Effective interactions between two impurities in quasi-two-dimensional dipolar Bose-Einstein condensates

We investigate the effective interaction between two heavy impurities immersed in a quasi-two-dimensional dipolar Bose-Einstein condensate via a variation approach. We show that the mediated interaction is highly tunable via the contact and the dipole-dipole interactions between the background gas atoms. Interestingly, the mediated interaction potential may become an oscillating function of inter-impurity distance when roton excitation emerges under sufficiently strong dipolar interaction. Our system therefore provides an efficient way for tuning the mediated interaction between impurities.