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International Journal of Theoretical Physics

Effect of Dipolar Interaction on Information Entropy in Precession Bose-Einstein Condensates

Qiang Zhao, Shichao Yang, Xiaoyu Li

Published May 11, 2020• 2 citations
Publisher
DOI
10.1007/s10773-020-04455-8

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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.

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The dynamics of vortex in a trapped quasi-two-dimensional Bose-Einstein condensate (BEC), which produce vortex-sound interaction was discussed. It was observed that a vortex precession in a trapped quasi-2D BEC at low temperature emits dipolar radiation, which becomes modified into a spiral wave pattern due to the motion of the vortex. The results show that the vortex energy decays at a rate proportional to its acceleration squared and inversely proportional to the precession frequency. It was suggested that sound emission and reabsorption can be controlled by varying the depth of the dimple.

•Dec 31, 2004•0 citations
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.
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.
The dynamics of vortex in a trapped quasi-two-dimensional Bose-Einstein condensate (BEC), which produce vortex-sound interaction was discussed. It was observed that a vortex precession in a trapped quasi-2D BEC at low temperature emits dipolar radiation, which becomes modified into a spiral wave pattern due to the motion of the vortex. The results show that the vortex energy decays at a rate proportional to its acceleration squared and inversely proportional to the precession frequency. It was suggested that sound emission and reabsorption can be controlled by varying the depth of the dimple.