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Europhysics Letters (EPL)

Nonlinear chiral quantum dynamics of Bose-Einstein condensates under a density-dependent gauge field

Chun-Long Ma, Ai‐Xia Zhang, Xin Qiao, Fang-Qi Hu, Ju-Kui Xue

Published Sep 22, 2026• 0 citations
Publisher

Abstract

Abstract We investigate chiral quantum dynamics of a Bose-Einstein condensate confined in a finite-depth potential well under a density-dependent gauge field. The interplay of the finite-depth potential well and the gauge field results in rich chiral dynamics. When the external potential is strong, coherent chiral collective dynamics, i.e. , chiral breathing dynamics accompanied by the dipole dynamics emerges. The wave packet in the well undergoes periodic directional-dependent compression/expansion. Notably, this chiral dynamics leads to the emergence of a Rabi-like oscillation of particles between the inside and outside well, providing an effective route to investigate the Rabi oscillation in the system. In a weak external potential well, the gauge field dominates and chiral tunneling and diffusion dynamics take place. Particularly, when diffusion and collapse coexist, a chiral moving soliton is generated, which plays a key role for coherent chiral quantum transport.

DOI
10.1209/0295-5075/aeab0b

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Abstract We investigate chiral quantum dynamics of a Bose-Einstein condensate confined in a finite-depth potential well under a density-dependent gauge field. The interplay of the finite-depth potential well and the gauge field results in rich chiral dynamics. When the external potential is strong, coherent chiral collective dynamics, i.e. , chiral breathing dynamics accompanied by the dipole dynamics emerges. The wave packet in the well undergoes periodic directional-dependent compression/expansion. Notably, this chiral dynamics leads to the emergence of a Rabi-like oscillation of particles between the inside and outside well, providing an effective route to investigate the Rabi oscillation in the system. In a weak external potential well, the gauge field dominates and chiral tunneling and diffusion dynamics take place. Particularly, when diffusion and collapse coexist, a chiral moving soliton is generated, which plays a key role for coherent chiral quantum transport.
Abstract In this work we study the effect of density-dependent gauge field on the collective dynamics of a harmonically trapped Bose–Einstein condensate (BEC), beyond the linear response regime. The density-dependent gauge field, as a backaction of the condensate, can in turn affect the condensate dynamics, resulting in highly nonlinear equations of motion. The dipole and breathing oscillations of the condensate along the direction of gauge field are coupled by this field. We find that, in the presence of this coupling, the collective motion of a quasi-one-dimensional condensate is still regular, i.e., periodic or quasiperiodic. In contrast, for a quasi-two-dimensional condensate, the collective dynamics of the condensate can become chaotic, when the density-dependent gauge field is strong. The mechanism is that the gauge field can also induce a Hall effect, manifested as an additional coupling between dipole and breathing oscillations in perpendicular direction, and chaotic motion is resulted from the interplay between these oscillations. Our findings reveal an important effect of dynamical gauge field on the nonlinear dynamics of a BEC.
We study the ground-state stability of the trapped one-dimensional Bose-Einstein condensate under a density-dependent gauge field by variational and numerical methods. The competition of density-dependent gauge field and mean-field atomic interaction induces the instability of the ground state, which results in irregular dynamics. The threshold of the gauge field for exciting the instability is obtained analytically and confirmed numerically. When the gauge field is less than the threshold, the system is stable, and the gauge field induces chiral dynamics of the wave packet. When the gauge field is greater than the threshold, the system is unstable, and the ground-state wave packet will be deformed and fragmented. Interestingly, we find that as the gauge field approaches the threshold, strong dipolar and breathing dynamics take place, and strong modes mixing occurs, the instability of the system sets in. In addition, we show that the stability of the system can be well controlled by periodical modulation of the trapping potential. We provide theoretical evidence to understand and control the irregular dynamics associated with chiral superfluid induced by density-dependent gauge field.
Abstract The collision between two chiral solitons in a Bose-Einstein Condensate (BEC) under density-dependent gauge potential is studied. By means of Poincaré-Lighthill-Kuo (PLK) perturbation method, the different kinds of colliding chiral soliton pairs self-consistently excited upon the background of the system are obtained analytically. The coupling of the current nonlinearity induced by the gauge potential and mean-field atomic interaction results in rich collision dynamics of chiral soliton pairs. When the atomic interaction is repulsive, head-on collisions of dark-dark and dark-bright solitons are observed. However, when the atomic interaction is attractive, unidirectional chiral dark soliton pairs are excited, and overtaking collision between two chiral dark solitons takes place. The phase shifts following the collision of soliton pairs are derived analytically and confirmed numerically. Interestingly, due to the contribution of the density-dependent gauge potential, the phase shifts of the two interacting chiral solitons are different from each other. This is distinct from the case without the density-dependent gauge potential, where the phase shifts of the two colliding ordinary solitons are the same. Thus, phase shifts of interacting chiral soliton pairs can be used to identify the chiral properties of solitons in BEC under density-dependent gauge potential. Furthermore, both elastic and inelastic collisions of chiral solitons in the system are presented numerically. The phase diagram for occurrence of elastic and inelastic collisions of chiral soliton is obtained, which strongly depends on the strength of density-dependent gauge potential.
We study the collective modes of a Bose-Einstein condensate subject to an optically induced density-dependent gauge potential. The corresponding interacting gauge theory lacks Galilean invariance, yielding an exotic superfluid state. The nonlinear dynamics in the presence of a current nonlinearity and an external harmonic trap are found to give rise to dynamics which violate Kohn's theorem; where the frequency of the dipole mode strongly depends on the strength of the mass current in the gas. The linearised spectrum reveals how the centre of mass and shape oscillations are coupled, whereas in the strongly nonlinear regime the dynamics is irregular.
We study the collective modes of a Bose-Einstein condensate subject to an optically induced density-dependent gauge potential. The corresponding interacting gauge theory lacks Galilean invariance, yielding an exotic superfluid state. The nonlinear dynamics in the presence of a current nonlinearity and an external harmonic trap are found to give rise to dynamics which violate Kohn's theorem; where the frequency of the dipole mode strongly depends on the strength of the mass current in the gas. The linearised spectrum reveals how the centre of mass and shape oscillations are coupled, whereas in the strongly nonlinear regime the dynamics are irregular.
We consider a cigar-shaped Bose-Einstein condensate (BEC) of two-level atoms subjected to laser-induced Rabi coupling. By expanding the geometric vector potential to second order in the density-dependent fields and developing a quasi-one-dimensional (1D) reduction of the full three-dimensional problem via wave-function factorization, we derive an extended chiral Gross-Pitaevskii (GP) equation. We also derive traveling-wave solutions of the extended chiral GP equation using a projection (orthogonality) method, obtaining both bright and dark chiral solitons whose amplitudes and widths depend explicitly on the propagation direction. The chiral character of these solutions is confirmed through analytical analysis and numerical simulations. A BEC confined in a ring-shaped trap is also analyzed, leading to chiral soliton ring geometries. We show that a subtle interplay among density-dependent gauge potentials, confinement-induced interaction corrections, and higher-order current nonlinearities can give rise to alternative topological states, including chiral solitons and chiral ring solitons, in quasi-1D ultracold Bose gases. These results illustrate how higher-order corrections enrich BEC dynamics and provide means to control spatiotemporal structures in density-dependent condensates.