Effect of Rashba spin-orbit and Rabi couplings on the excitation spectrum of binary Bose-Einstein condensates

TL;DR

This paper analyzes how Rashba spin-orbit and Rabi couplings influence the excitation spectrum and stability of binary Bose-Einstein condensates, revealing the conditions for phonon, roton, and maxon modes and their stability regimes.

Contribution

It provides a detailed study of the effects of spin-orbit and Rabi couplings on the excitation spectrum and stability of binary BECs using Bogoliubov-de Gennes theory and numerical simulations.

Findings

Roton mode depth depends on coupling strength

Increased SO coupling leads to instability

Rabi coupling stabilizes the system

Abstract

We present the collective excitation spectrum analysis of binary Bose-Einstein condensates (BECs) with spin-orbit (SO) and Rabi couplings in a quasi-two-dimensional system. In particular, we investigate the role of SO and Rabi coupling strengths in determining the dynamical stability of the coupled BECs using Bogoliubov-de Gennes (BdG) theory. Using the eigenergy of BdG spectrum, we confirm the existence of phonon, roton, and maxon modes with weak repulsive intra- and inter-species contact interactions. The depth of the minimum corresponding to the roton mode depends strongly on the coupling strength. We find that the increase of the SO coupling leads to instability, while the increase in the Rabi coupling stabilizes the system. Also the eigenvectors of BdG spectrum indicates the presence of density like mode in the stable regime and spin like modes in unstable regimes. A phase diagram demonstrating the stability regime in the plane of SO and Rabi coupling strengths is obtained. Finally, we complement the observation of the excitation spectrum with the direct numerical simulation results of coupled Gross-Pitaevskii equations.