In this study, we investigate the dynamics properties of spin-1 ferromagnetic Bose–Einstein condensates (BECs) with dipole–dipole interaction (DDI). Numerical results are obtained by solving the mean-field nonlocal Gross–Pitaevskii equation. We find that the population of the information entropy in momentum space [Formula: see text] is greatly affected by geometric structure and dipole strength. The prolate condensate is favorable to obtain bigger [Formula: see text] than oblate condensate. The density distribution verifies that the formation of magnetic domain is associated with the variation of [Formula: see text]. In addition, the kinetic energy displays that dramatical oscillation appears for strong dipolar interaction and it is larger in prolate condensate. Also, we use the order parameter to describe the order–disorder crossover. It is shown that BECs develop toward the disordered state with prolate condensate under strong DDI.
In this study, we investigate the dynamics properties of spin-1 ferromagnetic Bose–Einstein condensates (BECs) with dipole–dipole interaction (DDI). Numerical results are obtained by solving the mean-field nonlocal Gross–Pitaevskii equation. We find that the population of the information entropy in momentum space [Formula: see text] is greatly affected by geometric structure and dipole strength. The prolate condensate is favorable to obtain bigger [Formula: see text] than oblate condensate. The density distribution verifies that the formation of magnetic domain is associated with the variation of [Formula: see text]. In addition, the kinetic energy displays that dramatical oscillation appears for strong dipolar interaction and it is larger in prolate condensate. Also, we use the order parameter to describe the order–disorder crossover. It is shown that BECs develop toward the disordered state with prolate condensate under strong DDI.
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.
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 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 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.
Calculation of the Shannon information entropy (S) and its connection with the order-disorder transition and with inter-particle interaction provide a challenging research area in the field of quantum information. Experimental progress with cold trapped atoms has corroborated this interest. In the present work, S is calculated for the Bose-Einstein condensate (BEC) with dominant dipolar interaction for different dipole strengths, trap aspect ratios, and number of particles (N). Trapped dipolar bosons in an anisotropic trap provide an example of a system where the effective interaction is strongly determined by the trap geometry. The main conclusion of the present calculation is that the anisotropic trap reduces the number of degrees of freedom, resulting in more ordered configurations. Landsberg's order parameter exhibits quick saturation with the increase in scattering length in both prolate and oblate traps. We also define the threshold scattering length which makes the system completely disordered. Unlike non-dipolar BEC in a spherical trap, we do not find a universal linear relation between S and lnN, and we, therefore, introduce a general quintic polynomial fit rather well working for a wide range of particle numbers.