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arXiv:2111.11069 · New Journal of Physics

Chaotic dynamics of Bose–Einstein condensate induced by density-dependent gauge field

Lei Chen, Qizhong Zhu

Published May 1, 2022• 11 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1367-2630/ac6cfd

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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.
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.
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 analytically and numerically the nonlinear collective dynamics of quasi-one-dimensional spin–orbit coupled spin-1 Bose–Einstein condensates trapped in harmonic potential. The ground state of the system is determined by minimizing the Lagrange density, and the coupled equations of motions for the center-of-mass coordinate of the condensate and its width are derived. Then, two low energy excitation modes in breathing dynamics and dipole dynamics are obtained analytically, and the mechanism of exciting the anharmonic collective dynamics is revealed explicitly. The coupling among spin–orbit coupling, Raman coupling and spin-dependent interaction results in multiple external collective modes, which leads to the anharmonic collective dynamics. The cooperative effect of spin momentum locking and spin-dependent interaction results in coupling of dipolar and breathing dynamics, which strongly depends on spin-dependent interaction and behaves distinct characters in different phases. Interestingly, in the absence of spin-dependent interaction, the breathing dynamics is decoupled from spin dynamics and the breathing dynamics is harmonic. Our results provide theoretical evidence for deep understanding of the ground sate phase transition and the nonlinear collective dynamics of the system.
Abstract Nonlinear feedback between the gauge field and the material field can yield novel quantum phenomena. Here, the interplay between a density-dependent artificial gauge field and Bose–Einstein condensates (BECs) trapped in an optical lattice is studied. The energy spectrum and superfluidity represented by energetic and dynamical stabilities of the system are systematically discussed. A density-dependent artificial gauge field with a back-action between the BECs dynamics and the gauge field induces an effective atomic interaction that depends on the quasi-momentum and density of the condensates, resulting in a symmetry-broken energy spectrum and exotic stability phase diagram, that is, the system is only stable in a certain range of atoms density and under a limited lattice strength. The density-dependent artificial gauge field changes the sequence for the emergence of energetic and dynamical instability and the regimes of the energetic and dynamical instabilities are significantly separated, offering an efficient way to examine the energetic and dynamical instabilities of superfluids separately. In particular, the density-dependent artificial gauge field, as a mechanism for transferring momentum to the fluid, results in dynamic instability of the condensates even in free space. Our results provide deep insights into the dynamical response of superfluid systems to gauge fields and have potential applications for the coherent control of exotic superfluid states.
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 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.