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Chinese Physics Letters

Reverse Rotation of Ring-Shaped Perturbation on Homogeneous Bose–Einstein Condensates

Peng Gao, Zeyu Wu, Zhan-Ying Yang, Wen‐Li Yang

Published Oct 1, 2021• 4 citations
Publisher

Abstract

We numerically study the dynamics of rotating ring-shaped perturbation on two-dimensional homogeneous Bose–Einstein condensates, where a new ring-shaped structure with reverse rotation appears. The reversely rotating mode is directly caused by the existence of the plane wave (namely the homogeneous background). By the modified linear stability analysis method, we quantitatively predict the influence of the background's density on perturbation dynamics, including the velocity, amplitude, and frequency of the two rings. We construct an approximative solution to describe the short-lived dynamics of initial perturbation, which agrees well with our numerical results. Also, after the two rings separate, the transfer of atom number between them becomes linear, and the rate of transfer is impacted by the radial momentum of initial perturbation.

DOI
10.1088/0256-307x/38/9/090302

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We numerically study the dynamics of rotating ring-shaped perturbation on two-dimensional homogeneous Bose–Einstein condensates, where a new ring-shaped structure with reverse rotation appears. The reversely rotating mode is directly caused by the existence of the plane wave (namely the homogeneous background). By the modified linear stability analysis method, we quantitatively predict the influence of the background's density on perturbation dynamics, including the velocity, amplitude, and frequency of the two rings. We construct an approximative solution to describe the short-lived dynamics of initial perturbation, which agrees well with our numerical results. Also, after the two rings separate, the transfer of atom number between them becomes linear, and the rate of transfer is impacted by the radial momentum of initial perturbation.
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We numerically investigate the spatiotemporal dynamics of a circular flow mode in a ring array of Bose-Einstein condensates, which consists of MMM identical Bose-Einstein condensates that couple to the nearest-neighbor sites by tunneling. Introducing a rotational potential in the Gross-Pitaevskii equation, a series of circular flow modes is resonantly excited. For the initial conditions with uniform density and one-round phase difference of $2\ensuremath{\pi}\ensuremath{\ell}\phantom{\rule{0.3em}{0ex}}(l=0,1,\dots{},M\ensuremath{-}1)$, two circular flow modes are excited for each circulation-quantized number lll. It is shown that these circular flow modes periodically appear in time in the presence of the rotational field and persistently survive with a constant shape even after the external potential is removed, the transitions between the circular flow modes with different quantized number lll can be realized by applying the phase-imprinting optical pulses, and the rotational velocity of the circular flow mode can be continuously modulated by adiabatically tuning the scattering length in a magnetic field, i.e., by use of the Feshbach resonance.
We study the nonlinear dynamics of a three-dimensional Bose-Einstein condensate (BEC) excited by a vortex ring phase imprinting. We identify independent, integrated, and stationary modes of the center-of-mass oscillation of the condensate with respect to the vortex ring movement. We show that the oscillation amplitude of the center-of-mass of the condensate depends strongly on the initial radius of the vortex ring, the nonlinear inter-atomic interaction, and the aspect ratio of the trap, while the oscillation frequency is fixed and equals to the frequency of the harmonic trap in the direction of the ring movement. However, when applying Kelvin wave perturbations on the vortex ring, the center-of-mass oscillation of the BEC is changed non-trivially with respect to the perturbation modes, the long-scale perturbation strength as well as the wave number of the perturbations. The parity of the wave number of the Kelvin perturbations plays an important role on the mode of the center-of-mass oscillation of the condensate.
Soliton is an exotic topological excitation, and it widely exists in various nonlinear systems, such as nonlinear optics, Bose-Einstein condensates, classical and quantum fluids, plasma, magnetic materials, etc. A stable soliton can propagate with constant amplitude and velocity, and maintain its shape. Two-dimensional and three-dimensional solitons are usually hard to stabilize, and how to realize stable two-dimensional or three-dimensional solitons has aroused the great interest of the researchers. Ring dark soliton is a kind of two-dimensional soliton, which was first theoretically predicted and experimentally realized in nonlinear optical systems. Compared with the usual two-dimensional solitons, ring dark solitons have good stability and rich dynamical behaviors. Owing to their highly controllable capability, Bose-Einstein condensates provide a new platform for studying the ring dark solitons. Based on the recent progress in Bose-Einstein condensates and solitons, this paper reviews the research on the analytic solutions, stability, as well as the decay dynamics of ring dark solitons in Bose-Einstein condensates. A transform method is introduced, which generalizes the analytic solutions of ring dark solitons from a homogeneous system with time-independent nonlinearity to a harmonically trapped inhomogeneous system with time-dependent nonlinearity. The stability phase diagram of the ring dark soliton under deformation perturbations is discussed by numerically solving the Gross-Pitaevskii equations in the mean-field theory. A method of enhancing the stability of ring dark solitons by periodically modulating the nonlinear coefficients is introduced. It is also shown that the periodically modulated nonlinear coefficient can be experimentally realized by the Feshbach resonance technology. In addition, we discuss the dynamics of the decay of ring dark solitons. It is found that the ring dark soliton can decay into various vortex clusters composed of vortices and antivortices. This opens a new avenue to the investigation of vortex dynamics and quantum turbulence. It is also found that the ring dark solitons combined with periodic modulated nonlinearity can give rise to the pattern formation, which is an interesting nonlinear phenomenon widely explored in all the fields of nature. Finally, some possible research subjects about ring dark solitons in future research are also discussed.
Abstract We develop a multimode model that describes the dynamics on a rotating Bose–Einstein condensate confined by a ring-shaped optical lattice with large filling numbers. The parameters of the model are obtained as a function of the rotation frequency using full 3D Gross–Pitaevskii simulations. From such numerical calculations, we extract the velocity field induced at each site and analyze the relation and the differences between the phase of the hopping parameter of our model and the Peierls phase. To this end, a detailed discussion of such phases is presented in geometrical terms which takes into account the position of the junctions for different configurations. For circularly symmetric onsite densities a simple analytical relation between the hopping phase and the angular momentum is found for arbitrary number of sites. Finally, we confront the results of the rotating multimode model dynamics with Gross–Pitaevskii simulations finding a perfect agreement.
We develop a multimode model that describes the dynamics on a rotating Bose-Einstein condensate confined by a ring-shaped optical lattice with large filling numbers. The parameters of the model are obtained as a function of the rotation frequency using full 3D Gross-Pitaevskii simulations. From such numerical calculations, we extract the velocity field induced at each site and analyze the relation and the differences between the phase of the hopping parameter of our model and the Peierls phase. To this end, a detailed discussion of such phases is presented in geometrical terms which takes into account the position of the junctions for different configurations. For circularly symmetric onsite densities a simple analytical relation between the hopping phase and the angular momentum is found for arbitrary number of sites. Finally, we confront the results of the rotating multimode model dynamics with Gross-Pitaevskii simulations finding a perfect agreement.