Strong-Coupling Polarons in Dilute Gas Bose-Einstein Condensates

A neutral impurity atom immersed in a dilute Bose-Einstein condensate (BEC) can have a bound ground state in which the impurity is self-localized. In this polaronlike state, the impurity distorts the density of the surrounding BEC, thereby creating the self-trapping potential minimum. We describe the self-localization in a strong-coupling approach.

Figure 1

Radial wave function obtained through the iterative procedure for $\xi /R_0=4.7,5,10,20,30,40$ (from bottom to top). In bold black line, the initial Gaussian guess. In the inset, the energy of the ground wave function vs $\xi$ (dots). In dotted line, the variational result obtained numerically. The expansion for large $\xi /R_0$ is in dashed line, and the best fit $E_b/E_0\simeq -1/\pi +3R_0/2\xi$ in solid line.

Figure 2

Minimal $\sqrt{{\rho }_B^0{a}_{IB}^4/a_{BB}}$ value for localization of the impurity as a function of the mass ratio $m_B/m_I$ obtained from weak coupling ($\alpha >1$) [7] and strong coupling [Eq. (7) and $\beta >4.7$] descriptions, dashed and solid line, respectively.

Figure 3

Effective potential of the impurity as a function of distance to the trap center for (a) attractive and (b) repulsive boson-impurity interaction, using ${\rho }_B^0(0)|a_{IB}^3|={10}^{-3}$, $|a_{IB}|/a_{BB}={10}^3$, and $m_I=m_B$. (c), (d) have $a_{IB}>0$, but the former has ${\rho }_B^0(0)|a_{IB}^3|=0.05$ and $m_I=m_B$, while in the latter ${\rho }_B^0(0)|a_{IB}^3|={10}^{-3}$ and $m_B=14.5m_I$ (${}^6\mathrm{Li}$ impurities in a ${}^{87}\mathrm{Rb}$ BEC). The dashed lines show the values at which the localization condition, $\beta >4.7$, is not fulfilled.