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 $r ≪ c_{s} / T$ 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 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.

K. Fujii, M. Hongo, T. Enss, “Universal van der Waals Force between Heavy Polarons in Superfluids”, Phys. Rev. Lett. 129, 233401 (2022).

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.129.233401

Related to Project C02, C03