Strong coupling Bose polarons in a two-dimensional gas

We study the properties of Bose polarons in two dimensions using quantum Monte Carlo techniques. Results for the binding energy, the effective mass, and the quasiparticle residue are reported for a typical strength of interactions in the gas and for a wide range of impurity-gas coupling strengths. A lower and an upper branch of the quasiparticle exist. The lower branch corresponds to an attractive polaron and spans from the regime of weak coupling where the impurity acts as a small density perturbation of the surrounding medium to deep bound states which involve many particles from the bath and extend as far as the healing length. The upper branch corresponds to an excited state where due to repulsion a low-density bubble forms around the impurity but might be unstable against decay into many-body bound states. Interaction effects strongly affect the quasiparticle properties of the polaron. In particular, in the strongly correlated regime, the impurity features a vanishing quasiparticle residue, signaling the transition from an almost free quasiparticle to a bound state involving many atoms from the bath.

Figure 1

Average over many snapshots of the particle positions around the impurity for three characteristic values of the impurity-bath coupling constant $ln\left(k_{F}a\right)$. The impurity is located in the center, and distances are in units of the healing length $\xi$. The local density $n\left(r\right)$ is estimated by summing particles over a square grid of size $L/100$, where $L$ is the size of the simulation box, and the color bar indicates the ratio $n\left(r\right)/n$ over the bulk density $n$. At weak coupling, impurities form polarons, i.e., almost free quasiparticles slightly dressed by the medium (right and left upper panels). On the attractive branch as the coupling $ln\left(k_{F}a\right)>0$ is decreased, the impurity forms a many-body bound state involving up to few tens of particles, and whose size is as large as the healing length (central upper panel).

Figure 2

Polaron energy as a function of the coupling strength $ln\left(k_{F}a\right)$ for the attractive and repulsive branches (circles). The dashed line shows the dimer binding energy ${\epsilon }_b$, and the solid line shows the perturbation result from Eq. (5). The coupling constant of the gas is ${\tilde{g}}_B=0.136$.

Figure 3

Effective mass $m^{*}$ of the polaron as a function of the coupling strength $ln\left(k_{F}a\right)$. The coupling constant of the Bose gas is ${\tilde{g}}_B=0.136$.

Figure 4

Residue $Z_0$ of the polaron as a function of the coupling strength $ln\left(k_{F}a\right)$ [65]. The coupling constant of the gas is ${\tilde{g}}_B=0.136$.

Figure 5

Variational Monte Carlo results for the polaron energy interpolating between the attractive and the repulsive branches. Circles show the diffusion Monte Carlo results reported in Fig. 2 in the main text. Solid lines correspond to the perturbation theory results in Eq. (5) of the main text.