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arXiv:2509.13800

Anomalous Trajectory Drift and Geometric Phases of Cyclic Spinor Solitons Induced by Virtual Magnetic Monopoles

Wu, Ruo-Yun, Ning Mao, Xiaolin Li, Jie Liu, Li-Chen Zhao

Published Sep 17, 2025• 0 citations
arXivHTMLPDF

Abstract

We investigate the dynamics of a two-component Bose-Einstein condensate with spin-orbit coupling numerically and analytically. Under the drive of a weak segmented rotational external field, we observe that the system exhibits cyclic soliton motion; however, in contrast to the predictions of quasi-particle theory, the trajectory of the soliton center shows a distinct drift. The underlying mechanism of this anomalous drift is revealed: the moving soliton experiences a Lorentz force induced by a virtual magnetic monopole field in momentum space. We further calculate the phase evolution of the soliton during this cyclic motion and find that its geometric component comprises both an adiabatic Berry phase and a nonadiabatic Aharonov-Anandan phase. Notably, the Berry phase can be expressed in terms of the magnetic flux of the aforementioned virtual monopole field. Our findings hold implications for geometric phase theory and experiments on two-component Bose-Einstein condensates, and may establish a novel link between quantum geometry and soliton dynamics.

DOI
10.48550/arxiv.2509.13800

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We investigate the dynamics of a two-component Bose-Einstein condensate with spin-orbit coupling numerically and analytically. Under the drive of a weak segmented rotational external field, we observe that the system exhibits cyclic soliton motion; however, in contrast to the predictions of quasi-particle theory, the trajectory of the soliton center shows a distinct drift. The underlying mechanism of this anomalous drift is revealed: the moving soliton experiences a Lorentz force induced by a virtual magnetic monopole field in momentum space. We further calculate the phase evolution of the soliton during this cyclic motion and find that its geometric component comprises both an adiabatic Berry phase and a nonadiabatic Aharonov-Anandan phase. Notably, the Berry phase can be expressed in terms of the magnetic flux of the aforementioned virtual monopole field. Our findings hold implications for geometric phase theory and experiments on two-component Bose-Einstein condensates, and may establish a novel link between quantum geometry and soliton dynamics.
For a spin-carrying particle moving in a spatially varying magnetic field, effective electromagnetic forces can arise due to the geometric phase associated with adiabatic spin rotation of the particle. We report the observation of a geometric Hall effect in a spinor Bose-Einstein condensate with a skyrmion spin texture. Under translational oscillations of the spin texture, the condensate resonantly develops a circular motion in a harmonic trap, demonstrating the existence of an effective Lorentz force. When the condensate circulates, quantized vortices are nucleated in the boundary region of the condensate and the vortex number increases over 100 without significant heating. We attribute the vortex nucleation to the shearing effect of the effective Lorentz force from the inhomogeneous effective magnetic field.
We theoretically establish that non-Hermitian perturbations induce a topological transformation of point-like Dirac monopoles into extended monopole distributions, characterized by distinct charge configurations emergent from three distinct Berry connection forms. Using piecewise adiabatic evolution, we confirm the validity of these configurations through observations of complex geometric phases. Most critically, we find a quantitative relation Δϕd=ΔϕgΔϕ_d = Δϕ_gΔϕd​=Δϕg​, which quantifies how cumulative minute energy differences (ΔϕdΔϕ_dΔϕd​) manifest as geometric phase shifts (ΔϕgΔϕ_gΔϕg​) uniquely in non-Hermitian systems. We further propose a scheme leveraging soliton dynamics in dissipative two-component Bose-Einstein condensates, enabling direct measurement of these topological signatures. These results establish a milestone for understanding Dirac monopole charge distributions and measuring complex geometric phases in non-Hermitian systems, with far-reaching implications for topological quantum computing and non-Hermitian photonics.
Magnetic monopoles describe isolated north or south magnetic poles. The practical detection of the free magnetic monopoles, due to their extremely heavy masses, remains challenging so far. However, Bose-Einstein condensates offer an ideal observable platform for probing monopoles. In particular, the recent realization of spin-orbit (SO) coupling, owing to its high controllability and tunability, provides an unprecedented opportunity to explore exotic structures and phase transitions of monopoles unrealizable elsewhere. Here we report Dirac monopoles attached to the polar-core vortex induced by SO coupling in ferromagnetic Bose-Einstein condensates, which can be readily observed via time of flight measurements in experiment. The results show that, a cyclic phase transition from Dirac monopoles with polar-core vortex to that with Mermin-Ho vortex, is induced by SO coupling. Our studies may open a new direction to realize exotic topological defects and phase transitions in quantum systems.
We report families of two-dimensional (2D) composite solitons in spinor dipolar Bose-Einstein condensates, with two localized components linearly mixed by the spin-orbit coupling (SOC), and the intrinsic nonlinearity represented by the dipole-dipole interaction (DDI) between atomic magnetic moments polarized in plane by an external magnetic field. Recently, stable solitons were predicted in the form of semivortices (composites built of coupled fundamental and vortical components) in the 2D system combining the SOC and contact attractive interactions. Replacing the latter by the anisotropic long-range DDI, we demonstrate that, for a fixed norm of the soliton, the system supports a continuous family of stable spatially asymmetric vortex solitons (AVSs), parameterized by an offset of the pivot of the vortical component relative to its fundamental counterpart. The offset is limited by a certain maximum value, while the energy of the AVS practically does not depend on the offset. At small values of the norm, the vortex solitons are subject to a weak oscillatory instability. In the present system, with the Galilean invariance broken by the SOC, the composite solitons are set in motion by a kick the strength of which exceeds a certain depinning value. The kicked solitons feature a negative effective mass, drifting along a spiral trajectory opposite to the direction of the kick. A critical angular velocity, up to which the semivortices may follow rotation of the polarizing magnetic field, is found too.
For a spin-carrying particle moving in a spatially varying magnetic field, effective electromagnetic forces can arise due to the geometric phase associated with adiabatic spin rotation of the particle. We report the observation of a geometric Hall effect in a spinor Bose-Einstein condensate with a Skyrmion spin texture. Under translational oscillations of the spin texture, the condensate resonantly develops a circular motion in a harmonic trap, demonstrating the existence of an effective Lorentz force. When the condensate circulates, quantized vortices are nucleated in the boundary region of the condensate and the vortex number increases over 100 without significant heating. We attribute the vortex nucleation to the shearing effect of the effective Lorentz force from the inhomogeneous effective magnetic field.
We propose a method to simulate adiabatically driven two-level quantum systems and detect the Berry phase induced in the cyclic evolution by observing the classical orbit motion of a charged particle under a time-varying magnetic field. Analogy between the dynamics of these two species of systems is revealed and the correspondence relationship is established by virtue of their equations of motion, i.e., the von Neumman equation of the quantum binary system and the Newton-Lorentz equation of the charged particle. In particular, we show how the complex phase information of the quantum system, say, the Berry phase shift acquired by its wave function during the loop evolution, can be visually captured by examining the spatial motion of the classical particle.