Refractive Contribution to the Mass of an Elementary Excitation in a Dilute Bose-Einstein Condensate

Since the pioneering works of Landau and Feynman, the origin of a roton minimum in the excitation spectrum of a quantum Bose liquid has been debated. A consensus has been reached on relation of the roton to eventual solidification, but this viewpoint still remains to be connected to the polaronic concept of an impurity pushing through a dense medium. The diagrammatic theory allows one to approach the problem qualitatively from a dilute limit. We revisit the equation for the elementary excitation spectrum obtained in the ladder approximation and argue that polaronic renormalization of the quasiparticle mass has a contribution due to matter-wave refraction. At low energies attenuation of the quasiparticle wave turns out to be dramatically suppressed by the condensate. Refractive correction to the mass is enhanced by Bose statistics at high momenta and produces autolocalization of an elementary excitation upon increasing the density.