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International Journal of Modern Physics B

Information entropy in spin–orbit coupled dipolar condensates with magnetic field

Qiang Zhao

Published Aug 17, 2024• 0 citations
Publisher

Abstract

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.

DOI
10.1142/s0217979225500845

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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 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 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 properties of information entropy in spin–orbit coupled spin-1 Bose–Einstein condensates. Our discussion is divided into two parts, stationary state and dynamics. For the former, we find that the coordinate component Sr and total entropy S increase with the strength of the spin–orbit coupling [Formula: see text]. The momentum component Sk shows a discontinuity behavior, it increases with [Formula: see text] when [Formula: see text] is lesser than a critical value [Formula: see text], while it decreases with [Formula: see text] when [Formula: see text] is greater than [Formula: see text]. In order to characterize the disorder-to-order transition, we introduce an order parameter [Formula: see text]. Numerical results display that [Formula: see text] gradually increases with increasing [Formula: see text] and reaches its saturation, which implies that the system becomes more and more ordered. For the latter, the Sr increases and Sk decreases with increasing [Formula: see text] at the same time. The entropic uncertainty relation is well obeyed at fixed [Formula: see text]. Moreover, [Formula: see text] decreases as a function of t. The strength effect of spin–orbit coupling on order-to-disorder transition becomes weak.
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 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 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.