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arXiv:2306.14669 · Physical Review A

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, Sandeep Gautam

Published Oct 25, 2023• 10 citations
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Abstract

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.

DOI
10.1103/physreva.108.043310

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Modern Physics Letters B•Mar 20, 2022•1 citation
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 investigate the ground-state phase diagram and excitation spectrum of an interacting spinor Bose-Einstein condensate with spin-orbital-angular-momentum (SOAM) coupling realized in recent experiments by introducing atomic Raman transition with a pair of copropagating Laguerre-Gaussian laser beams that carry different orbital angular momenta (OAM) [Chen et al., Phys. Rev. Lett. 121, 113204 (2018) and Zhang et al., Phys. Rev. Lett. 122, 110402 (2019)]. Because of the ground-state degeneracy of the single-particle Hamiltonian at vanishing detuning, several angular-stripe phases, which are the superposition of states with different angular quantum numbers, appear in the phase diagram. However, these phases normally exist at small detuning, which makes them hard to be probed in experiments. We show that for a large OAM difference of the laser beams, an asymmetric kind of angular-stripe phase can exist even at large detuning. The excitation spectra in different phases exhibit distinct features: In the angular-stripe phase there exist two gapless bands corresponding to the broken U(1)\mathrm{U}(1)U(1) and rotational symmetries, while in the half-skyrmion phase the gapless band exhibits a rotonlike structure. Our predictions of the angular-stripe phases and the low-energy excitations can be examined in recently realized Bose-Einstein condensates with SOAM coupling.
We present a theoretical study of the collective excitations of the supersolid annular stripe phase of a spin-orbital-angular-momentum-coupled (SOAM-coupled) spin-1 Bose-Einstein condensate. The annular stripe phase simultaneously breaks two continuous symmetries, namely rotational and U(1)U(1)U(1) gauge symmetry, and is more probable in the condensates with a larger orbital angular momentum transfer imparted by a pair of Laguerre-Gaussian beams than what has been considered in the recent experiments. Accordingly, we consider a SOAM-coupled spin-1 condensate with a $4\ensuremath{\hbar}$ orbital angular momentum transferred by the lasers. Depending on the values of the Raman coupling strength and quadratic Zeeman term, the condensate with realistic antiferromagnetic interactions supports three ground-state phases: the annular stripe, the vortex necklace, and the zero angular momentum phase. We numerically calculate the collective excitations of the condensate as a function of coupling and quadratic Zeeman field strengths for a fixed ratio of spin-dependent and spin-independent interaction strengths. At low Raman coupling strengths, we observe a direct transition from the zero angular momentum to the annular stripe phase, characterized by the softening of a double symmetric roton mode, which serves as a precursor to supersolidity.
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 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 $\mathrm{\ensuremath{\Omega}}\ensuremath{\sim}0$ 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.
The low-lying excitations of coreless vortex states in F=1F=1F=1 spinor Bose-Einstein condensates (BECs) are theoretically investigated using the Gross-Pitaevskii and Bogoliubov--de Gennes equations. The spectra of the elementary excitations are calculated for different spin-spin interaction parameters and ratios of the number of particles in each sublevel. There exist dynamical instabilities of the vortex state which are suppressed by ferromagnetic interactions, and, conversely, enhanced by antiferromagnetic interactions. In both of the spin-spin interaction regimes, we find vortex-splitting instabilities in analogy with scalar BECs. In addition, a phase-separating instability is found in the antiferromagnetic regime.
A theoretical model of a Bose-Einstein condensate with angular spin-orbit coupling has recently been proposed and it has been established that a half-skyrmion represents the ground state in a certain regime of spin-orbit coupling and interaction. Here we investigate low-lying excitations of this phase by using the Bogoliubov method and numerical simulations of the time-dependent Gross-Pitaevskii equation. We find that a sudden shift of the trap bottom results in a complex two-dimensional motion of the system's center of mass that is markedly different from the response of a competing phase, and comprises two dominant frequencies. Moreover, the breathing mode frequency of the half-skyrmion is set by both the spin-orbit coupling and the interaction strength, while in the competing state it takes a universal value. Effects of interactions are especially pronounced at the transition between the two phases.
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