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 is irregular.

arXiv:1408.6886Aug 28, 20140 citations

Excitation spectrum of vortex-lattice modes in a rotating condensate with a density-dependent gauge potential

Rony Boral, Swarup K. Sarkar, Matthew Edmonds +2 more

We investigate the collective excitation spectrum of a quasi-two-dimensional Bose-Einstein condensate trapped in a harmonic confinement with nonlinear rotation induced by a density-dependent gauge potential. Using a Bogoliubov--de Gennes (BdG) analysis, we show that the dipole mode frequency depends strongly on the nonlinear interaction strength, violating Kohn's theorem which is also well complemented by the analytical expression for the dipole and breathing modes obtained employing a variational analysis. We identify four different vortex displacement modes, Tkachenko, circular, quadratic, and rational, whose frequencies are rotation sensitive. An analytical Tkachenko mode frequency from a hydrodynamic approach agrees well with that computed using BdG and Fourier analysis. The excitation spectrum remains symmetric around the angular quantum number $l=0$ , but energy splitting between $l$ and $\ensuremath{-}l$ varies with the sign and strength of the nonlinear rotation. Finally, we demonstrate that the surface mode excitation frequency increases (decreases) with an increase in the positive (negative) nonlinear rotation strength.We investigate the collective excitation spectrum of a quasi-two-dimensional Bose-Einstein condensate trapped in a harmonic confinement with nonlinear rotation induced by a density-dependent gauge potential. Using a Bogoliubov--de Gennes (BdG) analysis, we show that the dipole mode frequency depends strongly on the nonlinear interaction strength, violating Kohn's theorem which is also well complemented by the analytical expression for the dipole and breathing modes obtained employing a variational analysis. We identify four different vortex displacement modes, Tkachenko, circular, quadratic, and rational, whose frequencies are rotation sensitive. An analytical Tkachenko mode frequency from a hydrodynamic approach agrees well with that computed using BdG and Fourier analysis. The excitation spectrum remains symmetric around the angular quantum number $l=0$, but energy splitting between $l$ and $\ensuremath{-}l$ varies with the sign and strength of the nonlinear rotation. Finally, we demonstrate that the surface mode excitation frequency increases (decreases) with an increase in the positive (negative) nonlinear rotation strength.

arXiv:2505.01031Physical Review ASep 12, 20252 citations

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

Lei Chen, Qizhong Zhu

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 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.

arXiv:2111.11069New Journal of PhysicsMay 1, 202211 citations

Revealing Unconventional Properties of a Spin-Orbit Coupled Bose-Einstein Condensate from Collective Dipole Oscillation

Shuai Chen, Jinyi Zhang, Si-Cong Ji +5 more

Interaction between matter field and gauge field plays a fundamental role in many areas of physics. Recently, a non-abelian gauge field has been successfully synthesized in laboratory for ultracold neutral bosonic atoms, yielding the coupling between the pseudo-spin of an atom and its orbital motion. This new superfluid has many unconventional properties remaining to be explored. Here we study the collective oscillation of a spin-orbit coupled Bose-Einstein condensate in a harmonic trap. We find that the frequency of dipole oscillation deviates from the harmonic trap frequency and depends on the oscillation amplitude. Such an unharmonic behavior reveals the nonabelain character of the gauge field. We also observe that a magnetization oscillation is induced by the dipole motion, as a manifestation of the absence of the Galilean invariance of this system. We develop a variational wave-function method that well describes the dipole oscillation, except in the regime with two degenerate single-particle energy minima separated by a low barrier. In this regime, since the harmonic trapping potential plays an analogous role as kinetic energy in a real-space double-well potential, macroscopic quantum tunneling in momentum space is observed in the dipole oscillation.Interaction between matter field and gauge field plays a fundamental role in many areas of physics. Recently, a non-abelian gauge field has been successfully synthesized in laboratory for ultracold neutral bosonic atoms, yielding the coupling between the pseudo-spin of an atom and its orbital motion. This new superfluid has many unconventional properties remaining to be explored. Here we study the collective oscillation of a spin-orbit coupled Bose-Einstein condensate in a harmonic trap. We find that the frequency of dipole oscillation deviates from the harmonic trap frequency and depends on the oscillation amplitude. Such an unharmonic behavior reveals the nonabelain character of the gauge field. We also observe that a magnetization oscillation is induced by the dipole motion, as a manifestation of the absence of the Galilean invariance of this system. We develop a variational wave-function method that well describes the dipole oscillation, except in the regime with two degenerate single-particle energy minima separated by a low barrier. In this regime, since the harmonic trapping potential plays an analogous role as kinetic energy in a real-space double-well potential, macroscopic quantum tunneling in momentum space is observed in the dipole oscillation.

Jan 29, 20120 citations

Dynamics of a trapped Bose Einstein condensate in the presence of a one-dimensional optical lattice

F. S. Cataliotti, L. Fallani, Francesca Ferlaino +3 more

We explore the dynamics of a Bose–Einstein condensate created in the combined potential of a far-detuned laser standing wave superimposed to a 3D harmonic magnetic potential. We report the investigation of low-lying collective modes showing that the macroscopic dynamics along the optical lattice is strongly modified, resulting in a shift of the dipole and quadrupole mode frequencies depending on the height of the optical lattice, whereas the transverse breathing mode, occurring perpendicularly to the lattice axis, is not perturbed. The experimental findings are compared with the theoretical treatment that generalizes the hydrodynamic equation of superfluids for a weakly interacting Bose gas to include the effects of the periodic potential. We show that the array of condensates trapped in the optical wells and driven by the harmonic magnetic potential is equivalent to an array of Josephson junctions. In the regime of ‘small’ amplitude dipole oscillation the system performs a collective motion and we investigate the current–phase dynamics measuring the critical Josephson current. Increasing the amplitude of the dipole oscillation, we observe a transition from the coherent oscillation (superfluid regime) to a localization of the condensates in the harmonic trap (‘insulator’ regime). The onset of the coherent regime breakdown is interpreted as the result of a discrete modulational instability occurring when the velocity of the centre of mass of the system is larger than a critical velocity proportional to the tunnelling rate between adjacent wells.We explore the dynamics of a Bose–Einstein condensate created in the combined potential of a far-detuned laser standing wave superimposed to a 3D harmonic magnetic potential. We report the investigation of low-lying collective modes showing that the macroscopic dynamics along the optical lattice is strongly modified, resulting in a shift of the dipole and quadrupole mode frequencies depending on the height of the optical lattice, whereas the transverse breathing mode, occurring perpendicularly to the lattice axis, is not perturbed. The experimental findings are compared with the theoretical treatment that generalizes the hydrodynamic equation of superfluids for a weakly interacting Bose gas to include the effects of the periodic potential. We show that the array of condensates trapped in the optical wells and driven by the harmonic magnetic potential is equivalent to an array of Josephson junctions. In the regime of ‘small’ amplitude dipole oscillation the system performs a collective motion and we investigate the current–phase dynamics measuring the critical Josephson current. Increasing the amplitude of the dipole oscillation, we observe a transition from the coherent oscillation (superfluid regime) to a localization of the condensates in the harmonic trap (‘insulator’ regime). The onset of the coherent regime breakdown is interpreted as the result of a discrete modulational instability occurring when the velocity of the centre of mass of the system is larger than a critical velocity proportional to the tunnelling rate between adjacent wells.

Journal of Optics B Quantum and Semiclassical OpticsApr 1, 200315 citations

Stability of trapped Bose-Einstein condensate under a density-dependent gauge field

An-Qing Zhang, Chen Jiao, Zi-Fa Yu +3 more

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.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.

Physical review. EFeb 27, 20233 citations

l=0

, but energy splitting between

l

and $\ensuremath{-}l$ varies with the sign and strength of the nonlinear rotation. Finally, we demonstrate that the surface mode excitation frequency increases (decreases) with an increase in the positive (negative) nonlinear rotation strength.