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New Journal of Physics

Stable double-pair skyrmion in an antiferromagneticF= 1 Bose–Einstein condensate

Yong-Kai Liu, Shi-Jie Yang

Published Jun 28, 2017• 5 citations
Publisher

Abstract

The recent experimental realization of spin-orbit coupling (SOC) in spin-1 ultracold atoms opens up an interesting avenue for exploring new quantum states and novel quantum phenomena in large-spin systems. Two types of two-dimensional double-pair vortices that are connected by a domain-wall can be accommodated in the antiferromagnetic spin-1 Bose–Einstein condensate (BEC). One type, named a 2D double-pair skyrmion, which differs from the conventional 2D skyrmion in the F = 1 polar BEC, hosts a pair of vortices and displays a meron-pair texture with a unit topological charge. The other type has a meron-pair texture but with null topological charge. These two types of double-pair vortices can be naturally generated from a vortex-free Gaussian wave packet by incorporating a non-Abelian gauge field into the spinor condensate.

DOI
10.1088/1367-2630/aa7330

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The recent experimental realization of spin-orbit coupling (SOC) in spin-1 ultracold atoms opens up an interesting avenue for exploring new quantum states and novel quantum phenomena in large-spin systems. Two types of two-dimensional double-pair vortices that are connected by a domain-wall can be accommodated in the antiferromagnetic spin-1 Bose–Einstein condensate (BEC). One type, named a 2D double-pair skyrmion, which differs from the conventional 2D skyrmion in the F = 1 polar BEC, hosts a pair of vortices and displays a meron-pair texture with a unit topological charge. The other type has a meron-pair texture but with null topological charge. These two types of double-pair vortices can be naturally generated from a vortex-free Gaussian wave packet by incorporating a non-Abelian gauge field into the spinor condensate.
Three types of vortex-pair are identified in two-component Bose–Einstein condensates (BEC) of different kinds of spin-orbit coupling. One type holds the two vortices in one component of the twocomponent condensates. Both the other two types hold a vortex in each component of the twocomponent condensates, and exhibit meron-pair textures that have either null or unit topological charge, respectively. The cores of the two vortices are connected by a string of the relative phase jump. These vortex pairs can be generated from a vortex-free wave packet by incorporating different non- Abelian gauge field into the BEC. When a Rabi coupling is introduced, the distance between the two cores is effectively controlled by the Rabi coupling strength and a transition of vortex configurations is observed.
The spin degrees of freedom in multicomponent Bose–Einstein condensates allow for various types of topological excitations, such as skyrmions and knots. Systems with high spins offer a broader range of internal symmetries. For instance, in spin-1 Bose–Einstein condensates, one can observe not only the two-dimensional (2D) skyrmion spin texture but also the bimeron spin texture. However, it remains challenging to experimentally create or stabilize a bimeron and identify the conditions that facilitate its formation. In this context, our research predicts a novel form of topological structure known as the domain wall bimeron in ferromagnetic spin-1 Bose–Einstein condensates by manipulating the magnetic field. Unlike conventional 2D skyrmions, this unique bimeron exhibits a non-axisymmetric spin texture and features complex off-axis vortices whose cores are connected by domain walls. This work significantly contributes to the study of 2D topological excitations in quantum matter with high spins.
We present the creation and time evolution of two-dimensional Skyrmion excitations in an antiferromagnetic spinor Bose-Einstein condensate. Using a spin rotation method, the Skyrmion spin textures were imprinted on a sodium condensate in a polar phase, where the two-dimensional Skyrmion is topologically protected. The Skyrmion was observed to be stable on a short time scale of a few tens of ms but to dynamically deform its shape and eventually decay to a uniform spin texture. The deformed spin textures reveal that the decay dynamics involves breaking the polar phase inside the condensate without having topological charge density flow through the boundary of the finite-sized sample. We discuss the possible formation of half-quantum vortices in the deformation process.
Atomic-molecular Bose-Einstein condensates (BECs) offer brand new opportunities to revolutionize quantum gases and probe the variation of fundamental constants with unprecedented sensitivity. The recent realization of spin-orbit coupling (SOC) in BECs provides a new platform for exploring completely new phenomena unrealizable elsewhere. In this study, we find a way of creating a Rashba-Dresselhaus SOC in atomic-molecular BECs by combining the spin-dependent photoassociation and Raman coupling, which can control the formation and distribution of a different type of topological excitation---carbon-dioxide-like skyrmion. This skyrmion is formed by two half-skyrmions of molecular BECs coupling with one skyrmion of atomic BECs, where the two half-skyrmions locate at both sides of one skyrmion. Carbon-dioxide-like skyrmion can be detected by measuring the vortices structures using the time-of-flight absorption imaging technique in real experiments. Furthermore, we find that SOC can effectively change the occurrence of the Chern number in kkk space, which causes the creation of topological spin textures from some separated carbon-dioxide-like monomers each with topological charge $\ensuremath{-}2$ to a polymer chain of the skyrmions. This work helps in creating dual SOC atomic-molecular BECs and opens avenues to manipulate topological excitations.
We consider a spin-1 ferromagnetic Bose–Einstein condensate with Rashba spin–orbit coupling (SOC) and dipole–dipole interaction (DDI) in a double-well potential. For the nonrotating case, the ground state of the system is obtained by using the imaginary time propagation method, and a ground-state phase diagram is given with respect to the SOC strength and the DDI strength. It is shown that the nonrotating system sustains rich exotic ground-state phases including the ox-horn phase with hidden vortices and antivortices, density droplet phase with vortex–antivortex pairs, modulated stripe phase with vortex–antivortex chains, checkerboard phase with visible vortex–antivortex chains and hidden vortex–antivortex pairs, and the triangular vortex–antivortex lattice phase. For the rotating case, the dynamics of the system is investigated by using a phenomenological dissipation model. The effects of SOC, DDI and rotation on the unique dynamic behaviors of the rotating system and the final steady-state structures are revealed and analyzed. In particular, the rotating system supports fascinating novel spin textures and skyrmion excitations, and experiences a series of topological structure transitions such as the transitions from an interlaced skyrmion–antiskyrmion lattice pair to a skyrmion–meron lattice pair and then to a meron lattice pair.
Motivated by recent studies of Bose Einstein condensates (BECs) under synthetic gauge fields, we study the textures of F = 2 BECs with a Rashba like spin-orbit coupling (SOC). By analyzing the SOC term, we demonstrate that the SOC favors a helical modulation of order parameters (OPs). In addition, we find the stable textures obtained by the numerical minimization of the Gross-Pitaevskii energy functional and interpret them as a one- or two-dimensional helical modulation. In the parameter region where the polar OP is favored, the emergence of the skyrmion of the uniaxial polar OP and its energetics relative to one-dimensional helical modulation of biaxial polar OP are discussed in details. Through the comparison of the lattice texture in the cyclic favored parameter region and uniaxial polar skyrmion, we show the instability of the lattice of the uniaxial polar skyrmion.