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

Rajamanickam Ravisankar, Henrique Fabrelli+3 more|arXiv (Cornell University)|Jan 1, 2021

Cold Atom Physics and Bose-Einstein Condensates76 references31 citations

TL;DR

This study investigates the collective excitation spectrum and dynamical stability of quasi-two-dimensional binary Bose-Einstein condensates with Rashba spin-orbit and Rabi couplings using Bogoliubov-de Gennes (BdG) theory. It reveals that increasing Rashba coupling induces instability, while Rabi coupling stabilizes the system, with the roton minimum depth strongly dependent on coupling strengths, confirmed by BdG eigenspectrum and direct GPE simulations.

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.

Motivation & Objective

• To analyze the dynamical stability of spin-orbit and Rabi coupled binary Bose-Einstein condensates in quasi-two dimensions.
• To investigate the interplay between Rashba spin-orbit coupling and Rabi coupling on excitation modes and system stability.
• To identify the emergence of phonon, roton, and maxon modes under varying interaction and coupling strengths.
• To construct a phase diagram mapping the stability regime in the Rashba-Rabi coupling strength plane.
• To validate BdG results with direct numerical simulations of coupled Gross-Pitaevskii equations.

Proposed method

• Formulates a mean-field Hamiltonian including Rashba spin-orbit coupling and Rabi coupling for a two-component BEC.
• Derives the single-particle dispersion relation from the coupled Gross-Pitaevskii equations in dimensionless form.
• Applies Bogoliubov-de Gennes (BdG) theory to compute the excitation spectrum and analyze stability via eigenenergies and eigenvectors.
• Uses the BdG eigenspectrum to identify phonon, roton, and maxon modes and track their evolution with coupling parameters.
• Performs direct numerical simulations of the coupled Gross-Pitaevskii equations to validate BdG predictions on ground state stability.
• Constructs a phase diagram by scanning Rashba and Rabi coupling strengths to map stable and unstable regimes.

Experimental results

Research questions

• RQ1 How does Rashba spin-orbit coupling affect the dynamical stability of a quasi-2D binary BEC?
• RQ2 What role does Rabi coupling play in stabilizing or destabilizing the system?
• RQ3 How do the excitation modes (phonon, roton, maxon) evolve with varying spin-orbit and Rabi coupling strengths?
• RQ4 What is the dependence of the roton minimum depth on the coupling parameters?
• RQ5 How do the eigenvectors of the BdG spectrum reflect the nature of collective modes in stable and unstable phases?

Key findings

• Increasing Rashba spin-orbit coupling leads to dynamical instability in the binary BEC system.
• Rabi coupling stabilizes the system, counteracting the destabilizing effect of Rashba coupling.
• The depth of the roton minimum in the excitation spectrum strongly depends on both Rashba and Rabi coupling strengths.
• In the stable regime, BdG eigenvectors show density-like modes; in unstable regimes, spin-like modes dominate.
• A phase diagram in the Rashba-Rabi coupling strength plane clearly delineates the stability regime.
• Direct simulations of the coupled Gross-Pitaevskii equations confirm the BdG-based stability analysis and excitation spectrum features.