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 () resulting from the exchange of two superfluid phonons. We also clarify finite temperature effects from the same two-phonon exchange process. The temperature introduces the additional length scale with the speed of sound . Leading corrections at finite temperature scale as for distances smaller than the thermal length. For larger distances the potential shows a nonrelativistic van der Waals behavior () instead of the relativistic one. Our EFT formulation applies not only to weakly coupled Bose or Fermi superfluids but also to those composed of strongly correlated 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.
- Received 10 June 2022
- Revised 22 September 2022
- Accepted 2 November 2022
DOI:https://doi.org/10.1103/PhysRevLett.129.233401
© 2022 American Physical Society