We study the phase separation in three-component spin-orbit-angular-momentum coupled Bose–Einstein condensate with spin-1 in three dimensions. Different types of phase-separation are acquired upon an increase of the coupling strength, magnetic gradient strength, spin-dependent interaction strength and particle number above a critical value. Increasing the value of coupling strength and other related parameters shows distinct behaviors which are produced by repulsion for large strengths of spin-orbit angular-momentum (SOAM) coupling. The present investigation is carried out through a numerical Crank–Nicolson method of the underlying mean-field Gross–Pitaevskii equation.
We study the phase separation in three-component spin-orbit-angular-momentum coupled Bose–Einstein condensate with spin-1 in three dimensions. Different types of phase-separation are acquired upon an increase of the coupling strength, magnetic gradient strength, spin-dependent interaction strength and particle number above a critical value. Increasing the value of coupling strength and other related parameters shows distinct behaviors which are produced by repulsion for large strengths of spin-orbit angular-momentum (SOAM) coupling. The present investigation is carried out through a numerical Crank–Nicolson method of the underlying mean-field Gross–Pitaevskii equation.
In this study, we study the circularly-symmetric phase separation in spin-1 spin-orbit-angular-momentum coupled (SOAMC) [Formula: see text] Bose–Einstein condensate (BEC) system in the [Formula: see text]-plane using a numerical solution of the mean-field Gross–Pitaevskii equation. The increase of the coupling strength [Formula: see text] in such a system is found to generate annular structures. The phase-separated had different structures with the spin and linear momentum coupling BEC. Our results are in good agreement with the new experiment H. R. Chen, K. Y. Lin, P. K. Chen, N. C. Chiu, J. B. Wang and C.-A. Chen, Phys. Rev. Lett. 121 (2018) 113204. We also analyzed the influence of different parameters of SOAMC on coupling strength [Formula: see text], spin correlation coefficient [Formula: see text], the number of particles [Formula: see text], and the anisotropy of the potential in the three-component equations. The dynamical stability of the phase separation is demonstrated by real-time propagation numerically.
We study the phase separation in three-component bright vector solitons in a quasi-one-dimensional spin-orbit-coupled hyperfine spin F=1 ferromagnetic Bose-Einstein condensate upon an increase of the strength of spin-orbit (SO) coupling ${p}_{x}{\mathrm{\ensuremath{\Sigma}}}_{z}$ above a critical value, where px is the linear momentum and ${\mathrm{\ensuremath{\Sigma}}}_{z}$ is the z component of the spin-1 matrix. The bright vector solitons are demonstrated to be mobile and dynamically stable. The collision between two such vector solitons is found to be elastic at all velocities with the conservation of density of each vector soliton. The two colliding vector solitons repel at small separation and at very small colliding velocity, they come close and bounce back with the same velocity without ever encountering each other. This repulsion produced by SO coupling is responsible for the phase separation in a vector soliton for large strengths of SO coupling. The collision dynamics is found to be completely insensitive to the relative phase of the colliding solitons. However, in the absence of SO coupling, at very small velocity, the two colliding vector solitons attract each other and form a vector soliton molecule and the collision dynamics is sensitive to the relative phase as in scalar solitons. The present investigation is carried out through a numerical solution and an analytic variational approximation of the underlying mean-field Gross-Pitaevskii equation.
In this article, we study the vortex formation in spin-1 spin–orbit coupling rotating Bose–Einstein condensates. Numerical results are obtained by solving the spinor Gross–Pitaevskii equation. We mainly focus on the influences of external magnetic fields on vortex structures and dynamics properties. With the increase in magnetic field strength, the populations of magnetic components j=±1 reach the identical value. For the density profile, the three components present identical density structures, and the size of condensates is nearly the same. In addition, some related physical quantities, such as the time taken for the arrival of a steady population and root-mean-square size, kinetic energy, and total angular momentum, are calculated. The results show that these quantities decrease as the magnetic field strength increases. Moreover, we also investigate the time evolution of angular momentum. It is seen that the dynamic behavior of the magnetic components j=±1 is exactly consistent, and the total angular momentum reduces in the presence of the strong magnetic field. This reflects the fact that the introduction of the strong magnetic field makes it difficult to rotate the condensate, and thus, it is disadvantageous for generating more vortices.
In this paper, we investigate the dynamic properties of spin–orbit coupling spin-1 ferromagnetic Bose–Einstein condensates with different trap geometry. Our results are obtained in terms of the three-component Gross–Pitaevskii equation of mean-field theory. Two kinds of trap potential are discussed: isotropic and anisotropic. It is shown that the spin-exchange dynamics are greatly influenced by trap geometry. For the latter with weak spin–orbit coupling strength, we find that the three-component oscillation accelerates and some small difference emerges between component m=1 and m=-1. With the increase in spin–orbit coupling strength, the three components reach almost the same population. In addition, the kinetic energy of the system changes within a small scope for strong spin–orbit coupling, as opposed to a constant value in an isotropic trap. The density distributions display that the stripe phase appears with the increase in spin–orbit coupling strength. The method of generating stripe structure is different from the ground state of ferromagnetic condensate. For isotropic trap, the spatial separation of top and bottom spin–orbit condensates in component m=1 and m=-1 occurs at weak spin–orbit coupling, and square lattice appears at strong spin–orbit coupling.
In this paper, we study the ground state of two-component spin–orbit-coupled (SOC) Bose–Einstein condensates with mass imbalance. Our results are based on the framework of mean-field Gross–Pitaevskii theory. The effects of unequal atomic mass and SOC strength are studied. Different density structures such as heliciform stripes, linear stripes and string vortex chains are found. Different density structures such as heliciform stripes, linear stripes and string vortex chains are found. With the increase of SOC strength, the azimuthal phase separation is kept while radial phase separation is broken. In addition, increasing the mass ratio is unfavorable to vortex formation, whereas more vortices can be generated by increasing the SOC strength. We also discuss the physical quantities such as angular momentum per atom and spin polarisation, for a larger mass ratio, showing that angular momentum gets a little bigger as the SOC strength increases and the first-order phase transition does not exist.
We study the ground-state phases of two-dimensional spin-orbit coupled spin-1 Bose-Einstein condensate loaded in a plane quadrupole field. In the absence of rotation, for the fixed spin-orbit coupling strength, the ordinary stripe phase is found when the strength of the magnetic field gradient is small. As the strength of magnetic field gradient enhances, the system realizes the phases with three layer vortices along the radial direction. The number of vortices in the second layer is successively increased and the vortices in the outermost layer disappear when the strength of magnetic field gradient surpass the critical value. For the large strength of magnetic field gradient, the system only has the inner layer vortices. The magnetic field inhibits the region of vortices. For the fixed magnetic field gradient strength, the vortices of the system elongate along the radial direction and form a series of vortex lines, the number of the vortex line increases as the strength of spin-orbit coupling enhances. By adding the rotation, for the fixed strengths of spin-orbit coupling and magnetic field gradient, the number of second layer vortices also successively increases as the rotational frequency increases. The number of vortices in the certain layer of the ground-state density can be regularly changed under the effects of the magnetic field and spin-orbit coupling.