Universal van der Waals Force Between Heavy Polarons in Superfluids,Physical Review Letters

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Universal van der Waals Force Between Heavy Polarons in Superfluids
Physical Review Letters ( IF 8.1 ) Pub Date : 2022-11-30 , DOI: 10.1103/physrevlett.129.233401
Keisuke Fujii ₁ , Masaru Hongo _{2,

3} , Tilman Enss ₁

Affiliation

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.

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