Quasiparticle properties of an impurity in a Fermi gas

Abstract

We report a study of a spin-down impurity strongly coupled to a spin-up Fermi sea (a so-called Fermi polaron) with the diagrammatic Monte Carlo (DiagMC) technique. Conditions of zero temperature and three dimensions are considered for an ultracold atomic gas with resonant interactions in the zero-range limit. A Feynman diagrammatic series is developed for the one-body and two-body propagators providing information about the polaron and molecule channel, respectively. The DiagMC technique allows us to reach diagram orders that are high enough for extrapolation to infinite order. The robustness of the extracted results is examined by checking various resummation techniques and by running the simulations with various choices for the propagators and vertex functions. It turns out that dressing the lines in the diagrams as much as possible is not always the optimal choice. We also identify classes of dominant diagrams for the one-body and two-body self-energy in the region of strong interaction. These dominant diagrams turn out to be the leading processes of the strong-coupling limit. The quasiparticle energies and Z factor are obtained as a function of the interaction strength. We find that the DiagMC results for the molecule and polaron properties are very similar to those obtained with a variational ansatz. Surprisingly, this variational ansatz gives very good predictions for the quasiparticle residue even when this residue is significantly less than 1.

Ultrafast many-body interferometry of impurities coupled to a Fermi sea

“…Indeed, for a mobile impurity and for sufficiently weak attraction where the attractive polaron is the ground state, the TBM correctly describes the long-time behavior S(t) → |α 0 | 2 e −iεpt/h . Here, |α 0 | 2 is the polaron residue (squared overlap with the non-interacting state) and ε p is the polaron energy, which are both accurately determined using a wave function of the form (8) [34].…”

Ab initioLattice Results for Fermi Polarons in Two Dimensions

“…But with increasing particle interaction strength, molecules will form by capturing one or even two particles from the Fermi sea, and this behavior has been shown to depend on the mass ratio of the two components of the Fermi gas for the 3D case [2][3][4][5][6][7][8][9][10]. In 1D, the exact analytical solution for equal masses shows that the polaron-molecule transition is a smooth crossover [11,12].In 2D the Fermi polaron properties have been studied using different theoretical and experimental approaches, and these have predicted various scenarios for the existence or absence of a polaron-molecule transition [13][14][15][16][17][18][19][20][21]. The Fermi polaron system has been studied using diagrammatic Monte Carlo (diag MC) [20,21].…”

“…The Fermi polaron system has been studied using diagrammatic Monte Carlo (diag MC) [20,21]. The diag MC method uses a worm algorithm to stochastically sample Feynman diagrams to high orders in the coupling constant.…”

“…In 2D the Fermi polaron properties have been studied using different theoretical and experimental approaches, and these have predicted various scenarios for the existence or absence of a polaron-molecule transition [13][14][15][16][17][18][19][20][21]. The Fermi polaron system has been studied using diagrammatic Monte Carlo (diag MC) [20,21].…”

Excitonic states of an impurity in a Fermi gas

“…Surprisingly, for the polaron, a simple variational calculation [12] with only one particle-hole dressing gives very accurate results compared with more sophisticated Monte Carlo calculations [4,13] and can be extended to study other possible states of the system. For example, away from the unitary regime and approaching the Bose-Einstein-condensate side ( Fig.…”