The dynamics of a filled massive vortex is studied numerically and analytically using a two-dimensional model of a two-component Bose–Einstein condensate trapped in a harmonic trap. This condensate exhibits phase separation. In the framework of the coupled Gross–Pitaevskii equations, it is demonstrated that, in a certain range of parameters of the nonlinear interaction, the precession of a sufficiently massive vortex around the center is strongly slowed down and even reverses its direction with a further increase in the mass. An approximate ordinary differential equation is derived that makes it possible to explain this behavior of the system.
The dynamics of a filled massive vortex is studied numerically and analytically using a two-dimensional model of a two-component Bose–Einstein condensate trapped in a harmonic trap. This condensate exhibits phase separation. In the framework of the coupled Gross–Pitaevskii equations, it is demonstrated that, in a certain range of parameters of the nonlinear interaction, the precession of a sufficiently massive vortex around the center is strongly slowed down and even reverses its direction with a further increase in the mass. An approximate ordinary differential equation is derived that makes it possible to explain this behavior of the system.
We study the stability of vortices in a binary system of Bose-Einstein condensat es, with their wave functions modeled by a set of coupled, time-dependent Gross-Pitaevskii equations. Beginning with an effective two-dimensional system, we identify miscible and immiscible regimes characterized by the inter- and intra-atomic interactions and the initial configuration of the system. We then consider a binary system of Bose-Einstein condensates placed in a rotating harmonic trap and study the single united vortex state in this system. We derive an approximate form for the energy of a single united vortex in the binary system and the critical angular velocity for the global stability of a vortex at the center of the trap. We also compute the metastability onset angular velocity for the local stability of a vortex at the center of the trap. Numerical solutions to the Gross-Pitaevskii equations support these expressions. These rotational results inform us of a novel bimodal formation within the miscible regime of the binary condensate system. We thus demonstrate the nontrivial aspects of vortex stability in interacting binary Bose-Einstein condensates as a result of their nonlinear interactions.
We study the massive point-vortex model introduced in Richaud et al. [A. Richaud, V. Penna, R. Mayol, and M. Guilleumas, Phys. Rev. A 101, 013630 (2020)], which describes two-dimensional point vortices of one species that have small cores of a different species. We derive the relevant Lagrangian itself, based on the time-dependent variational method with a two-component Gross-Pitaevskii (GP) trial function. The resulting Lagrangian resembles that of charged particles in a static electromagnetic field, where the canonical momentum includes an electromagnetic term. The simplest example is a single vortex with a rigid circular boundary, where a massless vortex can only precess uniformly. In contrast, the presence of a sufficiently large filled vortex core renders such precession unstable. A small core mass can also lead to small radial oscillations, which are, in turn, clear evidence of the associated inertial effect. Detailed numerical analysis of coupled two-component GP equations with a single vortex and small second-component core confirms the presence of such radial oscillations, implying that this more realistic GP vortex also acts as if it has a small massive core.
Based on the two-dimensional Gross–Pitaevskii equation model, we investigated the asymmetric vortex evolution of two-dimensional Bose–Einstein condensates in a harmonic potential trap with polar direction perturbation. This corresponds to the generation of an asymmetric vortex evolution mode under initial vortex light manipulation together with polar direction perturbation. Unlike most of the prior work on this topic that uses a pure numerical method for the system under study, we use an exact analytical method rather than numerical simulation to investigate the key features of the system evolution dynamics in this study. Based on the variational method, and for different system parameter settings including the strength of the harmonic oscillator potential and the nonlinear interaction, we derived two evolution modes, namely, the periodic evolution oscillation mode and the monotonic decay mode, and pictorially demonstrated the evolution patterns of the system. In addition, we investigated the scenario when the system is in the rotating state, which corresponds to the action of the quadratic centrifugal potential. Notably, we also identified the damping effects for the two modes with increasing angular velocity, whose upper limit value corresponds to the constant vortex pattern of the system. Our theoretical results can be used to guide the experimental investigation of asymmetric vortex evolution in two-dimensional Bose–Einstein condensates.
The dynamic behavior of vortex pairs in two-component coherently (Rabi) coupled Bose-Einstein condensates is investigated in the presence of harmonic trapping. We discuss the role of the surface tension associated with the domain wall connecting two vortices in condensates of atoms occupying different spin states and its effect on the precession of the vortex pair. The results, based on the numerical solution of the Gross-Pitaevskii equations, are compared with the predictions of an analytical macroscopic model and are discussed as a function of the size of the pair, the Rabi coupling, and the intercomponent interaction. We show that the increase of the Rabi coupling results in the disintegration of the domain wall into smaller pieces, connecting vortices of newly created vortex pairs. The resulting scenario is the analog of quark confinement and string breaking in quantum chromodynamics.
We study the evolution of vortex solitons in two-component Bose-Einstein condensates (BEC) trapped with harmonic potential. Based on the Gross-Pitaevskii equation model and variational method, We derived the analytical vortex soliton solution that is stable under certain parametric setting. The evolutionary pattern of the vortex soliton is pictorially demonstrated showing the periodic oscillatory behavior of the systems’s distribution width. The theoretical results obtained can be used to guide corresponding vortex soliton observation in two-component BEC systems.
We study the motion of a vortex dipole in a Bose-Einstein condensate confined to an anisotropic trap. We focus on a system of ordinary differential equations describing the vortices' motion, which is in turn a reduced model of the Gross-Pitaevskii equation describing the condensate's motion. Using a sequence of canonical changes of variables, we reduce the dimension and simplify the equations of motion. We uncover two interesting regimes. Near a family of periodic orbits known as guiding centers, we find that the dynamics is essentially that of a pendulum coupled to a linear oscillator, leading to stochastic reversals in the overall direction of rotation of the dipole. Near the separatrix orbit in the isotropic system, we find other families of periodic, quasi-periodic, and chaotic trajectories. In a neighborhood of the guiding center orbits, we derive an explicit iterated map that simplifies the problem further. Numerical calculations are used to illustrate the phenomena discovered through the analysis. Using the results from the reduced system we are able to construct complex periodic orbits in the original, partial differential equation, mean-field model for Bose-Einstein condensates, which corroborates the phenomenology observed in the reduced dynamical equations.