Topological interface physics of defects and textures in spinor Bose-Einstein condensates

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...

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“…For an overview, see, e.g., Refs. [5,43]. Here we are interested in nonsingular coreless vortex states that mix the two phases.…”

Section: Coreless Vortexmentioning

confidence: 99%

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

2014

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“…However in our spatially dependent SOC BEC, the ground state supports vortices at the interface between two distinct SW phases. Similar defect formation at the interface of two distinct ground state phases was studied for spin-1 BECs with tunable inter-and intra-species interactions [28,29].…”

Section: Ground-state Phases Of the Sobecmentioning

confidence: 66%

Position-dependent spin–orbit coupling for ultracold atoms

Gou

Liu

et al. 2015

New J. Phys.

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We theoretically explore atomic Bose-Einstein condensates (BECs) subject to position-dependent spin-orbit coupling (SOC). This SOC can be produced by cyclically laser coupling four internal atomic ground (or metastable) states in an environment where the detuning from resonance depends on position. The resulting spin-orbit coupled BEC (SOBEC) phase separates into domains, each of which contain density modulations-stripes-aligned either along the x or y direction. In each domain, the stripe orientation is determined by the sign of the local detuning. When these stripes have mismatched spatial periods along domain boundaries, non-trivial topological spin textures form at the interface, including skyrmions-like spin vortices and anti-vortices. In contrast to vortices present in conventional rotating BECs, these spin-vortices are stable topological defects that are not present in the corresponding homogenous stripe-phase SOBECs. 87in which SOC and the desired spatial dependance coexist. We then explore the resulting equilibrated pseudospin-1/2 spin-orbit coupled Bose-Einstein condensates (SOBECs) resulting from this construction. These SOBECs contain domains of differently oriented stripe phases. When the stripe's projection onto the domain-boundaries are spatially mismatched (see figure 1), arrays of non-trivial topological structures such as vortices and anti-vortices in the spin degree of freedom-skyrmions-form.The paper is organized as follows: in section 2 we present a simple physical picture elucidating implications of the position-dependent SOC; in section 3 we formulate the light-atom interaction for the specific example of Rb 87 , and derive the associated position-dependent spin-orbit coupled Hamiltonian for ground-state atoms; and in section 4 we use the Gross-Pitaevskii equation (GPE) to study the ground state structure of these inhomogeneous systems. Finally, section 5 summaries our findings.

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“…For an overview, see, e.g., Refs. [13,61]. Here we are interested in vortex states that mix the two phases.…”

Section: Vortex-core Wave Functionsmentioning

confidence: 99%

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

2016

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We demonstrate how conservation of longitudinal magnetization can have pronounced effects on both stability and structure of vortices in the atomic spin-1 Bose-Einstein condensate by providing a systematic characterization of nonsingular and singular vortex states. Constructing spinor wave functions for vortex states that continuously connect ferromagnetic and polar phases, we systematically derive analytic models for nonrotating cores of different singular vortices and for composite defect states with distinct small-and large-distance topology. We explain how the conservation law provides a stabilizing mechanism when the coreless vortex imprinted on the condensate relaxes in the polar regime of interatomic interactions. The resulting structure forms a composite defect: The inner ferromagnetic coreless vortex deforms toward an outer singly quantized polar vortex. We also numerically show how other even more complex hierarchies of vortex-core topologies may be stabilized. Moreover, we analyze the structure of the coreless vortex also in a ferromagnetic condensate and show how reducing magnetization leads to a displacement of the vortex from the trap center and eventually to the deformation and splitting of its core where a singular vortex becomes a lower-energy state. For the case of singular vortices, we find that the stability and the core structure are notably less influenced by the conservation of magnetization.

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Topological interface physics of defects and textures in spinor Bose-Einstein condensates

Cited by 14 publications

References 114 publications

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

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

Position-dependent spin–orbit coupling for ultracold atoms

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

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