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arXiv:1007.2027 · Physical Review A

Spin textures in condensates with large dipole moments

J. A. M. Huhtamäki, Masahiro O. Takahashi, Tapio Simula, Takeshi Mizushima, K. Machida

Published Jun 14, 2010• 22 citations

Abstract

We have solved numerically the ground states of a Bose-Einstein condensate in the presence of dipolar interparticle forces using a semiclassical approach. Our motivation is to model, in particular, the spontaneous spin textures emerging in quantum gases with large dipole moments, such as $^{52}\mathrm{Cr}$ or $\mathrm{Dy}$ condensates, or ultracold gases consisting of polar molecules. For a pancake-shaped harmonic (optical) potential, we present the ground-state phase diagram spanned by the strength of the nonlinear coupling and dipolar interactions. In an elongated harmonic potential, we observe a helical spin texture. The textures calculated according to the semiclassical model in the absence of external polarizing fields are predominantly analogous to previously reported results for a ferromagnetic $F=1$ spinor Bose-Einstein condensate, suggesting that the spin textures arising from the dipolar forces are largely independent of the value of the quantum number $F$ or the origin of the dipolar interactions.

DOI: 10.1103/physreva.81.063623

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We have solved numerically the ground states of a Bose-Einstein condensate in the presence of dipolar interparticle forces using a semiclassical approach. Our motivation is to model, in particular, the spontaneous spin textures emerging in quantum gases with large dipole moments, such as

^{52}\mathrm{Cr}

or

\mathrm{Dy}

condensates, or ultracold gases consisting of polar molecules. For a pancake-shaped harmonic (optical) potential, we present the ground-state phase diagram spanned by the strength of the nonlinear coupling and dipolar interactions. In an elongated harmonic potential, we observe a helical spin texture. The textures calculated according to the semiclassical model in the absence of external polarizing fields are predominantly analogous to previously reported results for a ferromagnetic

F=1

spinor Bose-Einstein condensate, suggesting that the spin textures arising from the dipolar forces are largely independent of the value of the quantum number

F

or the origin of the dipolar interactions.

We numerically study elongated helical spin textures in ferromagnetic spin-1 Bose-Einstein condensates subject to dipolar interparticle forces. Stationary states of the Gross-Pitaevskii equation are solved and analyzed for various values of the helical wave vector and dipolar coupling strength. We find two helical spin textures which differ by the nature of their topological defects. The spin structure hosting a pair of Mermin-Ho vortices with opposite mass flows and aligned spin currents is stabilized for a nonzero value of the helical wave vector.

Helical spin textures in a 87Rb F=1 spinor Bose-Einstein condensate are found to decay spontaneously toward a spatially modulated structure of spin domains. The formation of this modulated phase is ascribed to magnetic dipolar interactions that energetically favor the short-wavelength domains over the long-wavelength spin helix. The reduction of dipolar interactions by a sequence of rf pulses results in a suppression of the modulated phase, thereby confirming the role of dipolar interactions in this process. This study demonstrates the significance of magnetic dipole interactions in degenerate 87Rb F=1 spinor gases.

We have numerically solved the low-energy excitation spectra of ferromagnetic Bose-Einstein condensates subject to dipolar interparticle interactions. The system is assumed to be harmonically confined by purely optical means, thereby maintaining the spin degree of freedom of the condensate order parameter. Using a zero-temperature spin-1 model, we solve the Bogoliubov excitations for different spin textures, including a spin-vortex state in the absence of external magnetic fields and a rapidly rotating polarized spin texture in a finite homogeneous field. In particular, we consider the effect of dipolar interactions on excitations characteristic of ferromagnetic condensates. The energies of spin waves and magnetic quadrupole modes are found to increase rapidly with the dipolar coupling strength, whereas the energies of density oscillations change only slightly.

We study the spontaneous spin textures induced by magnetic dipole-dipole interaction in ferromagnetic spinor condensates under various trap geometries. At the mean-field level, we show the system is dual to a Dirac string gas with a negative string tension in which the ground state spin texture can be easily determined. We find that three-dimensional condensates prefer a meronlike vortex texture, quasi-one-dimensional condensates prefer the axially polarized flare texture, while condensates in quasi-two-dimensions exhibit either a meron texture or an in-plane polarized texture.

We report on a study of the spin-1 ferromagnetic Bose-Einstein condensate with magnetic dipole-dipole interactions. By solving the nonlocal Gross-Pitaevskii equations for this system, we find three ground-state phases. Moreover, we show that a substantial orbital angular momentum accompanied by chiral symmetry breaking emerges spontaneously in a certain parameter regime. We predict that all these phases can be observed in the spin-1 87Rb condensate by changing the number of atoms or the trap frequency.