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 (∼ 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 cs/T with the speed of sound cs. Leading corrections at finite temperature scale as T 6 /r for distances r cs/T smaller than the thermal length. For larger distances the potential shows a nonrelativistic van der Waals behavior (∼ 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 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.

Polarons and bipolarons in a two-dimensional square lattice

“…In these gases, the quasiparticle, called a polaron, consists of an impurity atom interacting with a surrounding atomic gas and we now have an accurate description of individual polarons formed in fermionic gases [16,17], whereas open questions remain regarding polarons in Bose-Einstein condensates (BECs) for strong interactions. So far, these experiments have however not revealed much information regarding the interactions between the quasiparticles, even though they have been predicted to exist both for polarons in Fermi [18][19][20][21][22][23] and Bose gases [23][24][25][26][27]. This is an important open question, since such interactions are an inherent property of quasiparticles as they affect each other by modulating the surrounding medium.…”

Collective excitations of a Bose–Einstein condensate of hard-core bosons and their mediated interactions: from two-body bound states to mediated superfluidity

“…Specifically, studies of phonon-like excitations of a weakly interacting Bose-Einstein condensate (BEC) have predicted intriguing few-and many-body phases, such as conventional superfluidity [6][7][8][9][10][11], topological superfluidity [12][13][14][15][16], bipolarons [17][18][19][20][21][22][23][24], and few-body states [25]. These studies have encouraged further investigation into the intrinsic nature of mediated interactions [26,27] and the interaction between charged particles [28,29]. However, generating, probing, and measuring experimentally induced interactions in quantum gases remains a complex challenge [30,31].…”

Trapped Ideal Bose Gas with a Few Heavy Impurities

“…Particularly important to the problem of induced forces between immersed atoms in a bosonic medium is the Bose bipolaron [40][41][42][43][44][45][46]; the problem of two (typically mutually non-interacting) impurities in a dilute Bose gas. In realistic systems, the boson-boson interaction does not allow the exact solution of the problem even in the limit of a single impurity, and only the universal tail of the induced potential at a large separation between immersed particles is accessible [47][48][49][50][51][52][53]. An exception is media formed by non-interacting particles, where all details of the (in general N -body) effective interaction can be obtained for point-like impurities.…”