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Acta Physica Sinica

Rotating Dipolar Quantum Gas in a Box Trap

LI Shicheng, WANG Shuai, Xingcan Yao

Published Sep 4, 2026• 0 citations

Abstract

盒型势阱提供了均匀且边界锐利的囚禁势，有效避免了简谐势阱所固有的势场非均匀性，为研究偶极量子气体的旋转效应提供了理想平台。本文在旋转参考系下求解三维扩展 Gross–Pitaevskii方程，采用分步 Crank–Nicolson 方法结合虚时演化，系统研究了盒型势阱中偶极玻色气体的基态密度分布与旋转下的涡旋构型。数值研究发现，随接触散射长度 as 减小，径向环状密度调制连续增强，但体系始终保持旋转对称性；当 as 降至临界值时，旋转对称性发生自发破缺，角向密度调制突然涌现。引入旋转后，当转动频率超过临界值，表面模式的软化使多个涡旋近乎同时进入凝聚体，总环量量子数随之由零跃变为有限值。相对偶极强度的增大进一步软化了表面模式，降低了涡旋成核的能量代价，使涡旋在更低转动频率下即可出现。随转动频率继续升高，离心势将原子推向体系边缘，中心形成低密度区域；涡旋向中心汇聚，形成当前空间分辨率下不可分辨的，具有多环量量子数的中心结构，并与外围项链状单量子涡旋共存，这明显不同于简谐势阱中常见的 Abrikosov 涡旋晶格。上述结果表明，盒型势阱的锐利边界与偶极相互作用共同决定了旋转偶极超流中量子涡旋的空间构型，为后续实验研究盒型势阱中的偶极量子气体提供了理论参考。

DOI: 10.7498/aps.76.20260754

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盒型势阱提供了均匀且边界锐利的囚禁势，有效避免了简谐势阱所固有的势场非均匀性，为研究偶极量子气体的旋转效应提供了理想平台。本文在旋转参考系下求解三维扩展 Gross–Pitaevskii方程，采用分步 Crank–Nicolson 方法结合虚时演化，系统研究了盒型势阱中偶极玻色气体的基态密度分布与旋转下的涡旋构型。数值研究发现，随接触散射长度 as 减小，径向环状密度调制连续增强，但体系始终保持旋转对称性；当 as 降至临界值时，旋转对称性发生自发破缺，角向密度调制突然涌现。引入旋转后，当转动频率超过临界值，表面模式的软化使多个涡旋近乎同时进入凝聚体，总环量量子数随之由零跃变为有限值。相对偶极强度的增大进一步软化了表面模式，降低了涡旋成核的能量代价，使涡旋在更低转动频率下即可出现。随转动频率继续升高，离心势将原子推向体系边缘，中心形成低密度区域；涡旋向中心汇聚，形成当前空间分辨率下不可分辨的，具有多环量量子数的中心结构，并与外围项链状单量子涡旋共存，这明显不同于简谐势阱中常见的 Abrikosov 涡旋晶格。上述结果表明，盒型势阱的锐利边界与偶极相互作用共同决定了旋转偶极超流中量子涡旋的空间构型，为后续实验研究盒型势阱中的偶极量子气体提供了理论参考。

We study the formation and dynamics of vortices in quasi two-dimensional dipolar Bose-Einstein condensates (BECs). We solve the time dependent two-dimensional Gross-Pitaevskii equation by using a combined split-step Crank-Nicolson (SSCN) and Fast Fourier-Transform (FFT) based numerical scheme and investigate the vortex dynamics in dipolar BECs trapped with harmonic and optical lattice potentials. The consequence of dipole-dipole interaction on vortex nucleation and number of vortices has been analysed. We observe that the breaking of symmetry due to anisotropic dipolar interaction enormously increase the speed of creation of vortices.

We study a system of ultra-cold dipolar Bose gas atoms confined in a two-dimensional (2D) harmonic trap with a dipolar impurity implanted at the center of the trap. Due to recent experimental progress in dipolar condensates, we focused on calculating properties of dipolar impurity systems that might guide experimentalists if they choose to study impurities in dipolar gases. We used the Gross–Pitaevskii formalism solved numerically via the split-step Crank–Nicolson method. We chose parameters of the background gas to be consistent with dysprosium (Dy), one of the strongest magnetic dipoles and of current experimental interest, and used chromium (Cr), erbium (Er), terbium (Tb), and Dy for the impurity. The dipole moments were aligned by an external field along what was chosen to be the z-axis, and we studied 2D confinements that were perpendicular or parallel to the external field. We show density contour plots for the two confinements, 1D cross-sections of the densities, calculated self-energies of the impurities while varying both number of atoms in the condensate and the symmetry of the trap. We also calculated the time evolution of the density of an initially pure system where an impurity is introduced. Our results show that while the self-energy increases in magnitude with increasing number of particles, it is reduced when the trap anisotropy follows the natural anisotropy of the gas, i.e., elongated along the z-axis in the case of parallel confinement. This work builds upon work conducted in Bose gases with zero-range interactions and demonstrates some of the features that could be found when exploring dipolar impurities in 2D Bose gases.