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arXiv:2512.05691

Quenching dynamics of vortex in spin-orbit coupled Bose-Einstein condensates

Juan Wang, Zhenze Fan, Yan Li

cond-mat.quant-gasphysics.atom-phquant-phSubmitted Dec 5, 2025• Announced Dec 8, 2025• 0 citations
v1 · Dec 5, 2025v2 · Dec 15, 2025
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Abstract

We investigate the ground states and rich dynamics of vortices in spin-orbit coupled Bose-Einstein condensates (BEC) subject to position-dependent detuning. Such a detuning plays the role of an effective rotational frequency, causing the generation of a synthetic magnetic field. Through scanning the detuning gradient, we numerically obtain static vortex lattice structures containing 1 to 6 vortices using the coupled Gross-Pitaevskii equations. When quenching detuning gradient below its initial value, the vortex lattices exhibit interesting periodic rotation motion, and their dynamical stability can persist for up to 1000ms. In particular, depending on the detuning gradient, the twin vortices exhibit either a scissors-like rotational oscillation or a clockwise periodic rotation, reflecting the response to the magnetic field gradient experienced by the condensates. We fit the numerical results to quantitatively analyze the relation between rotation dynamics and magnetic field gradients. When quenching the detuning gradient beyond its initial value, additional vortices appear. Our findings may motivate further experimental studies of vortex dynamics in synthetic magnetic fields and offer insights for engineering a BEC-based magnetic field gradiometer.

Comments
9 pages, 10 figures

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We investigate the ground states and rich dynamics of vortices in spin-orbit coupled Bose-Einstein condensates (BEC) subject to position-dependent detuning. Such a detuning plays the role of an effective rotational frequency, causing the generation of a synthetic magnetic field. Through scanning the detuning gradient, we numerically obtain static vortex lattice structures containing 1 to 6 vortices using the coupled Gross-Pitaevskii equations. When quenching detuning gradient below its initial value, the vortex lattices exhibit interesting periodic rotation motion, and their dynamical stability can persist for up to 1000ms. In particular, depending on the detuning gradient, the twin vortices exhibit either a scissors-like rotational oscillation or a clockwise periodic rotation, reflecting the response to the magnetic field gradient experienced by the condensates. We fit the numerical results to quantitatively analyze the relation between rotation dynamics and magnetic field gradients. When quenching the detuning gradient beyond its initial value, additional vortices appear. Our findings may motivate further experimental studies of vortex dynamics in synthetic magnetic fields and offer insights for engineering a BEC-based magnetic field gradiometer.
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We study the collective oscillations of spin-orbit-coupled Bose-Einstein condensates in the presence of position-dependent detuning. Specifically, we explore the quadrupole modes of the system using both numerical and analytical approaches based on the Gross-Pitaevskii equation and hydrodynamic theory. Due to spin-orbit coupling and the synthetic magnetic field, the x y scissors mode couples with a superposition of the three diagonal quadrupole modes ( x 2 , y 2 , and z 2 ), resulting in the characteristic beating effect. The remaining two scissors modes, x z and y z , are coupled, giving rise to a Lissajous-like pattern that is highly sensitive to the excitation method and orientation of the synthetic magnetic field. Furthermore, we find that anisotropic interactions as well as the direction of the synthetic magnetic field, can significantly influence the oscillation amplitude and frequency of the quadrupole modes. These findings highlight the potential of Bose-Einstein condensates under synthetic magnetic fields for quantum sensing applications, such as magnetic field gradient measurements, and provide a promising foundation for future experimental research and technological development.
Two-component Bose-Einstein condensate offers an ideal platform for investigating many intriguing topological defects due to the interplay between intraspecies and interspecies interactions. The recent realization of spin-orbit coupling in two-component Bose-Einstein condensate, owing to coupling between the spin and the centre-of-mass motion of the atom, provides possibly new opportunities to search for novel quantum states. In particular, the gradient magnetic field in the Bose-Einstein condensate has brought a new way to create topologically nontrivial structures including Dirac monopoles and quantum knots. Previous studies of the gradient magnetic field effect in the Bose-Einstein condensate mainly focused on the three-component case. However, it remains unclear how the gradient magnetic field affects the ground state configuration in the rotating two-component Bose-Einstein condensate with spin-orbit coupling. In this work, by using quasi two-dimensional Gross-Pitaevskii equations, we study the ground state structure of a rotating two-component Bose-Einstein condensate with spin-orbit coupling and gradient magnetic field. We concentrate on the effects of the spin-orbit coupling and the gradient magnetic field on the ground state. The numerical results show that increasing the strength of the spin-orbit coupling can induce a phase transition from skyrmion lattice to skyrmion chain in the presence of the gradient magnetic field. Unlike the study of skyrmion in rotating two-component Bose-Einstein condensate with only spin-orbit coupling, the skyrmion chain can occur under the isotropic spin-orbit coupling when the gradient magnetic field is considered. It is worth noting that the skyrmion chain here is arrayed along the diagonal direction. Next we examine the effect of the gradient magnetic field on spin-orbit coupled two-component Bose-Einstein condensate. For the case of weak spin-orbit coupling and the slow rotation, a phase transition from a single plane-wave to half-skyrmion is found through increasing magnetic field gradient strength. For the case of strong spin-orbit coupling and the fast rotation, the nature of the ground state is shown to support the formation of a hidden vortex as the gradient magnetic field is enhanced. These hidden vortices have no visible cores in density distributions but have phase singularities in phase distributions, which are arrayed along the diagonal direction. This result confirms a new method of creating the hidden vortices in the two-component Bose-Einstein condensate. These topological structures can be detected by using the time-of-flight absorption imaging technique. Our results illustrate that the gradient magnetic field not only provides an opportunity to explore the exotic topological structures in spin-orbit coupled spinor Bose-Einstein condensate, but also is crucial for realizing the phase transitions among different ground states. This work paves the way for the future exploring of topological defect and the corresponding dynamical stability in quantum systems subjected to a gradient magnetic field.
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Realistic methods to create vortices in spin-orbit-coupled Bose-Einstein condensates are discussed. It is shown that, contrary to common intuition, rotation of the trap containing a spin-orbit condensate does not lead to an equilibrium state with static vortex structures but gives rise instead to nonequilibrium behavior described by an intrinsically time-dependent Hamiltonian. We propose here the following alternative methods to induce thermodynamically stable static vortex configurations: (i) to rotate both the lasers and the anisotropic trap and (ii) to impose a synthetic Abelian field on top of synthetic spin-orbit interactions. Effective Hamiltonians for spin-orbit condensates under such perturbations are derived for most currently known realistic laser schemes that induce synthetic spin-orbit couplings. The Gross-Pitaevskii equation is solved for several experimentally relevant regimes. The new interesting effects include spatial separation of left- and right-moving spin-orbit condensates, the appearance of unusual vortex arrangements, and parity effects in vortex nucleation where the topological excitations are predicted to appear in pairs. All these phenomena are shown to be highly nonuniversal and depend strongly on a specific laser scheme and system parameters.