Impurity in a Bose-Einstein condensate: Study of the attractive and repulsive branch using quantum Monte Carlo methods

Abstract

We investigate the properties of an impurity immersed in a dilute Bose gas at zero temperature using quantum Monte Carlo methods. The interactions between bosons are modeled by a hard-sphere potential with scattering length a, whereas the interactions between the impurity and the bosons are modeled by a short-range, square-well potential where both the sign and the strength of the scattering length b can be varied by adjusting the well depth. We characterize the attractive and the repulsive polaron branch by calculating the binding energy and the effective mass of the impurity. Furthermore, we investigate the structural properties of the bath, such as the impurity-boson contact parameter and the change of the density profile around the impurity. At the unitary limit of the impurity-boson interaction, we find that the effective mass of the impurity remains smaller than twice its bare mass, while the binding energy scales with 2 n 2/3 /m, where n is the density of the bath and m is the common mass of the impurity and the bosons in the bath. The implications for the phase diagram of binary Bose-Bose mixtures at low concentrations are also discussed.

Bose Polarons in the Strongly Interacting Regime

“…We report measurements of the Bose polaron energies and lifetimes using RF spectroscopy of fermionic 40 K impurities in a BEC of 87 Rb atoms. We tune the impurityboson interactions using a Feshbach resonance, and our measurements reveal both an attractive and a repulsive polaron branch, whose energies agree with recent predictions [11][12][13]. We find that the Bose polaron exists across the strongly interacting regime and has a larger binding energy than does the low-density, two-body molecular state.…”

“…Impurity atoms immersed in a degenerate bosonic or fermionic atomic gas are a convenient experimental realization for Bose or Fermi polaron physics, respectively. Recent theoretical work [2][3][4][5][6][7][8][9] has explored the Bose polaron case, and the ability to use a Feshbach resonance to tune [10] the impurity-boson scattering length a IB opens the possibility of exploring the Bose polaron in the strongly interacting regime [11][12][13][14]. Experiments to date [15][16][17][18][19][20] have focused on the weak Bose polaron limit.…”

Repulsive polarons in alkaline-earth-metal-like atoms across an orbital Feshbach resonance

“…As the limiting case of a many-body system in the large polarization limit, mobile impurity and its associated quasi-particle excitations contain valuable information of the underlying system. Whereas impurity problems in the background of Bose gases or Fermi condensates have attracted considerable attention in recent years [44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60][61][62][63], here we focus on the case of an impurity against a non-interacting Fermi sea. In alkali atoms, it has been shown that the impurity can either form a tightly bound molecule with a majority atom, or induce collective particle-hole excitations in the Fermi sea arXiv:1710.05166v1 [cond-mat.quant-gas] 14 Oct 2017…”

Impurity states in the one-dimensional Bose gas

“…Recently, a great attention of theorists [1][2][3][4][5][6][7][8][9][10][11] has been paid to the analysis of a mobile impurity properties in the Bose gas. Such a renascence of the old problem well-studied in the context of a single 3 He atom immersed in liquid 4 He (see, for instance [13][14][15][16], and references there) is stimulated by the success of the experimental techniques [17,18] where the possibility to control a small amount of impurity particles strongly coupled to the bosonic bath is demonstrated.…”