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arXiv:1302.5862 · International Journal of Modern Physics B

FRACTIONAL WINDINGS OF THE SPINOR CONDENSATES ON A RING

Yong-Kai Liu, Shi-Jie Yang

Published May 20, 2013• 0 citations
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Abstract

We study the uniform solutions to the one-dimensional (1D) spinor Bose–Einstein condensates on a ring. These states explicitly display the associated motion of the super-current and the spin rotation, which give rise to fractional winding numbers according to the various compositions of the hyperfine states. It simultaneously yields a fractional factor to the global phase due to the spin-gauge symmetry. All fractional windings can be denoted as nk/(m+n), with nk<m+n<2F, for arbitrary spin-F Bose–Einstein condensation (BEC). Our method can be applied to explore the fractional vortices by identifying the ring as the boundary of two-dimensional (2D) spinor condensates.

DOI
10.1142/s0217979213500707

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We study the uniform solutions to the one-dimensional (1D) spinor Bose–Einstein condensates on a ring. These states explicitly display the associated motion of the super-current and the spin rotation, which give rise to fractional winding numbers according to the various compositions of the hyperfine states. It simultaneously yields a fractional factor to the global phase due to the spin-gauge symmetry. All fractional windings can be denoted as nk/(m+n), with nk<m+n<2F, for arbitrary spin-F Bose–Einstein condensation (BEC). Our method can be applied to explore the fractional vortices by identifying the ring as the boundary of two-dimensional (2D) spinor condensates.
We explore the hysteretic dynamics of spinor Bose-Einstein condensates of ultracold atoms loaded in static 2D ring geometries and subjected to varying synthetic magnetic fields. Electrically neutral, pseudo-spin-1/2 condensates are probed by one-component weak-link potentials that make available paths for the transit of vortices into and out of the ring in both components, and thus can control the number of flux quanta threading the ring hole. For perpendicular fields, domain walls that are dynamically generated in the relative phase of the spin components are shown to play a key role in driving the hysteretic behavior of the whole system through changes in the net magnetic flux. In the presence of spin-orbit coupling, hysteresis is exhibited around the phase transitions found by the metastable current states for varying fields.
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We explore the hysteretic dynamics of spinor Bose-Einstein condensates of ultracold atoms loaded in static 2D ring geometries and subjected to varying synthetic magnetic fields. Electrically neutral, pseudo-spin-1/21/21/2 condensates are probed by one-component weak-link potentials that make available paths for the transit of vortices into and out of the ring in both components, and thus can control the number of flux quanta threading the ring hole. For perpendicular fields, domain walls that are dynamically generated in the relative phase of the spin components are shown to play a key role in driving the hysteretic behaviour of the whole system through changes in the net magnetic flux. In the presence of spin-orbit-coupling, hysteresis is exhibited around the phase transitions found by the metastable current states for varying fields.
In this thesis we study the nonlinear dynamics of spin-1 and spin-2 Bose-Einstein condensates, with particular application to antiferromagnetic systems exhibiting nematic (beyond magnetic) order. Firstly, we give a derivation of the spinor energy functionals with a focus on the connections between the nonlinear terms. We derive a hierarchy of nonlinear irreducible multipole observables sensitive to different levels of nematic order, and explore the various nematic states in terms of their multipolar order, representations of their symmetries, and topological defects.\n\nWe then develop an exact solution to the nonlinear dynamics of spinor Bose-Einstein condensates. We use this solution to construct efficient and accurate numerical algorithms to evolve the spinor Gross-Pitaevskii equation in time. We demonstrate the advantages of our algorithms with several 1D numerical test problems, comparing with existing methods in the literature.\n\nWe apply our numerical methods to simulating quenches of the condensate between various antiferromagnetic phases for spin-1 and spin-2. For spin-1, we carry out quenches for a theoretical uniform system in 2D, and then specialize to the parameters used in a recent harmonically trapped experiment in 3D. We connect the long-time coarsening growth law of the relevant order parameter to the decay of half-quantum vortices, which are the relevant topological defects of the ground state.\n\nFor the spin-2 system, we investigate a novel quench from two different quadrupolar-nematic phases to an octupolar-nematic “cyclic” phase which supports 1/3 fractional vortices. We develop appropriate order parameter observables which couple to the spin and superfluid currents generated by these defects, and show that a new growth law appears with exponent 1/3.
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