A Kaleidoscope of Topological Structures in Dipolar Bose-Einstein Condensates with Weyl-Like Spin-Orbit Coupling in Anharmonic Trap

TL;DR

This work analyzes the ground states of a quasi-2D two-component dipolar Bose-Einstein condensate featuring Weyl-like spin-orbit coupling in an anharmonic trap under rotation. By solving the coupled Gross-Pitaevskii equations with dipole-dipole interactions, SOC, and rotation, the authors uncover a kaleidoscope of density topologies (disks, rings, wheels, droplets) and complex spin textures, including centric vortices and various (fractional) skyrmions, with transitions and critical behavior governed by the interplay of $\varepsilon_{dd}$, $k$, and $\Omega$. They demonstrate how repulsive and attractive DDI, SOC strength, rotation, and trap anharmonicity jointly sculpt phase separation, miscibility, and multi-layer topological structures, and show that Rashba-type SOC yields similar density patterns but different in-plane spin orientations compared to Weyl-like SOC. The results highlight tunable density and spin topology as resources for quantum metrology and deepen understanding of topological excitations in dipolar quantum gases under synthetic gauge fields.

Abstract

Dipole-dipole interaction (DDI) possesses characteristics different from the conventional isotropic s-wave interaction in Bose-Einstein condensates (BECs), the interplay of DDI with spin-orbit coupling (SOC) and rotation may induce novel quantum properties. We systematically analyze the effects of the DDI, Weyl-like SOC, rotation and trap anharmonicity in the ground state of two-componen BECs. The interplay of these factors leads to a kaleidoscope of quantum states of quantum defects and quantum droplets in lattice, wheel and ring forms of distributions, with transitions of topology of density and a critical behavior in varying the parameters. We also show a bunch of exotic spin topological structures, including centric vortex surrounded by layers of spin flows, compound topological structure of edge defect, and various coexistence states of skyrmions with different topological charge. In particular, we find quarter skyrmions and other possible fractional skyrmions. Rashba-type SOC and Weyl-like SOC are compared as well. Our study implies that one can manipulate both the density topology and the spin topological structure via these tunable parameters in BECs. The abundant variations of the topological structures and particularly the revealed critical behavior may provide various quantum resources for potential applications in quantum metrology.

Figures (7)

• Figure 1: Effect of varying the DDI strength $\varepsilon_{dd}$ on the ground-state density distribution with fixed SOC strength $k=0.8$ and rotation frequency $\Omega=0.3$. (a) $\varepsilon_{dd}=0.0$, (b) $\varepsilon_{dd}=0.2$, (c) $\varepsilon_{dd}=0.5$, (d) $\varepsilon_{dd}=1.0$. (e) $\varepsilon_{dd}=2.5$. (f) $\varepsilon_{dd}=-0.2$. (g) $\varepsilon_{dd}=-0.5$. (h) $\varepsilon_{dd}=-1.0$. (i) $\varepsilon_{dd}=-1.5$. Other parameters are $\beta_{11}=50,\beta_{22}=80,\beta_{12}=200$. The upper two rows represent the density distribution $|\psi_1|^2,|\psi_2|^2$, and the lower two rows denote the phase distribution arg$(\psi_1)$,arg$(\psi_2)$ respectively. The color bar in the first row denotes the density range with the maximum value $0.015$ for (a)-(h) and $160$ for (i).
• Figure 2: Collapse transition and critical behavior in attractive DDI: Density radius of the second component $R$ versus the DDI strength $\varepsilon_{dd}$. Here $k=0.8$, $\Omega=0.3$, $\beta_{11}=50,\beta_{22}=80,\beta_{12}=200$ as in Fig. \ref{['Fig-DDI']}
• Figure 3: Effect of varying the SOC strength $k$ on the ground-state density distribution in fixed DDI $\varepsilon_{dd}=0.5$ and rotation frequency $\Omega=0.4$. (a) $k=0.4$, (b) $k=0.7$, (c) $k=1$, (d) $k=1.2$, (e) $k=1.6$, (f) $k=2$, (g) $k=3.5$. Other parameters are $\beta_{11}=50,\beta_{22}=80,\beta_{12}=200$. The first two rows represent the density distribution, and the last two rows represent the phase distribution. respectively.
• Figure 4: Effect of rotation on the ground-state density distribution in fixed DDI $\varepsilon_{dd}=0.5$ and SOC $k=1.5$. (a) $\Omega=0$, (b) $\Omega=0.2$, (c) $\Omega=0.4$, (d) $\Omega=0.5$, (e) $\Omega=0.6$, (f) $\Omega=0.7$, (g) $\Omega=0.83$. Other parameters are $\beta_{11}=50,\beta_{22}=80,\beta_{12}=200$. The first two rows represent the density distribution, and the last two rows represent the phase distribution. respectively.
• Figure 5: Comparison of harmonic potential and anharmonic potential. (a)-(c) are the density plots of harmonic traps corresponding to the parameters in Figs. \ref{['Fig-Rotation']}(e)-\ref{['Fig-Rotation']}(g) which are replotted here in (d)-(f) for better comparison.