Dynamic vortex evolution of harmonically trapped coupled Bose–Einstein condensate with quintic nonlinearity

2021 ◽  
Author(s):  
Yunsong Guo ◽  
Yubin Jiao ◽  
Xiaoning Liu ◽  
Xiangbo Zhu ◽  
Ying Wang
Keyword(s):  
Periodic Breathing ◽  
Oscillation Period ◽  
Angular Frequency ◽  
Equation Model ◽  
Einstein Condensate ◽  
Pitaevskii Equation ◽  
Atomic Systems ◽  
Bose Einstein Condensate ◽  
Two Component ◽  
Bose Einstein

In this study, we investigate the evolution of vortex in harmonically trapped two-component coupled Bose–Einstein condensate with quintic-order nonlinearity. We derive the vortex solution of this two-component system based on the coupled quintic-order Gross–Pitaevskii equation model and the variational method. It is found that the evolution of vortex is a metastable state. The radius of vortex soliton shrinks and expands with time, resulting in periodic breathing oscillation, and the angular frequency of the breathing oscillation is twice the value of the harmonic trapping frequency under infinitesimal nonlinear strength. At the same time, it is also found that the higher-order nonlinear term has a quantitative effect rather than a qualitative impact on the oscillation period. With practical experimental setting, we identify the quasi-stable oscillation of the derived vortex evolution mode and illustrated its features graphically. The theoretical results developed in this work can be used to guide the experimental observation of the vortex phenomenon in ultracold coupled atomic systems with quintic-order nonlinearity.

Sonic horizon formation for coupled one-dimensional Bose–Einstein condensate in an elongated harmonic potential

2018 ◽  
Vol 32 (29) ◽  
pp. 1850352
Author(s):  
Ying Wang ◽  
Shuyu Zhou
Keyword(s):  
Expansion Method ◽  
Einstein Condensate ◽  
Wave Functions ◽  
Harmonic Potential ◽  
Pitaevskii Equation ◽  
Two Component System ◽  
One Dimensional ◽  
Bose Einstein Condensate ◽  
Two Component ◽  
Bose Einstein

We theoretically studied the sonic horizon formation problem for coupled one-dimensional Bose–Einstein condensate trapped in an external elongated harmonic potential. Based on the coupled (1[Formula: see text]+[Formula: see text]1)-dimensional Gross–Pitaevskii equation and F-expansion method under Thomas–Fermi formulation, we derived analytical wave functions of a two-component system, from which the sonic horizon’s occurrence criteria and location were derived and graphically demonstrated. The theoretically derived results of sonic horizon formation agree pretty well with that from the numerically calculated values.

scholarly journals Modulation Instability in Two Component Bose-Einstein Condensate with Dissipation

2019 ◽  
Keyword(s):  
Modulation Instability ◽  
Einstein Condensate ◽  
Dissipative Function ◽  
Positive Interaction ◽  
Friction Forces ◽  
Bose Einstein Condensate ◽  
First Case ◽  
Two Component ◽  
Repulsive Forces ◽  
Bose Einstein

In this paper, we consider the dynamic evolution of a binary mixture of a Bose-Einstein condensate taking into account the presence of dissipation inside the components. Using the introduction of the dissipative function, the modified Gross-Pitaevskii equations are obtained. These equations, in contrast to the usual Gross-Pitaevskii equations for two-component condensate, allow us to take into account the dissipation in the system. The influence of dissipative processes on the development of modulation instability in a spatially homogeneous two-component Bose-Einstein condensate is investigated. In contrast to the one-component Bose-Einstein condensate, in which modulation instability arises only when there are forces of attraction between atoms, in a two-component Bose-Einstein condensate nonlinear dynamics, leading to modulation instability is more complex. It essentially depends on the signs and values of the constant interaction of the components, which leads to a greater variety of possible scenarios for the development of modulation instability. The paper considers two cases. The first case is when repulsive forces act inside the components, and the second is when repulsive forces act in the first component, and in the second one - attractive forces. At the same time, the situation when there is a repulsion in the first component, and attraction between the particles in the second component differs significantly from the case of only positive interaction inside the components. The relations between the interaction constants that determine the development of the modulation instability turn out to be different. Given the relations between the interaction constants, taking into account dissipation processes, the occurrence of modulation instability in two-component Bose-Einstein condensates was studied, the maximum growth rate of oscillations was found, and the limits of the existence of modulation instability in the space of wave numbers were found. It is shown that the small effect of dissipation on the modulation instability in the Bose – Einstein condensate is explained not only by the smallness of the friction forces. For wave vectors corresponding to a mode with a maximum increment, the contribution of dissipation in the linear approximation with respect to the dissipative parameter is strictly zero. Thus, the condition for the development of the most rapidly growing mode of oscillations, which determines the beginning of the modulation instability, remains the same as in the nondissipative case.

scholarly journals Two-component axionic dark matter halos

2020 ◽  
Vol 35 (26) ◽  
pp. 2050227 ◽  
Author(s):  
Gennady P. Berman ◽  
Vyacheslav N. Gorshkov ◽  
Vladimir I. Tsifrinovich ◽  
Marco Merkli ◽  
Vladimir V. Tereshchuk
Keyword(s):  
Dark Matter ◽  
Ground State ◽  
Mass Density ◽  
Mean Field ◽  
Einstein Condensate ◽  
Dark Matter Halo ◽  
Bose Einstein Condensate ◽  
Interesting Connection ◽  
Two Component ◽  
Bose Einstein

We consider a two-component dark matter halo (DMH) of a galaxy containing ultra-light axions (ULA) of different mass. The DMH is described as a Bose–Einstein condensate (BEC) in its ground state. In the mean-field (MF) limit, we have derived the integro-differential equations for the spherically symmetrical wave functions of the two DMH components. We studied, numerically, the radial distribution of the mass density of ULA and constructed the parameters which could be used to distinguish between the two- and one-component DMH. We also discuss an interesting connection between the BEC ground state of a one-component DMH and Black Hole temperature and entropy, and Unruh temperature.

PARAMETRIC EXCITATION OF SOLITONS IN DIPOLAR BOSE–EINSTEIN CONDENSATES

2013 ◽  
Vol 27 (25) ◽  
pp. 1350184 ◽  
Author(s):  
A. BENSEGHIR ◽  
W. A. T. WAN ABDULLAH ◽  
B. A. UMAROV ◽  
B. B. BAIZAKOV
Keyword(s):  
Parametric Excitation ◽  
Einstein Condensate ◽  
Quantum Gases ◽  
Variational Approximation ◽  
Pitaevskii Equation ◽  
Nonlocal Nonlinearity ◽  
Bose Einstein Condensate ◽  
Atomic Interactions ◽  
Theoretical Predictions ◽  
Bose Einstein

In this paper, we study the response of a Bose–Einstein condensate with strong dipole–dipole atomic interactions to periodically varying perturbation. The dynamics is governed by the Gross–Pitaevskii equation with additional nonlinear term, corresponding to a nonlocal dipolar interactions. The mathematical model, based on the variational approximation, has been developed and applied to parametric excitation of the condensate due to periodically varying coefficient of nonlocal nonlinearity. The model predicts the waveform of solitons in dipolar condensates and describes their small amplitude dynamics quite accurately. Theoretical predictions are verified by numerical simulations of the nonlocal Gross–Pitaevskii equation and good agreement between them is found. The results can lead to better understanding of the properties of ultra-cold quantum gases, such as 52 Cr , 164 Dy and 168 Er , where the long-range dipolar atomic interactions dominate the usual contact interactions.

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