Analytical study on parameter regions of dynamical instability for two-component Bose--Einstein condensates with coaxial quantized vortices

TL;DR

This paper analytically investigates the parameter regions leading to dynamical instability in two-component Bose--Einstein condensates with coaxial vortices, using a perturbative approach to identify instability conditions without extensive numerical computation.

Contribution

It provides an analytic method to determine instability regions in two-component BECs with vortices, distinguishing behaviors between co-rotating and counter-rotating systems.

Findings

Identified parameter ranges for dynamical instability in two-component BECs.

Found that counter-rotating systems exhibit more complex instability behavior.

Radial excitations significantly influence instability in counter-rotating systems.

Abstract

The dynamical instability of weakly interacting two-component Bose--Einstein condensates with coaxial quantized vortices is analytically investigated in a two-dimensional isotopic harmonic potential. We examine whether complex eigenvalues appear on the Bogoliubov--de Gennes equation, implying dynamical instability. Rather than solving the Bogoliubov--de Gennes equation numerically, we rely on a perturbative expansion with respect to the coupling constant which enables a simple, analytic approach. For each pair of winding numbers and for each magnetic quantum number, the ranges of inter-component coupling constant where the system is dynamically unstable are exhaustively obtained. Co-rotating and counter-rotating systems show distinctive behaviors. The latter is much more complicated than the former with respect to dynamical instability, particularly because radial excitations contribute to complex eigenvalues in counter-rotating systems.