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arXiv:1901.02595 · Physical Review Research

Angular stripe phase in spin-orbital-angular-momentum coupled Bose condensates

Xiao-Long Chen, Shi-Guo Peng, Peng Zou, Xia-Ji Liu, Hui Hu

Published Jul 28, 2020• 27 citations
arXivHTMLPDF

Abstract

We propose that a superfluid with supersolidlike properties, i.e., angular stripe phase, can be realized in a pancakelike spin-1/2 Bose gas with spin-orbital-angular-momentum coupling.We predict a rich ground-state phase diagram, including the vortex-antivortex pair phase, the half-skyrmion phase, and two different angular stripe phases.The stripe phases feature a modulated angular density-density correlation with a sizable contrast and can occupy a relatively large parameter space.The low-lying collective excitations, such as the dipole and breathing modes, show distinct behaviors in different phases.The existence of the stripe phase is also clearly indicated in the energetic and dynamic instabilities of collective modes near phase transitions.Our predictions of the angular stripe phase could be readily examined in current cold-atom experiments with 87 Rb and 41 K.

DOI
10.1103/physrevresearch.2.033152

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We propose that a superfluid with supersolidlike properties, i.e., angular stripe phase, can be realized in a pancakelike spin-1/2 Bose gas with spin-orbital-angular-momentum coupling.We predict a rich ground-state phase diagram, including the vortex-antivortex pair phase, the half-skyrmion phase, and two different angular stripe phases.The stripe phases feature a modulated angular density-density correlation with a sizable contrast and can occupy a relatively large parameter space.The low-lying collective excitations, such as the dipole and breathing modes, show distinct behaviors in different phases.The existence of the stripe phase is also clearly indicated in the energetic and dynamic instabilities of collective modes near phase transitions.Our predictions of the angular stripe phase could be readily examined in current cold-atom experiments with 87 Rb and 41 K.
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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 report on a theoretical study of a ring-shaped Bose-Einstein condensate with Raman-induced spin-orbital-angular-momentum coupling. We analyze the structure of the ground state of the system depending on different physical parameters and reveal a peculiar fine structure within the stripe phase on the phase diagram. We demonstrate the existence of the predicted stripe subphases within a wide range of physical parameters, and their traceability through physical observables, and compare the results with several commonly used variational approximations. We also show that predicted subphases of the stripe phase can be observed within experimentally realizable conditions.
Supersolid is a special state of matter with both superfluid properties and spontaneous modulation of particle density. In this paper we focus on the supersolid stripe phase realized in a spin-orbit-coupled Bose-Einstein condensate and explore the properties of a class of metastable supersolids. In particular, we study a one-dimensional supersolid whose characteristic wave number kkk (magnitude of wave vector) deviates from km{k}_{m}km​, i.e., the one in the ground state. In other words, the period of density modulation is shorter or longer than the one in the ground state. We find that this class of supersolids can still be stable if their wave numbers fall in the range kc1<k<kc2{k}_{c1}<k<{k}_{c2}kc1​<k<kc2​, with two thresholds kc1{k}_{c1}kc1​ and kc2{k}_{c2}kc2​. Stripes with kkk outside this range suffer from dynamical instability with a complex Bogoliubov excitation spectrum at long wavelength. Experimentally, these stripes with kkk different from km{k}_{m}km​ are accessible by exciting the longitudinal spin dipole mode, resulting in temporal oscillation of the stripe period as well as kkk. Within the mean-field Gross-Pitaevskii theory, we numerically confirm that for a large enough amplitude of spin dipole oscillation, the stripe states become unstable through breaking periodicity, in qualitative agreement with the existence of thresholds of kkk for stable stripes. Our work extends the concept of supersolid and uncovers an unconventional class of metastable supersolids to explore.
Abstract Recently, stripe phases in spin–orbit coupled Bose–Einstein condensates (BECs) have attracted much attention since they are identified as supersolid phases. In this paper, we exploit experimentally reachable parameters and show that annular stripe phases with large stripe spacing and high stripe contrast can be achieved in spin–orbital-angular-momentum coupled (SOAMC) BECs. In addition to using Gross–Pitaevskii numerical simulations, we develop a variational ansatz that captures the essential interaction effects to first order, which are not present in the ansatz employed in previous literature. Our work should open the possibility towards directly observing stripe phases in SOAMC BECs in experiments.
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.