Exact solutions of the Gross-Pitaevskii equation for stable vortex modes in two-dimensional Bose-Einstein condensates

2010 ◽  
Vol 81 (6) ◽  
Author(s):  
Lei Wu ◽  
Lu Li ◽  
Jie-Fang Zhang ◽  
Dumitru Mihalache ◽  
Boris A. Malomed ◽  
...  
Keyword(s):  
Exact Solutions ◽  
Pitaevskii Equation ◽  
Two Dimensional ◽  
Bose Einstein ◽  
Stable Vortex

scholarly journals A method to create disordered vortex arrays in atomic Bose–Einstein condensates

2009 ◽  
Vol 87 (9) ◽  
pp. 1013-1019 ◽  
Author(s):  
Enikö J.M. Madarassy
Keyword(s):  
Wave Function ◽  
Quantum Turbulence ◽  
Einstein Condensate ◽  
Complex Conjugate ◽  
Pitaevskii Equation ◽  
Two Dimensional ◽  
Bose Einstein Condensate ◽  
Phase Profile ◽  
Bose Einstein

We suggest a method to create quantum turbulence (QT) in a trapped atomic Bose–Einstein condensate (BEC). By replacing in the upper half of our box the wave function, Ψ, with its complex conjugate, Ψ*, new negative vortices are introduced into the system. The simulations are performed by solving the two-dimensional Gross–Pitaevskii equation (2D GPE). We study the successive dynamics of the wave function by monitoring the evolution of density and phase profile.

DYNAMICS OF VORTICES IN TWO-DIMENSIONAL BOSE–EINSTEIN CONDENSATES

2002 ◽  
Vol 12 (04) ◽  
pp. 739-764 ◽  
Author(s):  
SHU-MING CHANG ◽  
WEN-WEI LIN ◽  
TAI-CHIA LIN
Keyword(s):  
Numerical Simulation ◽  
Differential Equations ◽  
Time Dependent ◽  
Pitaevskii Equation ◽  
Two Dimensional ◽  
Motion Equations ◽  
Trap Potential ◽  
Asymptotic Motion ◽  
Bose Einstein ◽  
Kirchhoff Problem

We derive the asymptotic motion equations of vortices for the time-dependent Gross–Pitaevskii equation with a harmonic trap potential. The asymptotic motion equations form a system of ordinary differential equations which can be regarded as a perturbation of the standard Kirchhoff problem. From the numerical simulation on the asymptotic motion equations, we observe that the bounded and collisionless trajectories of three vortices form chaotic, quasi 2- or quasi 3-periodic orbits. Furthermore, a new phenomenon of 1:1-topological synchronization is observed in the chaotic trajectories of two vortices.

HALF-SKYRMION IN SPINOR BOSE–EINSTEIN CONDENSATES

2013 ◽  
Vol 27 (25) ◽  
pp. 1350183 ◽  
Author(s):  
YONG-KAI LIU ◽  
CONG ZHANG ◽  
SHI-JIE YANG
Keyword(s):  
Exact Solutions ◽  
Topological Charge ◽  
Three Dimensional ◽  
Dimensional System ◽  
Two Dimensional ◽  
Two Dimensional System ◽  
Bose Einstein ◽  
Nontrivial Topology

In this paper, we present exact solutions to the F = 1 spinor Bose–Einstein condensates with only spin-independent energy by adopting a method of separating the variables, which exhibit nontrivial topology. These solutions can form solitonic fractional vortex and solitonic half-skyrmion with a Q = 1/2 topological charge in the two-dimensional system. We further address a three-dimensional prototype solution.

scholarly journals EXACT SOLUTIONS TO THE THREE-DIMENSIONAL GROSS–PITAEVSKII EQUATION WITH MODULATED RADIAL NONLINEARITY

2013 ◽  
Vol 27 (14) ◽  
pp. 1350105
Author(s):  
WEI-TING WANG ◽  
YING-YING LI ◽  
SHI-JIE YANG
Keyword(s):  
Exact Solutions ◽  
Three Dimensional ◽  
Einstein Condensate ◽  
Pitaevskii Equation ◽  
Bose Einstein Condensate ◽  
Symmetrical Potential ◽  
Bose Einstein

We study the Bose–Einstein condensate trapped in a three-dimensional spherically symmetrical potential. Exact solutions to the stationary Gross–Pitaevskii equation are obtained for properly modulated radial nonlinearity. The solutions contain vortices with different winding numbers and exhibit the shell-soliton feature in the radial distributions.

scholarly journals Dipolar condensed atomic mixtures and miscibility under rotation

2020 ◽  
Author(s):  
Lauro Tomio ◽  
Ramavarmaraja Kishor Kumar ◽  
Arnaldo Gammal
Keyword(s):  
Binary Mixtures ◽  
Spatial Separation ◽  
Pitaevskii Equation ◽  
Polarization Angle ◽  
Two Dimensional ◽  
Dipole Interactions ◽  
Quartic Term ◽  
Vortex Patterns ◽  
Bose Einstein ◽  
Dipole Polarization

By considering symmetric- and asymmetric-dipolar coupled mixtures (with dysprosium and erbium isotopes), we report a study on relevant anisotropic effects, related to spatial separation and miscibility, due to dipole-dipole interactions (DDIs) in rotating binary dipolar Bose-Einstein condensates. The binary mixtures are kept in strong pancake-like traps, with repulsive two-body interactions modeled by an effective two-dimensional (2D) coupled Gross-Pitaevskii equation. The DDI are tuned from repulsive to attractive by varying the dipole polarization angle. A clear spatial separation is verified in the densities for attractive DDIs, being angular for symmetric mixtures and radial for asymmetric ones. Also relevant is the mass-imbalance sensibility observed by the vortex-patterns in symmetric- and asymmetric-dipolar mixtures. In an extension of this study, here we show how the rotational properties and spatial separation of these dipolar mixture are affected by a quartic term added to the harmonic trap of one of the components.

Sign in / Sign up

Export Citation Format

Share Document