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arXiv:2506.09341 · Physical Review Research

Collective oscillations of Bose-Einstein condensates in a synthetic magnetic field

Huaxin He, Fengtao Pang, Yongping Zhang, Chunlei Qu

Published Feb 27, 2025• 2 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevresearch.7.013219

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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.
We study the scissors modes of a harmonically trapped Bose-Einstein condensate under the influence of a synthetic magnetic field, which induces rigid rotational components in the velocity field. Our investigation reveals that the scissors mode, excited in the plane perpendicular to the synthetic magnetic field, becomes coupled to the quadrupole modes of the condensate, giving rise to typical beating effects. Moreover, the two scissors modes excited in the vertical planes are also coupled together by the synthetic magnetic field, resulting in intriguing gyroscope dynamics. Our analytical results, derived from a spinor hydrodynamic theory, are further validated through numerical simulations of the three-dimensional Gross-Pitaevskii equation. These predictions for the condensates subject to a synthetic magnetic field are experimentally accessible with current cold-atom setups and hold promise for potential applications in quantum sensing.
We systematically investigate the ground state and dynamics of spinor Bose-Einstein condensates subject to a position-dependent detuning. This detuning induces three related quantities (a synthetic magnetic field, an angular velocity, and an angular momentum), which, due to trap anisotropy, may point in different directions. When the dipole frequencies along the three symmetric axes of the harmonic trap are degenerate, the dipole motion can decompose into two coupled transverse modes in the plane perpendicular to the synthetic magnetic field, and another decoupled longitudinal mode, enabling controllable Foucault-like precession or biconical trajectories depending on the excitation protocol. Furthermore, quenching the orientation of the synthetic magnetic field excites multiple coupled quadrupole modes. We develop a hydrodynamic theory whose predictions match well with Gross-Pitaevskii simulations. This study contributes to a deeper understanding of the effects of the synthetic magnetic field and the excitations of the collective mode in quantum fluids, providing a foundation for future developments in quantum simulation and high-precision sensing technologies.
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.
We investigate the expansion dynamics of spin-orbit-coupled Bose-Einstein condensates subjected to a synthetic magnetic field, after their release from an external harmonic trap. Our findings reveal that the condensate experiences a spin-dependent rotation and separation due to the rigid-like rotational velocity field, which leads to a spin-density deflection. The deflection angle reaches a peak at an expansion time that is inversely related to the trap frequency. When the detuning gradient is below a critical value for vortex nucleation, our analytical results derived from a spinor hydrodynamic theory align closely with numerical results using the coupled Gross-Pitaevskii equations. Beyond this critical value, we also numerically simulated the expansion dynamics of the condensates containing vortices with negative circulation. Our findings highlight the pivotal role of the rigid-like rotational velocity field on the dynamics of the condensate and may stimulate further experimental investigations into the rich superfluid dynamics induced by synthetic magnetic fields.
We theoretically investigate quadrupolar collective excitations in two-component Bose-Einstein condensates and their nonlinear dynamics associated with harmonic generation and mode coupling. Under the Thomas-Fermi approximation and the quadratic polynomial ansatz for density fluctuations, the linear analysis of the superfluid hydrodynamic equations predicts excitation frequencies of three normal modes constituted from monopole and quadrupole oscillations, and those of three scissors modes. These six modes are bifurcated into in-phase and out-of-phase modes by the intercomponent interaction, yielding the nonlinear dynamics that are absent in a single-component condensate. We obtain analytically the resonance conditions for the second-harmonic generation in terms of the trap aspect ratio and the strength of intercomponent interaction. The numerical simulation of the coupled Gross-Pitaevskii equations vindicates the validity of the analytical results and reveals the dynamics of the second-harmonic generation and nonlinear mode coupling that lead to nonlinear oscillations of the condensate with damping and recurrence reminiscent of the Fermi-Pasta-Ulam problem.
By applying a position-dependent detuning to a spin-orbit-coupled Hamiltonian with equal Rashba and Dresselhaus coupling, we exploit the behavior of the angular momentum of a harmonically trapped Bose-Einstein condensed atomic gas and discuss the distinctive role of its canonical and spin components. By developing the formalism of spinor hydrodynamics, we predict the precession of the dipole oscillation caused by the synthetic rotational field, in analogy with the precession of the Foucault pendulum, the excitation of the scissors mode, following the sudden switching off of the detuning, and the occurrence of Hall-like effects. When the detuning exceeds a critical value, we observe a transition from a vortex free, rigidly rotating quantum gas to a gas containing vortices with negative circulation which results in a significant reduction of the total angular momentum.