Effective interactions in a quantum Bose-Bose mixture
Serguey Andreev, ITMO University, St. Petersburg, Russia
Application of the methods of Quantum Electrodynamics (QED) to a system of bosons at absolute zero temperature put forward by Spartak Beliaev in 1958 has been one of the most powerful analytical methods in studies of Bose-Einstein condensates. The Beliaev theory provides a prescription of replacement of the actual microscopic interaction by an effective potential which can be used for perturbative expansion of the many-body Hamiltonian. Originally designed for one-component systems, the method has recently been applied to binary Bose mixtures in the context of supersolidity and stabilization of collapsing Bose-Einstein condensates by quantum fluctuations. The present work is aimed at investigation of legitimacy of extrapolation of the Beliaev prescription to two-component systems. We show that quantum scatterings of different components, which until now have been assumed independent, can interfere due to the Andreev-Bashkin entrainment effect. The effect manifests itself in renormalization of the elementary excitations of the system. This result has escaped the earlier considerations based on the Fourier expansion of small-amplitude oscillations of the order parameter. We explain how one can account for the effect by using a properly generalized Bogoliubov approach. In 3D the effect appears in the second order of the perturbation theory, which makes possible using the concept of effective potential in this case. The entrainment arises due to « dressing » of magnons with Bogoliubov phonon modes, by analogy with the physics of Bose polaron. We exploit this fruitful analogy to speculate on possible formation of a magnon crystal in the strongly-interacting regime.