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arXiv:1905.10125 · Physical Review A

Two-dimensional repulsive Fermi polarons with short- and long-range interactions

Raúl Bombín, Tommaso Comparin, Gianluca Bertaina, Ferran Mazzanti, S. Giorgini, Jordi Boronat

Published Aug 9, 2019• 15 citations
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Abstract

We study the repulsive polaron problem in a two-component two-dimensional system of fermionic atoms. We use two different interaction models: a short-range (hard-disk) potential and a dipolar potential. In our approach, all the atoms have the same mass and we consider the system to be composed of a uniform bath of a single species and a single atomic impurity. We use the diffusion Monte Carlo method to evaluate polaron properties such as its chemical potential and pair distribution functions, together with a discussion on the deficit of volume induced by the impurity. We also evaluate observables that allow us to determine the validity of the quasiparticle picture: the quasiparticle residue and the effective mass of the polaron. Employing two different potentials allows us to identify the universality regime, where the properties depend only on the gas parameter $n{a}_{s}^{2}$ fixed by the bath density and the two-dimensional scattering length.

DOI
10.1103/physreva.100.023608

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Quantum Monte Carlo techniques are employed to study the properties of polarons in an ultracold Fermi gas, at T=0T=0T=0, and in the unitary regime using both a zero-range model and a square-well potential. For a fixed density, the potential range is varied and results are extrapolated and compared against a zero-range model. A discussion regarding the choice of an interacting potential with a finite range is presented. We compute the polaron effective mass, the polaron binding energy, and the effective coupling between them. The latter is obtained using the Landau-Pomeranchuk's weakly interacting quasiparticle model. The contact parameter is estimated by fitting the pair distribution function of atoms in different spin states.
We construct the simplest density functional for the problem of a single impurity interacting with a Fermi gas via a long-ranged potential using the Thomas-Fermi approach. We find that the Fermi polaron is fully bosonized in two dimensions, as the model results in the Landau-Pekar functional known from the Bose polaron problem, and in its many-image extension in other dimensions. We discuss applications of our theory for the two-dimensional exciton-polaron and the ionic polaron problem and compute the effective mass for these cases, finding a self-trapping transition with order dependent on the dimensionality.