| Popis: |
The Bose polaron problem is concerned with an impurity particle moving through a Bose-Einstein condensate, which is an instance of the general concept of a particle in medium. This dissertation investigates the theory of the Bose polaron with a focus on the region of strong coupling between impurity and condensate that marks the transition between attractive and repulsive scattering processes as a scattering resonance is crossed. We use an analytical study of a heavy impurity in an ideal condensate to obtain detailed insights on the emergence of many-body physics from two-body physics and derive the exact solution of the time evolution. The interacting Bose gas is treated by the widely-adopted Bogoliubov method, which results in a theory beyond the classical Fröhlich description of polarons. At strong coupling, the Bogoliubov description is found to be no longer applicable and a new theory for strongly deformed condensates is derived in the form of a non-local extension of Gross-Pitaevskii theory. We find that the impurity-boson bound state that exists for repulsive coupling is responsible for long-lived coherent oscillations in a number of observables, such as the number of bosons attracted by the impurity, Tan's contact and the density profile of the condensate around the impurity. The latter exhibits a remarkable depletion halo, which periodically reaches zero density at a certain distance to the impurity. Polaron trajectories show that the impurity eventually moves like a free quasi-particle with enhanced effective mass for attractive coupling and present velocity oscillations on the repulsive side, leading to stop-and-go motion. Close to the in-medium resonance, a dynamical transition from a repulsive to an attractive polaron is observed. |
