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Register a new userNonlinear Waves in an Experimentally Motivated Ring-shaped Bose-Einstein Condensate Setup
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We systematically construct stationary soliton states in a one-component, two-dimensional, repulsive, Gross-Pitaevskii equation with a ring-shaped target-like trap similar to the potential used to confine a Bose-Einstein condensate in a recent experiment [Eckel, et al. {em Nature} {bf 506}, 200 (2014)]. In addition to the ground state configuration, we identify a wide variety of excited states involving phase jumps (and associated dark solitons) inside the ring. These configurations are obtained from a systematic bifurcation analysis starting from the linear, small atom density, limit. We study the stability, and when unstable, the dynamics of the most basic configurations. Often these lead to vortical dynamics inside the ring persisting over long time scales in our numerical experiments. To illustrate the relevance of the identified states, we showcase how such dark-soliton configurations (even the unstable ones) can be created in laboratory condensates by using phase-imprinting techniques.
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We observe experimentally the spontaneous formation of star-shaped surface patterns in driven Bose-Einstein condensates. Two-dimensional star-shaped patterns with $l$-fold symmetry, ranging from quadrupole ($l=2$) to heptagon modes ($l=7$), are parametrically excited by modulating the scattering length near the Feshbach resonance. An effective Mathieu equation and Floquet analysis are utilized, relating the instability conditions to the dispersion of the surface modes in a trapped superfluid. Identifying the resonant frequencies of the patterns, we precisely measure the dispersion relation of the collective excitations. The oscillation amplitude of the surface excitations increases exponentially during the modulation. We find that only the $l=6$ mode is unstable due to its emergent coupling with the dipole motion of the cloud. Our experimental results are in excellent agreement with the mean-field framework. Our work opens a new pathway for generating higher-lying collective excitations with applications, such as the probing of exotic properties of quantum fluids and providing a generation mechanism of quantum turbulence.
We study the collapse of an attractive atomic Bose-Einstein condensate prepared in the uniform potential of an optical-box trap. We characterise the critical point for collapse and the collapse dynamics, observing universal behaviour in agreement with theoretical expectations. Most importantly, we observe a clear experimental signature of the counterintuitive weak collapse, namely that making the system more unstable can result in a smaller particle loss. We experimentally determine the scaling laws that govern the weak-collapse atom loss, providing a benchmark for the general theories of nonlinear wave phenomena.
In this work we present a systematic study of the three-dimensional extension of the ring dark soliton examining its existence, stability, and dynamics in isotropic harmonically trapped Bose-Einstein condensates. Detuning the chemical potential from the linear limit, the ring dark soliton becomes unstable immediately, but can be fully stabilized by an external cylindrical potential. The ring has a large number of unstable modes which are analyzed through spectral stability analysis. Furthermore, a few typical destabilization dynamical scenarios are revealed with a number of interesting vortical structures emerging such as the two or four coaxial parallel vortex rings. In the process of considering the stability of the structure, we also develop a modified version of the degenerate perturbation theory method for characterizing the spectra of the coherent structure. This semi-analytical method can be reliably applied to any soliton with a linear limit to explore its spectral properties near this limit. The good agreement of the resulting spectrum is illustrated via a comparison with the full numerical Bogolyubov-de Gennes spectrum. The application of the method to the two-component ring dark-bright soliton is also discussed.
In a shaken Bose-Einstein condensate, confined in a vibrating trap, there can appear different nonlinear coherent modes. Here we concentrate on two types of such coherent modes, vortex ring solitons and vortex rings. In a cylindrical trap, vortex ring solitons can be characterized as nonlinear Hermite-Laguerre modes, whose description can be done by means of optimized perturbation theory. The energy, required for creating vortex ring solitons, is larger than that needed for forming vortex rings. This is why, at a moderate excitation energy, vortex rings appear before vortex ring solitons. The generation of vortex rings is illustrated by numerical simulations for trapped $^{87}$Rb atoms.
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