A diagrammatic approach to composite, rotating impurities
Giacomo Bighin — Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria

The study of composite, rotating impurities interacting with a quantum many-body environment is extremely important for the description of several experimental settings: cold molecules in a Bose-Einstein condensate or embedded in helium nanodroplets, electronic excitations in a BEC or in a solid. In all these cases the vibrational and rotational degrees of freedom create an involved energy level structure, with a continuous exchange of angular momentum with the surrounding environment.

The recently-introduced angulon quasiparticle [1] formalises the concept of a rotating, interacting impurity. We introduce a description of the angulon problem making use of the path integral formalism, extending Feynman’s treatment for the polaron [2]. A clear advantage is that the bath degrees of freedom and the interaction can be integrated out exactly, resulting in an effective, single-particle description for the angulon in which the many-body character of the original problem is encoded in a time-non-local interaction term.

We show that this description sets the ground for a diagrammatic expansion, from which in turn one can derive the a peculiar set of Feynman rules for the angulon, allowing for a compact description of higher-order processes relevant in the strongly-interacting regime.

References:

[1] R. Schmidt and M. Lemeshko, Phys. Rev. Lett. 114, 203001 (2015) and Phys. Rev. X 6, 011012 (2016).
[2] G. Bighin and M. Lemeshko, Phys. Rev. B 96, 085410 (2017).