Excitations at the border of a condensate

TL;DR

This paper develops a new method to analyze boundary excitations in inhomogeneous condensates, revealing trapped modes that influence local density fluctuations and are excited during bulk mode reflections.

Contribution

It introduces a stable integration scheme using an adiabatic basis to solve Bogoliubov--de Gennes equations near a linear turning point, identifying boundary modes in condensates.

Findings

Identification of boundary modes trapped in a potential

Boundary modes are non-resonantly excited during bulk mode reflection

Significant contribution of these modes to local density fluctuations

Abstract

We solve the Bogoliubov--de Gennes equations for an inhomogeneous condensate in the vicinity of a linear turning point. A stable integration scheme is developed using a transformation into an adiabatic basis. We identify boundary modes trapped in a potential whose shape is similar to a Hartree-Fock mean-field treatment. These modes are non-resonantly excited when bulk modes reflect at the turning point and contribute significantly to the spectrum of local density fluctuations.