In this paper we study a mean field model for the dynamics of an interacting Bose-Einstein condensate in two dimensional pseudo-relativistic materials. This model is relatively simple, but contains stable solutions called oscillons which are absent in non-relativistic condensates. We report on a variety of scenarios including interactions between pairs of oscillons and oscillons propagating across an inhomogeneous material boundary. Hitherto relativistic oscillons have been studied only in high energy physics and cosmology and their relevance has not been highlighted so far in condensed matter physics.
Three-dimensional numerical simulation of long-lived quantum vortex knots and links in a trapped Bose-Einstein condensate
本文用三维Gross-Pitaevskii方程数值模拟了零温下各向异性简谐势阱中原子玻色-爱因斯坦凝聚体中最简单的环面型涡旋结、解结和链的动力学。这种准定常旋转涡结构的寿命已被发现相当长的系统在广泛的参数域。这一结果与先前基于近似描述涡丝动力学的简化一维模型的预测定性一致[V. P. Ruban，JETP 126，397（2018）]。
We demonstrate neuron-like spiking dynamics in the asymmetrically driven dissipative photonic Bose-Hubbard dimmer model which describes two coupled nonlinear passive Kerr cavities. Spiking dynamics appear due to the excitable nature of the system. In this context, excitable excursions in the phase space correspond to spikes in the temporal evolution of the field variables. In our case, excitability is mediated by the destruction of an oscillatory state in a global homoclinic bifurcation. In this type of excitability (known as type-I) the period of the oscillatory state diverges when approachin…
We perform a systematic study of the temporal dynamics emerging in the asymmetrically driven dissipative Bose-Hubbard dimer model. This model successfully describes the nonlinear dynamics of photonic diatomic molecules in linearly coupled Kerr resonators coherently excited by a single laser beam. Such temporal dynamics include self-pulsing oscillations, period doubled oscillatory states, chaotic dynamics, and spikes. The different states and dynamical regimes have been thoroughly characterized using bifurcation analysis. This analysis has allowed us to identify the main instabilities, i.e. bif…
A trapped Bose--Einstein-condensed mixture of two types of cold atoms with significantly different masses has been simulated numerically within the coupled Gross--Pitaevskii equations. A configuration consisting of a vortex-free core and a shell penetrated by quantum vortices is possible in the phase separation regime. The dynamic properties of vortices in the shell are determined by several parameters. Physically implementable parametric domains corresponding to long-lived strongly nonstationary systems of several vortices attached to the core have been sought. A number of realistic numerical…
We numerically study the breathing dynamics induced by collision between bright solitons in the one-dimensional Bose-Einstein condensates with strong dipole-dipole interaction. This breathing phenomenon is closely related to the after-collision short-lived attraction of solitons induced by the dipolar effect. The initial phase difference of solitons leads to the asymmetric dynamics after collision, which is manifested on their different breathing amplitude, breathing frequency, and atom number. We clarify that the asymmetry of breathing frequency is directly induced by the asymmetric atom numb…
We study general collisions between chiral solitons in Bose-Einstein condensates subject to combined attractive and current-dependent interatomic interactions. A simple analysis based on the linear superposition of the solitons allows us to determine the relevant time and space scales of the dynamics, which is illustrated by extensive numerical simulations. By varying the differential amplitude, the relative phase, the average velocity, and the relative velocity of the solitons, we characterize the different dynamical regimes that give rise to oscillatory and interference phenomena. Apart from…
Specific topological excitations of energetically stable "core-and-mantle" configurations of trapped two-component immiscible Bose-Einstein condensates are studied numerically within the coupled Gross-Pitaevskii equations. Non-stationary long-lived coherent structures, that consist of several quantum vortex filaments penetrating the "mantle" from outside to inside and vice-versa and demonstrate quite nontrivial dynamics, are observed in simulations for the first time. The ends of filaments can remain attached to the interface between the "mantle" and the "core" if the latter is large enough wh…
A two-component Bose-Einstein condensate of cold atoms with a strong intercomponent repulsion leading to the spatial separation of the components has been numerically studied. Configurations with a multiple quantized vortex in one component, where the vortex core is filled with the other component, are considered. The effective radius of the core can exceed the width of the transition layer between components, and then an analogy with a filled cylindrical vortex in the classical hydrodynamics of two immiscible ideal fluids appears. This analogy allows one to analyze the longitudinal "sausage" …
