Bose polaron problem: Effect of mass imbalance on binding energy

By means of quantum Monte Carlo methods we calculate the binding energy of an impurity immersed in a Bose-Einstein condensate at $T=0$. The focus is on the attractive branch of the Bose polaron and on the role played by the mass imbalance between the impurity and the surrounding particles. For an impurity resonantly coupled to the bath, we investigate the dependence of the binding energy on the mass ratio and on the interaction strength within the medium. In particular, we determine the equation of state in the case of a static (infinite mass) impurity, where three-body correlations are irrelevant and the result is expected to be a universal function of the gas parameter. For the mass ratio corresponding to ${}^{40}\mathrm{K}$ impurities in a gas of ${}^{87}\mathrm{Rb}$ atoms, we provide an explicit comparison with the experimental findings of a recent study carried out at JILA.

Figure 1

Binding energy of the polaron for resonant coupling ($1/b=0$) as a function of the mass ratio $m_B/m_I$. Results corresponding to different values of the interaction strength in the bath are shown. In particular, the value $n{a}^3=2.66\times {10}^{-5}$ refers to the conditions of the JILA experiment [1].

Figure 2

Inverse binding energy of the polaron for resonant coupling ($1/b=0$) as a function of the gas parameter in the bath. Results are shown for a mobile impurity with $m_B/m_I=1$ (see Ref. [8]) and for a static impurity ($m_B/m_I=0$). The solid (static impurity) and dashed line (mobile impurity) are polynomial fits to the data including first- and second-order terms in $n^{1/3}a$.

Figure 3

Binding energy of the impurity along the attractive branch as a function of the impurity-bath coupling $1/\left(n^{1/3}b\right)$. The mass ratio is $m_B/m_I=2$ and is close to the case of ${}^{40}\mathrm{K}$ impurities in a BEC of ${}^{87}\mathrm{Rb}$ atoms as in the JILA experiment [1]. The gas parameter has also been chosen to reproduce the experimental value $n{a}^3=2.66\times {10}^{-5}$. The experimental points are reproduced from Fig. 3 in Ref. [1]. The blue dashed line corresponds to the prediction of perturbation theory including first- and second-order terms.