids

Abstract

We investigate the long-range behavior of the induced Casimir interaction between two spinless heavy impurities, or polarons, in superfluid cold atomic gases. With the help of effective field theory (EFT) of a Galilean invariant superfluid, we show that the induced impurity-impurity potential at long distance universally shows a relativistic van der Waals-like attraction ($\sim 1/r^7$) resulting from the exchange of two superfluid phonons. We also clarify finite temperature effects from the same two-phonon exchange process. The temperature $T$ introduces the additional length scale $c_s/T$ with the speed of sound $c_s$. Leading corrections at finite temperature scale as $T^6/r$ for distances $r\ll c_s/T$ smaller than the thermal length. For larger distances the potential shows a nonrelativistic van der Waals behavior ($\sim T/r^6$) instead of the relativistic one. Our EFT formulation applies not only to weakly coupled Bose or Fermi superfluids but also to that composed of strongly-coupled unitary fermions with a weakly coupled impurity. The sound velocity controls the magnitude of the van der Waals potential, which we evaluate for the fermionic superfluid in the BCS-BEC crossover.

main text: 7 pages, 3 figures. Supplemental material: 5 pages, 2 figures

References in corpus (18)

• Chiral effective field theory and nuclear forces
• General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas
• Quantum transport through a Tonks-Girardeau gas
• Quantum Fluctuations in the Superfluid State of the BCS-BEC Crossover
• Goldstone mode and pair-breaking excitations in atomic Fermi superfluids
• Polarons in Ultracold Fermi Superfluids
• Polaronic atom-trimer continuity in three-component Fermi gases
• Polaron Interactions and Bipolarons in One-Dimensional Bose Gases in the Strong Coupling Regime
• Universal aspects of a strongly interacting impurity in a dilute Bose condensate
• Connecting few-body inelastic decay to many-body correlations: a weakly coupled impurity in a resonant Fermi gas
• Dynamical quantum Cherenkov transition of fast impurities in quantum liquids
• Casimir interaction among heavy fermions in the BCS-BEC crossover
• Pauli Blocking Effect on Efimov States Near Feshbach Resonance
• Heavy polarons in ultracold atomic Fermi superfluids at the BEC-BCS crossover: formalism and applications
• Field-theoretical approach to the Casimir-like interaction in a one-dimensional Bose gas
• Scattering of two heavy Fermi polarons: resonances and quasibound states
• Mediated interactions between ions in quantum degenerate gases
• Mean-field vs RPA calculation of the energy of an impurity immersed in a spin 1/2 superfluid

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• Modified mean field ansatz for charged polarons in a Bose-Einstein condensate
• Universal properties of dipolar Bose polarons in two dimensions
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