Nonlocal field theory of quasiparticle scattering in dipolar Bose-Einstein condensates

TL;DR

This paper develops a novel nonlocal field theory for quasiparticle scattering in dipolar Bose-Einstein condensates, revealing unique evanescent channels and transmission features due to dipolar interactions and roton minima.

Contribution

It introduces a hypersingular integral equation approach to model quasiparticle scattering without prior assumptions, highlighting effects of dipolar interactions absent in contact-only condensates.

Findings

Identification of a continuum of evanescent channels at the sound barrier.

Demonstration of accurate solutions with moderate discretization steps.

Discovery of peculiar transmission and reflection features due to roton minima.

Abstract

We consider the propagation of quasiparticle excitations in a dipolar Bose-Einstein condensate, and derive a nonlocal field theory of quasiparticle scattering at a stepwise inhomogeneity of the sound speed, obtained by tuning the contact coupling part of the interaction on one side of the barrier. To solve this problem $ab$ $initio$, i.e., without prior assumptions on the form of the solutions, we reformulate the dipolar Bogoliubov-de Gennes equation as a singular integral equation. The latter is of a $novel$ $hypersingular$ type, in having a kernel which is hypersingular at only two isolated points. Deriving its solution, we show that the integral equation reveals a continuum of evanescent channels at the sound barrier which is absent for a purely contact-interaction condensate. We furthermore demonstrate that by performing a discrete approximation for the kernel, one achieves an excellent solution accuracy for already a moderate number of discretization steps. Finally, we show that the non-monotonic nature of the system dispersion, corresponding to the emergence of a roton minimum in the excitation spectrum, results in peculiar features of the transmission and reflection at the sound barrier which are nonexistent for contact interactions.