We use the Gross-Pitaevskii equation (GPe) to study the motion of a heavy impurity immersed in a weakly interacting Bose-Einstein condensate and interacting with the bosons via an attractive boson-impurity potential. We construct a perturbative solution to the GPe in powers of impurity velocity in the case when the boson-impurity potential is tuned to unitarity, resulting in a unitary polaron, and calculate its effective mass. In addition, we calculate the interaction energy of two unitary polarons which are sufficiently far apart. Our formalism also reproduces the results for both the mass and interaction energy obtained at weak boson-impurity coupling.

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• Bose-Einstein condensates
• Polarons
• Atomic gases
• Mean field theory
• Variational approach