Scattering of two heavy Fermi polarons: Resonances and quasibound states

Abstract

Impurities in a Fermi sea, or Fermi polarons, experience a Casimir interaction induced by quantum fluctuations of the medium. When there is short-range attraction between impurities and fermions, also the induced interaction between two impurities is strongly attractive at short distance and oscillates in space for larger distances. We theoretically investigate the scattering properties and compute the scattering phase shifts and scattering lengths between two heavy impurities in an ideal Fermi gas at zero temperature. While the induced interaction between impurities is weakly attractive for weak impurity-medium interactions, we find that impurities strongly and attractively interacting with the medium exhibit resonances in the induced scattering with a sign change of the induced scattering length and even strong repulsion. These resonances occur whenever a threebody Efimov bound state appears at the continuum threshold. At energies above the continuum threshold, we find that the Efimov state in medium can turn into a quasi-bound state with a finite decay width.

Impurities in a one-dimensional Bose gas: the flow equation approach

“…We estimate the induced impurity-impurity interaction using the Born-Oppenheimer approximation [50][51][52] (see Refs. [53][54][55][56][57] for related studies in three spatial dimensions), i.e., for m → ∞. It is known that the Born-Oppenheimer approximation captures short-range correlations, which define overall properties of impurity-impurity interactions [50,58].…”

Effective pair interaction between impurity particles induced by a dense Fermi gas

“…The induced interaction is attractive and has the potential to overcompensate the repulsion between the polarons which may even cause the formation of a new quasi particle, the so-called bipolaron [1,3,6]. Other examples arise in the theory of ultra cold atoms, for instance, Casimir-type forces between heavy fermions placed into a Fermi sea [15] or effective interactions between Fermi polarons [5,13] or angulons [12]. The effect of fermionmediated interactions is known also for dilute mixtures of Bose-Fermi gases [7,10,16] for which experimental observations have been reported in [2,4].…”

Self-stabilized Bose polarons

“…Here a(r) and r eff (r) obey the boundary conditions a(0) = 0, r eff (0) = 0, and account for the phase shift accumulated by the scattering wave function (for the generalization of the variable phase equation to singular potentials see [49]). Correspondingly, the differential equations (11) are integrated from r = 0 .…”