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Physical Review A

Spin-orbit coupling manipulating composite topological spin textures in atomic-molecular Bose-Einstein condensates

Chaofei Liu, Gediminas Juzeliūnas, W. M. Liu

Published Feb 24, 2017• 17 citations
Publisher

Abstract

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 $k$ 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.

DOI
10.1103/physreva.95.023624

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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\ensuremath{-}2\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.
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. However, there is no study of SOC atomic-molecular BECs so far. Here, we find a novel 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 new 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 locates at both sides of one Skyrmion, which can be detected by measuring the vortices structures using the time-of-flight absorption imaging technique in real experiments.
We explore a way of producing the Rashba spin-orbit coupling (SOC) for ultracold atoms by using a two-component (spinor) atomic Bose-Einstein condensate (BEC) confined in a bilayer geometry. The SOC of the Rashba type is created if the atoms pick up a $\ensuremath{\pi}$ phase after completing a cyclic transition between four combined spin-layer states composed of two spin and two layer states. The cyclic coupling of the spin-layer states is carried out by combining an intralayer Raman coupling and an interlayer laser assisted tunneling. We theoretically determine the ground-state phases of the spin-orbit-coupled BEC for various strengths of the atom-atom interaction and the laser-assisted coupling. It is shown that the bilayer scheme provides a diverse ground-state phase diagram. In an intermediate range of the atom-light coupling two interlacing lattices of half-skyrmions and half-antiskyrmions are spontaneously created. In the strong-coupling regime, where the SOC of the Rashba type is formed, the ground state represents plane-wave or standing-wave phases depending on the interaction between the atoms. A variational analysis is shown to be in good agreement with the numerical results.
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.
We investigate the topological defects and spin structures of binary Bose-Einstein condensates (BECs) with Dresselhaus spin-orbit coupling (D-SOC) in a rotating anharmonic trap. Our results show that for initially mixed BECs without SOC the increasing rotation frequency can lead to the structural phase transition of the system. In the presence of isotropic D-SOC, the system sustains vortex pair,Anderson--Toulouse coreless vortices, circular vortex sheets, and combined vortex structures. In particular, when the rotation frequency is fixed above the radial trapping frequency the strong D-SOC results in a peculiar topological structure which is comprised of multi-layer visible vortex necklaces, hidden vortex necklaces and a hidden giant vortex. In addition, the system exhibits rich spin textures including basic skyrmion, meron cluster, skyrmion string and various skyrmion lattices. The skyrmions will be destroyed in the limit of large D-SOC or rotation frequency. Furthermore, the effects of anisotropic D-SOC and Rashba-Dresselhaus SOC on the topological structures of the system are discussed.
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 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 spin-orbit coupled BECs.
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.