Dark solitons in a trapped gas of long-range interacting bosons

TL;DR

This paper investigates how long-range interactions affect the existence, stability, and oscillation frequencies of dark solitons in a trapped one-dimensional Bose gas, revealing significant frequency upshifts due to these interactions.

Contribution

It provides a detailed analysis of dark solitons under combined short- and long-range interactions, highlighting their robustness and altered vibrational modes.

Findings

Dark solitons can exist and remain stable with long-range interactions.

Long-range interactions significantly increase the oscillation frequency of dark solitons.

Frequency upshift can be an order of magnitude compared to the standard trap frequency ratio.

Abstract

We consider the interplay of repulsive short-range and same-sign long-range interactions in the dynamics of dark solitons, as prototypical coherent nonlinear excitations in a trapped 1D Bose gas. First, the form of the ground state is examined, and then both the existence of the solitary waves and their stability properties are explored, and corroborated by direct numerical simulations. We find that single- and multiple-dark-soliton states can exist and are generically robust in the presence of long-range interactions. We analyze the modes of vibration of such excitations and find that their respective frequencies are significantly upshifted as the strength of the long-range interactions is increased. Indeed, we find that a prefactor of the long-range interactions considered comparable to the trap strength may upshift the dark soliton oscillation frequency by {\it an order of magnitude}, in comparison to the well established one of $\Omega/\sqrt{2}$ in a trap of frequency $\Omega$.