In this paper, we study the vortex formation of spin-orbit coupled (SOC) spin-1 dipolar Bose–Einstein condensates by numerically solving the Gross–Pitaevskii equation. We focus the effects of dipole–dipole interaction (DDI) on vortex structures and dynamics behavior. We find that the symmetry of density profiles in vortex lattice formation process and time evolution of the angular momentum is broken in the presence of DDI. This is due to the symmetry breaking of anisotropy DDI. Also, the total angular momentum decreases with increasing the relative dipole strength. However, it is shown that increasing SOC strength can improve the rotation efficiency. This result reflects the SOC dominates the DDI.
In this paper, we study the vortex formation of spin-orbit coupled (SOC) spin-1 dipolar Bose–Einstein condensates by numerically solving the Gross–Pitaevskii equation. We focus the effects of dipole–dipole interaction (DDI) on vortex structures and dynamics behavior. We find that the symmetry of density profiles in vortex lattice formation process and time evolution of the angular momentum is broken in the presence of DDI. This is due to the symmetry breaking of anisotropy DDI. Also, the total angular momentum decreases with increasing the relative dipole strength. However, it is shown that increasing SOC strength can improve the rotation efficiency. This result reflects the SOC dominates the DDI.
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 vortex formation in spin–orbit-coupled (SOC) spin-1 dipolar Bose–Einstein condensates. We focus on the differences in time evolution of several physical quantities such as vorticity profiles, integrated vorticity, angular momentum, and compressible and incompressible kinetic energy. Numerical results show that the three components exhibit rich dynamical behaviors, depending on the competition between SOC and dipole–dipole interactions. Additionally, we also compare different rotation frequencies and contact interactions, showing that they play a significant role in these physical quantities.
In this paper, we study the spin dynamics of spin-orbit-coupled (SOC) spin-2 Bose–Einstein condensates (BECs) with dipole–dipole interaction (DDI). Numerical results are obtained by solving the nonlocal Gross–Pitaevskii equation. Our discussions are divided into two parts. In the absence of DDI, the spin dynamics presents periodic oscillation. Increasing the magnetization makes the amplitude increase, and increasing SOC strength accelerates the spin dynamics and thus changes the period. Nevertheless, in the presence of DDI, the periodicity oscillation of spin dynamics is broken. The thermalization time decreases with the increase of magnetization for fixed SOC strength. In addition, the thermalization time becomes zero with strong SOC strength when magnetization is fixed. We also show the formation of domain in density profile when DDI is considered. Moreover, the components m = 2 and m = −2 exchange their location with a little increase of SOC strength. This is a specific reflection of the competition between the SOC and DDI.
In this paper, we consider the formation of vortices in multilayer stacks of Bose–Einstein condensates with tilted dipoles by numerical simulations of the Gross–Pitaevskii equation. Different dependencies of critical rotation frequency (CRF) and optical lattice height, vortex number, and rotation frequency are studied, depending on the direction of the dipole axis and dipole strength. Our results show that the CRF in z = 0 is minimum. When the optical lattice height is gradually increased, the CRF decreases gradually. Reducing of dipole strength in anisotropic dipole–dipole interaction (DDI) favours the formation of vortices, and such decline in isotropic DDI hinders the creation of vortices. The reason for this difference is that the repulsive interaction is favorable and the attractive interaction is disadvantageous for the vortex formation. In addition, we study the first-order correlation function and focus on variation of coherence. For small rotation frequency, the break of coherence occurs earlier in the case of purely repulsive interaction. With an increase in rotation frequency, the coherence concurrently disappears in layer z = 2. Moreover, we also investigate the quenched dynamics, showing that the increase of angular momentum is induced by changing the direction of dipoles and in this process the vortex number remains unchanged.
Abstract We consider the topological defects and spin structures of spin-1 Bose–Einstein condensates with spin–orbit coupling (SOC) and dipole–dipole interaction (DDI) in a rotating harmonic plus quartic trap. The combined effects of SOC, DDI and rotation on the ground-state phases of the system are analyzed. Our results show that for fixed rotation frequency structural phase transitions can be achieved by adjusting the magnitudes of the SOC and DDI. A ground-state phase diagram is given as a function of the SOC and DDI strengths. It is shown that the system exhibits rich quantum phases including vortex string phase with isolated density peaks (DPs), triangular (square) vortex lattice phase with DPs, checkerboard phase, and stripe phase with hidden vortices and antivortices. For given SOC and DDI strengths, the system can display pentagonal vortex lattice with DPs, vortex necklace with DPs, and exotic topological structure composed of multi-layer visible vortex necklaces, a hidden giant vortex and hidden vortex necklaces, depending on the rotation frequency. In addition, the system sustains fascinating novel spin textures and skyrmion excitations, such as an antiskyrmion pair, antiskyrmion-half-antiskyrmion (antiskyrmion–antimeron) cluster, skyrmion–antiskyrmion lattice, skyrmion–antiskyrmion cluster, skyrmion–antiskyrmion–meron–antimeron lattice, double-layer half-antiskyrmion necklaces, and composite giant-antiskyrmion–antimeron necklaces.