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Springer proceedings in complexity

Instabilities of Excitation Spectrum for Attractive Spin-Orbit Coupled Bose-Einstein Condensates in Quasi-one Dimension

Sonali Gangwar, Rajamanickam Ravisankar, Pankaj Kumar Mishra

Published Jan 1, 2022• 0 citations
Publisher
DOI
10.1007/978-3-030-99792-2_116

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Abstract We compute the Bogoliubov–de Gennes excitation spectrum in a trapped two-component spin-orbit-coupled (SOC) Bose–Einstein condensate (BEC) in quasi-two-dimensions as a function of linear and angular momentum and analyze them. The excitation spectrum exhibits a minima-like feature at finite momentum for the immiscible SOC-BEC configuration, which implies dynamical instability. We augment these results by computing the dynamic structure factor in the density and pseudo-spin sector, and discuss its interesting features that can be experimentally measured through Bragg spectroscopy of such ultracold condensates.
We present a unified description of different types of matter-wave solitons that can emerge in quasi one-dimensional spin-orbit coupled (SOC) Bose-Einstein condensates (BECs). This description relies on the reduction of the original two-component Gross-Pitaevskii SOC-BEC model to a single nonlinear Schrödinger equation, via a multiscale expansion method. This way, we find approximate bright and dark soliton solutions, for attractive and repulsive interatomic interactions respectively, for different regimes of the SOC interactions. Beyond this, our approach also reveals "negative mass" regimes, where corresponding "negative mass" bright or dark solitons can exist for repulsive or attractive interactions, respectively. Such a unique opportunity stems from the structure of the excitation spectrum of the SOC-BEC. Numerical results are found to be in excellent agreement with our analytical predictions.
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 eigenenergy of the BdG spectrum, we confirm the existence of phonon, roton, and maxon modes with weak repulsive intra- and interspecies contact interactions. The depth of the minimum corresponding to the roton mode strongly depends 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 the BdG spectrum indicate the presence of a densitylike mode in the stable regime and spinlike modes in the 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.