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 (54)

• Modern Theory of Nuclear Forces
• Chiral effective field theory and nuclear forces
• Nuclear effective field theory: status and perspectives
• Observation of Attractive and Repulsive Polarons in a Bose-Einstein Condensate
• Bose polarons in the strongly interacting regime
• Quantum dynamics of impurities in a 1D Bose gas
• General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas
• Motion of a heavy impurity through a Bose-Einstein condensate
• Field-theoretical study of the Bose polaron
• Quantum transport through a Tonks-Girardeau gas
• Quantum Fluctuations in the Superfluid State of the BCS-BEC Crossover
• Small polarons in dilute gas Bose-Einstein condensates
• Bose polarons near quantum criticality
• Impurity in a Bose-Einstein condensate: study of the attractive and repulsive branch using quantum Monte-Carlo methods
• Dynamics of single neutral impurity atoms immersed in an ultracold gas
• Quantum dynamics of ultracold Bose polarons
• Impurity in a Bose-Einstein condensate and the Efimov effect
• Evolution from BCS Superconductivity to Bose Condensation: Analytic Results for the crossover in three dimensions
• Creation of Rydberg Polarons in a Bose Gas
• Bipolarons in a Bose-Einstein Condensate
• Non-equilibrium quantum dynamics and formation of the Bose polaron
• Goldstone mode and pair-breaking excitations in atomic Fermi superfluids
• Casimir forces between defects in one-dimensional quantum liquids
• Coalescence of Two Impurities in a Trapped One-dimensional Bose Gas
• Landau Effective Interaction between Quasiparticles in a Bose-Einstein Condensate
• Universality of an impurity in a Bose-Einstein condensate
• Two impurities in a Bose-Einstein condensate: from Yukawa to Efimov attracted polarons
• Interaction of Impurity Atoms in Bose-Einstein-Condensates
• Polarons in Ultracold Fermi Superfluids
• Theory of excitation of Rydberg polarons in an atomic quantum gas
• Phonon-mediated Casimir interaction between mobile impurities in one-dimensional quantum liquids
• 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
• Theory of a resonantly interacting impurity in a Bose-Einstein 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
• The Casimir-like effect in a one-dimensional Bose gas
• Heavy polarons in ultracold atomic Fermi superfluids at the BEC-BCS crossover: formalism and applications
• Pauli Blocking Effect on Efimov States Near Feshbach Resonance
• 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
• Few vs many-body physics of an impurity immersed in a superfluid of spin 1/2 attractive fermions
• Phonon-mediated Casimir interaction between finite mass impurities
• Finite temperature effective field theory for dark solitons in superfluid Fermi gases
• Bose polaron in spherical trap potentials: Spatial structure and quantum depletion
• Derivation of the effective action of a dilute Fermi gas in the unitary limit of the BCS-BEC crossover
• BEC-Polaron gas in a boson-fermion mixture : a many-body extension of Lee-Low-Pines theory
• T-matrix approach to the phonon-mediated Casimir interaction
• Mean-field vs RPA calculation of the energy of an impurity immersed in a spin 1/2 superfluid
• Perfect screening of the inter-polaronic interaction
• Random walk of a massive quasiparticle in the phonon gas of an ultralow temperature superfluid

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• Polaronic neutron in dilute alpha matter: A $p$-wave Bose polaron
• Tunable Fujita-Miyazawa-Type Three-Body Force in Ultracold Atoms
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• Polaronic dressing of bound states
• Resonantly enhanced superconductivity mediated by spinor condensates
• The density of a one-dimensional Bose gas far from an impurity
• Complex-valued in-medium potential between heavy impurities in ultracold atoms