Self-localized impurities embedded in a one dimensional Bose-Einstein condensate and their quantum fluctuations

TL;DR

This paper investigates the self-localization of impurity atoms in a one-dimensional Bose-Einstein condensate, revealing soliton-like behavior and quantum fluctuations, with implications for spectroscopic detection.

Contribution

It introduces a strong coupling approach to model impurity self-localization and develops a Bogoliubov-de-Gennes formalism to analyze quantum fluctuations around the localized states.

Findings

Self-localized impurity states exhibit parametric soliton behavior.

Quantum fluctuations significantly modify the strong coupling predictions.

The excitation spectrum enables spectroscopic detection of localization.

Abstract

We consider the self-localization of neutral impurity atoms in a Bose-Einstein condensate in a 1D model. Within the strong coupling approach, we show that the self-localized state exhibits parametric soliton behavior. The corresponding stationary states are analogous to the solitons of non-linear optics and to the solitonic solutions of the Schroedinger-Newton equation (which appears in models that consider the connection between quantum mechanics and gravitation). In addition, we present a Bogoliubov-de-Gennes formalism to describe the quantum fluctuations around the product state of the strong coupling description. Our fluctuation calculations yield the excitation spectrum and reveal considerable corrections to the strong coupling description. The knowledge of the spectrum allows a spectroscopic detection of the impurity self-localization phenomenon.