In this paper, we study the dynamic properties of spin–orbit coupling (SOC) spin-1 antiferromagnetic Bose–Einstein condensates with inhomogeneous external magnetic field by numerical simulations of the multicomponent Gross–Pitaevskii equation. Our results show that the spin dynamics process is greatly affected by SOC when the system is in the absence of magnetic field. The periodicity of spin exchange dynamics disappears and the population of thermal clouds for [Formula: see text] and [Formula: see text] gradually increases and decreases and then reaches a steady value. In this case, a stable stripe phase emerges for three-component wavefunction. Nevertheless, the spin dynamics process becomes complex in the presence of magnetic field, depending on the competition between magnetic field and SOC. The influences of SOC are masked by the relatively strong magnetic field and the density structures are similar to the case of without or weak magnetic field.
In this paper, we study the dynamic properties of spin–orbit coupling (SOC) spin-1 antiferromagnetic Bose–Einstein condensates with inhomogeneous external magnetic field by numerical simulations of the multicomponent Gross–Pitaevskii equation. Our results show that the spin dynamics process is greatly affected by SOC when the system is in the absence of magnetic field. The periodicity of spin exchange dynamics disappears and the population of thermal clouds for [Formula: see text] and [Formula: see text] gradually increases and decreases and then reaches a steady value. In this case, a stable stripe phase emerges for three-component wavefunction. Nevertheless, the spin dynamics process becomes complex in the presence of magnetic field, depending on the competition between magnetic field and SOC. The influences of SOC are masked by the relatively strong magnetic field and the density structures are similar to the case of without or weak magnetic field.
In this paper, we study the dynamic properties of spin–orbit coupling (SOC) hyperfine f =1 spinor antiferromagnetic Bose–Einstein condensates with the external magnetic field. The condensate is confined in a toroidal trap and the numerical results are obtained based on the multicomponent Gross–Pitaevskii equation. Our results show that, in the presence of SOC, the spin dynamics for zero magnetic field slows with an increase of radius of the torus. However, this process accelerates when the magnetic field is considered. In addition, in this case, the oscillation behavior is almost consistent with the considered maximum radius. In the absence of SOC, the periodicity of spin dynamics vanishes. We also compare the thermalization time for different magnetic fields and radii, which decreases considerably for nonzero magnetic fields with the increase of radius. Furthermore, our analysis suggests that for stronger magnetic field strength the density structure can be regulated. As a consequence, the condensate recovers from the necklace to an annular-shaped state.
In this paper, we study the dynamics properties of three-component antiferromagnetic dipolar Bose–Einstein condensates with external magnetic field. Our results are obtained by numerical simulations of the spinor Gross–Pitaevskii equation. We find that the population of the spin components is seriously influenced by magnetic field. The dynamical evolution process is accelerated in the presence of magnetic field. As a result, the periodic oscillation of spin exchange dynamics emerges and the components [Formula: see text] have the same amplitude. In addition, the density profile displays that the influences of dipolar interaction are masked by magnetic field. Moreover, we introduce an order parameter to characterize the disorder-order crossover, where it is seen that the system develops toward the disordered state with strong dipole strength when magnetic field is included.
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 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 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 formation of Shannon information entropy in spin–orbit coupled (SOC) spin-1 antiferromagnetic dipolar Bose–Einstein condensates with external magnetic field. Our results show that, in the absence of magnetic field and with an increase in dipole–dipole interaction (DDI), information entropy in position space [Formula: see text] and momentum space [Formula: see text] remains almost unchanged and increases, respectively. Meanwhile, the order parameter [Formula: see text] decreases, which implies that the system develops toward a disorder state. With the increase of SOC strength, [Formula: see text], [Formula: see text] and [Formula: see text] show similar dynamics behavior. Whereas, in the presence of magnetic field, [Formula: see text] and [Formula: see text] are localized in the small scope by increasing the dipole and SOC strength. In addition, the value of [Formula: see text] is nearly the same in this process. These results embody that the introduction of external magnetic field suppresses the role of SOC and DDI, and impedes the condensates towards disorder state. At last, the influence of geometric structure and atom number on information entropy is investigated. It is seen that a narrower trap and fewer atom number make [Formula: see text] decrease and [Formula: see text] increase.