Energetic Stability of Coreless Vortices in Spin-1 Bose-Einstein Condensates with Conserved Magnetization

Abstract

We show that conservation of longitudinal magnetization in a spinor condensate provides a stabilizing mechanism for a coreless vortex phase-imprinted on a polar condensate. The stable vortex can form a composite topological defect with distinct small-and large-distance topology: the inner ferromagnetic coreless vortex continuously deforms toward an outer singular, singly quantized polar vortex. A similar mechanism can also stabilize a nonsingular nematic texture in the polar phase. A weak magnetization is shown to destabilize a coreless vortex in the ferromagnetic phase. DOI: 10.1103/PhysRevLett.112.075301 PACS numbers: 67.85.-d, 03.75.Lm, 03.75.Mn, 11.27.+d In ordinary superfluids, quantization of circulation around a singular core is a hallmark of superfluidity. In superfluids with internal degrees of freedom, circulation need not be quantized, and it becomes possible for angular momentum to be carried by nonsingular textures. Coreless vortices naturally occur in the ferromagnetic (FM) phase of the atomic spin-1 Bose-Einstein condensate (BEC), where the order parameter is determined by spatial spin rotations and circulation alone is not quantized [5,6]. Angular momentum is then carried by a characteristic, nonsingular fountainlike spin texture [7][8][9][10][11]. In the polar phase, by contrast, the expectation value of the spin vanishes, vortices are singular, and circulation is quantized [5,6].However, s-wave interactions between spin-1 atoms cannot change the longitudinal BEC magnetization M ¼ f þ − f − , where f AE denote the fraction of atom population in levels jm ¼ AE1i. Experiments have demonstrated that M is approximately conserved on the time scales of current alkali-metal atom experiments [12][13][14] and its value can be controlled. Constrained magnetization can force nonvanishing spin profiles to exist even in the polar regime. In strongly magnetized BECs, coreless vortices have indeed been prepared by phase-imprinting in the polar interaction regime [15][16][17] where nonsingular vortices would not be expected to appear by simple energetic arguments alone.Here we study coreless, nonsingular vortex textures of spin-1 BECs in the general case where the system is no longer confined to either the FM or polar ground-state manifold. In particular, in the polar regime we show that the coreless vortex, formed by the spin texture, can be energetically stable in a rotating trap for sufficiently strong magnetization. In the numerics, the stability of imprinted coreless textures is studied by strictly constraining M throughout the energy-relaxation process. We analyze the textures by constructing analytic models of their spinor wave functions that interpolate between the two manifolds. In the stable coreless polar vortex, the magnetization leads to a mixing of the polar and FM phases with a hierarchical core structure: The interior core region ρ ¼ ðx 2 þ y 2 Þ 1=2 ≲ η M , where η M is the characteristic length scale determined by the magnetization constraint [18], exhibits a coreless vortex analogous to t...

Stability and internal structure of vortices in spin-1 Bose-Einstein condensates with conserved magnetization

“…Note that in addition to the filled-core vortex states, we are now able construct inner cores with nontrivial, nonsingular textures. Such states become relevant, for example, when a FM coreless vortex is phase imprinted on a polar condensate [34]. In addition, we also find more exotic wave functions that connect singular vortices, as well as a smooth connection of nontrivial, nonsingular textures.…”

“…Such solutions representing coreless and nematic-coreless vortex textures appearing in the cores of singly quantized vortices were presented in Ref. [34]. Here, we expand the discussion and provide the full derivation and additional examples of phase-mixing vortex wave functions.…”

“…From our numerical results, we explain the mechanism by which a coreless vortex becomes energetically unstable when magnetization is weak and gives way to a singular-vortex ground state, as we briefly noted in Ref. [34].…”

“…We therefore generalize the nematic coreless-vortex solution to the spinor wave function given in Ref. [34] that also allows nonzero spin. We note that we wish to construct a vortex wherê…”

“…In Ref. [34] we demonstrated that a FM coreless vortex phase imprinted on a spin-1 BEC with polar interactions [6] can be energetically stable as a composite topological defect when the conserved magnetization causes the phases to mix. The coreless vortex appears as the extended core region in a defect structure that continuously approaches a singly quantized polar vortex away from the vortex line.…”