Supersolid phases and collective excitations in two-dimensional Rashba spin-orbit coupled spin-1 condensates

TL;DR

This paper analyzes the collective excitations and phase transitions in a two-dimensional spin-1 Bose-Einstein condensate with Rashba spin-orbit coupling, revealing signatures of quantum phase transitions and supersolid phases.

Contribution

It provides an analytical and numerical study of excitation spectra and instabilities, uncovering new dynamical signatures and supersolid phases in spinor condensates with tunable spin-orbit coupling.

Findings

Identification of mode softening and roton minima as signatures of phase transitions

Prediction of a dynamically unstable supersolid phase in antiferromagnetic interactions

Numerical confirmation of analytical excitation spectra and stability analysis

Abstract

We investigate the collective excitation spectrum and dynamics of a quasi two-dimensional spin-1 Bose-Einstein condensate with Rashba type spin-orbit (SO) coupling. Employing Bogoliubov-de-Gennes analysis, we analytically compute the excitation spectra across a wide range of interaction strengths and coupling parameters. By systematically varying the SO and Rabi couplings, we uncover distinct dynamical signatures of quantum phase transitions, including mode softening, the appearance of roton-like minima, and miscibility-driven instabilities in both ferromagnetic and antiferromagnetic interaction regimes. In the antiferromagnetic case, these instabilities lead to a dynamically unstable supersolid phase characterized by the coexistence of density modulation and global phase coherence. To corroborate the analytical predictions, we numerically solve the coupled Gross-Pitaevskii equations and analyze the dynamical stability of the condensate. Our results provide experimentally accessible signatures for spinor condensates with tunable spin-orbit coupling and demonstrate the rich interplay between spin-dependent interactions and synthetic couplings in nonequilibrium quantum fluids.