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Journal of Physics Condensed Matter

Spin–orbit coupling induced three-dimensional topological objects in attractive Bose–Einstein condensates

Liang-Liang Xu, Yong-Kai Liu, Shi-Jie Yang

Published Mar 9, 2018• 1 citation
Publisher

Abstract

Attractive Bose-Einstein condensates of dilute alkali gases are unstable against collapse in two- and three-dimensional free space. Nevertheless, we demonstrate that the spin-orbit coupling of the two-component condensates counteracts the tendency of collapse and makes the system preferable to an extended spatial distribution in the three-dimensional case. Furthermore, stable topological objects can be formed in the condensates, which are shown to be the lowest energy states. Two configurations of the density profiles, called three-dimensional skyrmion and three-dimensional dimeron, respectively, are identified depending on the strength of the spin-orbit coupling.

DOI
10.1088/1361-648x/aab55e

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Attractive Bose-Einstein condensates of dilute alkali gases are unstable against collapse in two- and three-dimensional free space. Nevertheless, we demonstrate that the spin-orbit coupling of the two-component condensates counteracts the tendency of collapse and makes the system preferable to an extended spatial distribution in the three-dimensional case. Furthermore, stable topological objects can be formed in the condensates, which are shown to be the lowest energy states. Two configurations of the density profiles, called three-dimensional skyrmion and three-dimensional dimeron, respectively, are identified depending on the strength of the spin-orbit coupling.
A finite-size quasi-two-dimensional Bose-Einstein condensate collapses if the attraction between atoms is sufficiently strong. Here we present a theory of collapse for condensates with the interatomic attraction and spin-orbit coupling. We consider two realizations of spin-orbit coupling: the axial Rashba coupling and the balanced, effectively one-dimensional Rashba-Dresselhaus one. In both cases spin-dependent ``anomalous'' velocity, proportional to the spin-orbit-coupling strength, plays a crucial role. For the Rashba coupling, this velocity forms a centrifugal component in the density flux opposite to that arising due to the attraction between particles and prevents the collapse at a sufficiently strong coupling. For the balanced Rashba-Dresselhaus coupling, the spin-dependent velocity can spatially split the initial state in one dimension and form spin-projected wave packets, reducing the total condensate density. Depending on the spin-orbit-coupling strength, interatomic attraction, and initial state, this splitting either prevents the collapse or modifies the collapse process. These results show that the collapse can be controlled by a spin-orbit coupling, thus extending the domain of existence of condensates of attracting atoms.
Searching for novel topological objects is always an intriguing task for scientists in various fields. We study a three-dimensional (3D) topological structure called a 3D dimeron in trapped two-component Bose-Einstein condensates. The 3D dimeron differs from the conventional 3D skyrmion for the condensates hosting two interlocked vortex rings. We demonstrate that the vortex rings are connected by a singular string and the complexity constitutes a vortex molecule. The stability of the 3D dimeron is examined in two different models using the imaginary time evolution method. We find that the stable 3D dimeron can be naturally generated from a vortex-free Gaussian wave packet incorporating a synthetic non-Abelian gauge potential into the condensates.
By means of variational methods and systematic numerical analysis, we demonstrate the existence of metastable solitons in three dimensional (3D) free space, in the context of binary atomic condensates combining contact self-attraction and spin-orbit coupling, which can be engineered by available experimental techniques. Depending on the relative strength of the intra- and intercomponent attraction, the stable solitons feature a semivortex or mixed-mode structure. In spite of the fact that the local cubic self-attraction gives rise to the supercritical collapse in 3D, and hence the setting produces no true ground state, the solitons are stable against small perturbations, motion, and collisions.
Stable vortex solitons (VSs) are objects of great interest for fundamental studies and various applications, including particle trapping, microscopy, data encoding, and matter-wave gyroscopes. However, three-dimensional (3D) VSs with high topological charges, supported by self-attractive nonlinearities, are unstable against fragmentation, which eventually leads to internal blowup (supercritical collapse) of the fragments. Here, we propose a scheme for realizing stable 3D VSs with topological charges up to 5 and 6 in the two components of a binary, Rydberg-dressed Bose-Einstein condensate with spin-orbit coupling (SOC). We show that, if the SOC strength exceeds a critical value, the rotational symmetry of the VSs in the transverse plane gets broken, resulting in a separation of the two components. Nevertheless, the VSs with the broken symmetry remain stable. The VS stability domains are identified in the system's parameter space. Moreover, application of torque to the stable VSs sets them in the state of robust gyroscopic precession.
It is commonly known that two-dimensional mean-field models of optical and matter waves with cubic self-attraction cannot produce stable solitons in free space because of the occurrence of collapse in the same setting. By means of numerical analysis and variational approximation, we demonstrate that the two-component model of the Bose-Einstein condensate with the spin-orbit Rashba coupling and cubic attractive interactions gives rise to solitary-vortex complexes of two types: semivortices (SVs, with a vortex in one component and a fundamental soliton in the other), and mixed modes (MMs, with topological charges 0 and ±1 mixed in both components). These two-dimensional composite modes can be created using the trapping harmonic-oscillator (HO) potential, but remain stable in free space, if the trap is gradually removed. The SVs and MMs realize the ground state of the system, provided that the self-attraction in the two components is, respectively, stronger or weaker than the cross attraction between them. The SVs and MMs which are not the ground states are subject to a drift instability. In free space (in the absence of the HO trap), modes of both types degenerate into unstable Townes solitons when their norms attain the respective critical values, while there is no lower existence threshold for the stable modes. Moving free-space stable solitons are also found in the present non-Galilean-invariant system, up to a critical velocity. Collisions between two moving solitons lead to their merger into a single one.