Induced Interactions and Bipolarons in Spin-Orbit Coupled Bose-Einstein Condensates

Impurities immersed in a Bose-Einstein condensate (BEC) can interact indirectly through the exchange of Bogoliubov excitations. These impurities, which form dressed quasiparticles known as Bose polarons due to their interaction with the BEC, can pair up to form a bound state called bipolarons, via an induced interaction. Previous studies on induced interactions have primarily focused on cases with an isotropic excitation spectrum. In this work, we investigate the properties of induced interactions and bipolarons mediated by anisotropic Bogoliubov excitations using field theory. Taking a BEC with spin-orbit coupling as an example, we show that the induced interaction becomes anisotropic. Notably, a double-minima feature appears in the induced interaction in momentum space due to the exchange of roton excitations. Additionally, we calculate the binding energy and wave functions of these bipolarons induced by anisotropic interactions. Unlike previously studied bipolarons formed through the exchange of isotropic phonon excitations, we identify a new type of bipolarons whose wave functions feature a double-peak structure under strong impurity-boson interactions. Our work extends the theory of induced interactions from isotropic to anisotropic systems, and reveals the novel features in both the induced interactions and bipolarons arising from BEC with an unconventional excitation spectrum.