Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2401.01310 · Physical Review A

Emergence of unstable avoided crossing in the collective excitations of spin-1 spin-orbit-coupled Bose-Einstein condensates

Sanu Kumar Gangwar, Rajamanickam Ravisankar, Henrique Fabrelli, Paulsamy Muruganandam, Pankaj Kumar Mishra

Published Apr 8, 2024• 8 citations
arXivHTMLPDF

Abstract

We present analytical and numerical results on the collective excitation spectrum of quasi-one-dimensional spin-orbit (SO)-coupled spin-1 spinor ferromagnetic Bose-Einstein condensates. The collective excitation spectrum, using Bogoliubov--de Gennes theory, reveals the existence of a diverse range of phases in the SO-coupling and Rabi coupling $({k}_{L}\text{\ensuremath{-}}\mathrm{\ensuremath{\Omega}})$ planes. Based on the nature of the eigenvalue of the excitation spectrum, we categorize the ${k}_{L}\text{\ensuremath{-}}\mathrm{\ensuremath{\Omega}}$ plane into three distinct regions, namely, I, II (IIa and IIb), and III. In region I, a stable mode with phononlike excitations is observed. In region IIa, single- and multiple-band instabilities are noted with a gapped mode, while multiband instability accompanied by a mode corresponding to no gap between low-lying and first-excited states is realized in region IIb, which also provides evidence of unstable avoided crossing between low-lying and first-excited modes, responsible for the ${I}_{o}$ type of oscillatory nonequilibrium dynamical pattern formation. The gap between low-lying and first-excited states increases upon increasing the Rabi coupling and decreases upon increasing the SO coupling. Using eigenvector analysis, we confirm the presence of the spin-dipole mode in the spinlike modes in region II. We corroborate the nature of the collective excitation through real-time dynamical evolution of the ground state perturbed with the quench of the trap using the mean-field Gross-Pitaevskii model. This analysis suggests the presence of dynamical instability leading to the disappearance of the zeroth component of the condensate. In region III, mainly encompassing $\mathrm{\ensuremath{\Omega}}\ensuremath{\sim}0$ and finite ${k}_{L}$, we observe phononlike excitations in both the first-excited and the low-lying state. The eigenvectors in this region reveal alternative in- and out-of-phase behaviors of the spin components. Numerical analysis reveals the presence of a superstripe phase for small Rabi coupling in this region, wherein the eigenvector indicates the presence of more complicated spinlike-density mixed modes.

DOI
10.1103/physreva.109.043306

Related papers

Double unstable avoided crossings and complex-domain-pattern formation in spin-orbit-coupled spin-1 condensates

Sanu Kumar Gangwar, Rajamanickam Ravisankar, Henrique Fabrelli +2 more

We analyze the impact of spin-orbit and Rabi couplings on the dynamical stability of spin-orbit-coupled spin-1 Bose-Einstein condensates for ferromagnetic (FM) and antiferromagnetic (AFM) interactions. Determining the collective excitation spectrum through Bogoliubov--de Gennes theory, we characterize the dynamical stability regime via modulational instability. For AFM interactions, the eigenspectrum reveals the presence of both stable and unstable avoided crossings (UACs), with the first-excited branch undergoing a double unstable avoided crossing. In contrast, with ferromagnetic interactions, only a single UAC, which occurs between the low-lying and first-excited branches, is observed. Furthermore, the eigenvectors demonstrate the transition from densitylike to spinlike behavior, as the collective excitation shows the transition from the stable to the unstable mode for both the FM and AFM interactions. In the multiband instability state, eigenvectors display spin-density mixed mode, while they show spin-flip nature in the avoided crossing regime. Our analysis suggests that spin-orbit coupling enhances the instability gain, while Rabi coupling plays the opposite role. Finally, we corroborate our analytical findings of stable and unstable regimes through numerical simulations of the dynamical evolution of the condensates by introducing the perturbations upon quenching the trap strength. The dynamical phases show the formation of complex domains with AFM interaction, which may be attributed to the double unstable avoided crossings in such a system.

arXiv:2504.01394•Physical Review A•Jun 5, 2025•2 citations

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

Sanu Kumar Gangwar, Sayan Chatterjee, Rajamanickam Ravisankar +3 more

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.

arXiv:2601.18568•Jan 26, 2026•0 citations

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

Rajamanickam Ravisankar, Henrique Fabrelli, A. Gammal +2 more

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.

arXiv:2107.04237•Physical Review A•Nov 17, 2021•28 citations

Quantum phases and the spectrum of collective modes in a spin-1 Bose-Einstein condensate with spin-orbital-angular-momentum coupling

Paramjeet Banger, Rajat Rajat, Arko Roy +1 more

Motivated by recent experiments [Chen et al., Phys. Rev. Lett. 121, 113204 (2018); Chen et al., Phys. Rev. Lett. 121, 250401 (2018)], we investigate the low-lying excitation spectrum of the ground-state phases of spin-orbital-angular-momentum-coupled (SOAM-coupled) spin-1 condensates. At vanishing detuning, a ferromagnetic SOAM-coupled spin-1 Bose-Einstein condensate (BEC) can have two ground-state phases, namely, coreless and polar-core vortex states, whereas an antiferromagnetic BEC supports only polar-core vortex solution. The angular momentum per particle, longitudinal magnetization, and excitation frequencies display discontinuities across the phase boundary between the coreless vortex and polar-core vortex phases. The low-lying excitation spectrum evaluated by solving the Bogoliubov--de Gennes equations is marked by avoided crossings and hence the hybridization of the spin and density channels. The spectrum is further confirmed by the dynamical evolution of the ground state subjected to a perturbation suitable to excite a density or a spin mode and a variational analysis for the density-breathing mode.

arXiv:2306.14669•Physical Review A•Oct 25, 2023•10 citations

Collective excitations in cigar-shaped spin-orbit-coupled spin-1 Bose-Einstein condensates

Rajat, Arko Roy, Sandeep Gautam

We study theoretically the collective excitations of a spin-orbit-coupled spin-1 Bose-Einstein condensate with antiferromagnetic spin-exchange interactions in a cigar-shaped trapping potential at zero and finite temperatures using the Hartree-Fock-Bogoliubov theory with Popov approximation. The collective modes at zero temperature are corroborated by real-time evolution of the ground state subjected to a perturbation suitable to excite a density or a spin mode. We also calculate a few low-lying modes analytically and find very good agreement with the numerical results. We confirm the presence of excitations belonging to two broad categories, namely, density and spin excitations, based on the calculation of dispersion. The degeneracy between a pair of spin modes is broken by the spin-orbit coupling. At finite temperature, spin and density excitations show qualitatively different behavior as a function of temperature.

arXiv:2204.06898•Physical Review A•Jul 6, 2022•20 citations

Collective excitations and universal coarsening dynamics of a spin-orbit-coupled spin-1 Bose-Einstein condensate

Rajat Rajat, Paramjeet Banger, Sandeep Gautam

We study the collective excitation spectrum of a Raman-induced spin-orbit-coupled spin-1 Bose-Einstein condensate confined in a quasi-one-dimensional harmonic trap while varying either the Raman coupling or quadratic Zeeman field strength by using the Bogoliubov approach. A few low-lying modes, which can be used to delineate the phase boundaries, are identified by exciting them with suitable perturbations. We also investigate the coarsening dynamics of a homogeneous quasi-two-dimensional spin-orbit-coupled spin-1 condensate by quenching from the zero momentum into the plane wave phase through a sudden change in Raman coupling or quadratic Zeeman field strength. We demonstrate that the correlation function of the order parameter displays dynamic scaling during the late-time dynamics, allowing us to determine the dynamic critical exponent.

arXiv:2410.22178•Physical Review A•Mar 20, 2025•2 citations
We present analytical and numerical results on the collective excitation spectrum of quasi-one-dimensional spin-orbit (SO)-coupled spin-1 spinor ferromagnetic Bose-Einstein condensates. The collective excitation spectrum, using Bogoliubov--de Gennes theory, reveals the existence of a diverse range of phases in the SO-coupling and Rabi coupling (kL\ensuremath-\ensuremathΩ)({k}_{L}\text{\ensuremath{-}}\mathrm{\ensuremath{\Omega}})(kL​\ensuremath-\ensuremathΩ) planes. Based on the nature of the eigenvalue of the excitation spectrum, we categorize the kL\ensuremath-\ensuremathΩ{k}_{L}\text{\ensuremath{-}}\mathrm{\ensuremath{\Omega}}kL​\ensuremath-\ensuremathΩ plane into three distinct regions, namely, I, II (IIa and IIb), and III. In region I, a stable mode with phononlike excitations is observed. In region IIa, single- and multiple-band instabilities are noted with a gapped mode, while multiband instability accompanied by a mode corresponding to no gap between low-lying and first-excited states is realized in region IIb, which also provides evidence of unstable avoided crossing between low-lying and first-excited modes, responsible for the Io{I}_{o}Io​ type of oscillatory nonequilibrium dynamical pattern formation. The gap between low-lying and first-excited states increases upon increasing the Rabi coupling and decreases upon increasing the SO coupling. Using eigenvector analysis, we confirm the presence of the spin-dipole mode in the spinlike modes in region II. We corroborate the nature of the collective excitation through real-time dynamical evolution of the ground state perturbed with the quench of the trap using the mean-field Gross-Pitaevskii model. This analysis suggests the presence of dynamical instability leading to the disappearance of the zeroth component of the condensate. In region III, mainly encompassing \ensuremathΩ\ensuremath∼0\mathrm{\ensuremath{\Omega}}\ensuremath{\sim}0\ensuremathΩ\ensuremath∼0 and finite kL{k}_{L}kL​, we observe phononlike excitations in both the first-excited and the low-lying state. The eigenvectors in this region reveal alternative in- and out-of-phase behaviors of the spin components. Numerical analysis reveals the presence of a superstripe phase for small Rabi coupling in this region, wherein the eigenvector indicates the presence of more complicated spinlike-density mixed modes.
We analyze the impact of spin-orbit and Rabi couplings on the dynamical stability of spin-orbit-coupled spin-1 Bose-Einstein condensates for ferromagnetic (FM) and antiferromagnetic (AFM) interactions. Determining the collective excitation spectrum through Bogoliubov--de Gennes theory, we characterize the dynamical stability regime via modulational instability. For AFM interactions, the eigenspectrum reveals the presence of both stable and unstable avoided crossings (UACs), with the first-excited branch undergoing a double unstable avoided crossing. In contrast, with ferromagnetic interactions, only a single UAC, which occurs between the low-lying and first-excited branches, is observed. Furthermore, the eigenvectors demonstrate the transition from densitylike to spinlike behavior, as the collective excitation shows the transition from the stable to the unstable mode for both the FM and AFM interactions. In the multiband instability state, eigenvectors display spin-density mixed mode, while they show spin-flip nature in the avoided crossing regime. Our analysis suggests that spin-orbit coupling enhances the instability gain, while Rabi coupling plays the opposite role. Finally, we corroborate our analytical findings of stable and unstable regimes through numerical simulations of the dynamical evolution of the condensates by introducing the perturbations upon quenching the trap strength. The dynamical phases show the formation of complex domains with AFM interaction, which may be attributed to the double unstable avoided crossings in such a system.
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.
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.
Motivated by recent experiments [Chen et al., Phys. Rev. Lett. 121, 113204 (2018); Chen et al., Phys. Rev. Lett. 121, 250401 (2018)], we investigate the low-lying excitation spectrum of the ground-state phases of spin-orbital-angular-momentum-coupled (SOAM-coupled) spin-1 condensates. At vanishing detuning, a ferromagnetic SOAM-coupled spin-1 Bose-Einstein condensate (BEC) can have two ground-state phases, namely, coreless and polar-core vortex states, whereas an antiferromagnetic BEC supports only polar-core vortex solution. The angular momentum per particle, longitudinal magnetization, and excitation frequencies display discontinuities across the phase boundary between the coreless vortex and polar-core vortex phases. The low-lying excitation spectrum evaluated by solving the Bogoliubov--de Gennes equations is marked by avoided crossings and hence the hybridization of the spin and density channels. The spectrum is further confirmed by the dynamical evolution of the ground state subjected to a perturbation suitable to excite a density or a spin mode and a variational analysis for the density-breathing mode.
We study theoretically the collective excitations of a spin-orbit-coupled spin-1 Bose-Einstein condensate with antiferromagnetic spin-exchange interactions in a cigar-shaped trapping potential at zero and finite temperatures using the Hartree-Fock-Bogoliubov theory with Popov approximation. The collective modes at zero temperature are corroborated by real-time evolution of the ground state subjected to a perturbation suitable to excite a density or a spin mode. We also calculate a few low-lying modes analytically and find very good agreement with the numerical results. We confirm the presence of excitations belonging to two broad categories, namely, density and spin excitations, based on the calculation of dispersion. The degeneracy between a pair of spin modes is broken by the spin-orbit coupling. At finite temperature, spin and density excitations show qualitatively different behavior as a function of temperature.
We study the collective excitation spectrum of a Raman-induced spin-orbit-coupled spin-1 Bose-Einstein condensate confined in a quasi-one-dimensional harmonic trap while varying either the Raman coupling or quadratic Zeeman field strength by using the Bogoliubov approach. A few low-lying modes, which can be used to delineate the phase boundaries, are identified by exciting them with suitable perturbations. We also investigate the coarsening dynamics of a homogeneous quasi-two-dimensional spin-orbit-coupled spin-1 condensate by quenching from the zero momentum into the plane wave phase through a sudden change in Raman coupling or quadratic Zeeman field strength. We demonstrate that the correlation function of the order parameter displays dynamic scaling during the late-time dynamics, allowing us to determine the dynamic critical exponent.