Localized waves and mixed interaction solutions with dynamical analysis to the Gross-Pitaevskii equation in the Bose-Einstein condensate

2021 ◽  
Author(s):  
Haotian Wang ◽  
Qin Zhou ◽  
Anjan Biswas ◽  
Wenjun Liu
Keyword(s):  
Rogue Wave ◽  
Rogue Waves ◽  
Transformation Method ◽  
Einstein Condensate ◽  
Dynamical Analysis ◽  
Pitaevskii Equation ◽  
Initial Profile ◽  
Interaction Solutions ◽  
Bose Einstein Condensate ◽  
Bose Einstein

Abstract We report a kind of breather, rogue wave and mixed interaction structures on a variational background height in the Gross-Pitaevskii equation in the Bose-Einstein condensate by the generalized Darboux transformation method, and the effects of related parameters on rogue wave structures are discussed. Numerical simulation can discuss the dynamics and stability of these solutions. We numerically confirm that these are correct, and can be reproduced from a deterministic initial profile. Results show that rogue waves and mixed interaction solutions can evolve with a small amplitude perturbation under the initial profile conditions, but breathers cannot. Therefore, these can be used to anticipate the feasibility of their experimental observation.

scholarly journals Matter rogue waves for the three-component Gross–Pitaevskii equations in the spinor Bose–Einstein condensates

2018 ◽  
Vol 474 (2209) ◽  
pp. 20170276 ◽  
Author(s):  
Wen-Rong Sun ◽  
Lei Wang
Keyword(s):  
Modulation Instability ◽  
Rogue Wave ◽  
Rogue Waves ◽  
Einstein Condensate ◽  
Rational Solutions ◽  
Algebraic Construction ◽  
Bose Einstein Condensate ◽  
Energy Transfers ◽  
Bose Einstein ◽  
The Waves

To show the existence and properties of matter rogue waves in an F =1 spinor Bose–Einstein condensate (BEC), we work on the three-component Gross–Pitaevskii (GP) equations. Via the Darboux-dressing transformation, we obtain a family of rational solutions describing the extreme events, i.e. rogue waves. This family of solutions includes bright–dark–bright and bright–bright–bright rogue waves. The algebraic construction depends on Lax matrices and their Jordan form. The conditions for the existence of rogue wave solutions in an F =1 spinor BEC are discussed. For the three-component GP equations, if there is modulation instability, it is of baseband type only, confirming our analytic conditions. The energy transfers between the waves are discussed.

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.

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.

Phase separation in spin-orbit-angular-momentum coupling Bose–Einstein condensate systems

2020 ◽  
Vol 34 (23) ◽  
pp. 2050241
Author(s):  
Jin Xu ◽  
Jinbin Li
Keyword(s):  
Angular Momentum ◽  
Phase Separation ◽  
Coupling Strength ◽  
Interaction Strength ◽  
Einstein Condensate ◽  
Three Dimensions ◽  
Pitaevskii Equation ◽  
Spin Orbit ◽  
Bose Einstein Condensate ◽  
Bose Einstein

We study the phase separation in three-component spin-orbit-angular-momentum coupled Bose–Einstein condensate with spin-1 in three dimensions. Different types of phase-separation are acquired upon an increase of the coupling strength, magnetic gradient strength, spin-dependent interaction strength and particle number above a critical value. Increasing the value of coupling strength and other related parameters shows distinct behaviors which are produced by repulsion for large strengths of spin-orbit angular-momentum (SOAM) coupling. The present investigation is carried out through a numerical Crank–Nicolson method of the underlying mean-field Gross–Pitaevskii equation.

scholarly journals DYNAMICS OF BISOLITONIC MATTER WAVES IN A BOSE–EINSTEIN CONDENSATE SUBJECTED TO AN ATOMIC BEAM SPLITTER AND GRAVITY

2010 ◽  
Vol 24 (30) ◽  
pp. 2911-2920 ◽  
Author(s):  
ALAIN MOÏSE DIKANDÉ ◽  
ISAIAH NDIFON NGEK ◽  
JOSEPH EBOBENOW
Keyword(s):  
Einstein Condensate ◽  
Matter Wave ◽  
Pitaevskii Equation ◽  
Transform Method ◽  
Perturbative Approach ◽  
Matter Waves ◽  
Bose Einstein Condensate ◽  
Scattering Transform ◽  
Experimental Implementation ◽  
Bose Einstein

A theoretical scheme for an experimental implementation involving bisolitonic matter waves from an attractive Bose–Einstein condensate, is considered within the framework of a non-perturbative approach to the associate Gross–Pitaevskii equation. The model consists of a single condensate subjected to an expulsive harmonic potential creating a double-condensate structure, and a gravitational potential that induces atomic exchanges between the two overlapping post condensates. Using a non-isospectral scattering transform method, exact expressions for the bright-matter–wave bisolitons are found in terms of double-lump envelopes with the co-propagating pulses displaying more or less pronounced differences in their widths and tails depending on the mass of atoms composing the condensate.

NEW INSIGHT ON THE CHAIN STATES AND BOSE-EINSTEIN CONDENSATE IN LIGHT NUCLEI

2008 ◽  
Vol 17 (10) ◽  
pp. 2150-2154 ◽  
Author(s):  
S. YU. TORILOV ◽  
K. A. GRIDNEV ◽  
W. GREINER
Keyword(s):  
Cluster Model ◽  
Einstein Condensate ◽  
Light Nuclei ◽  
Einstein Condensation ◽  
Pitaevskii Equation ◽  
Deformed Nuclei ◽  
Bose Einstein Condensation ◽  
Bose Einstein Condensate ◽  
Alpha Cluster ◽  
Bose Einstein

The simple alpha-cluster model was used for the consideration of the chain states and Bose-Einstein condensation in the light self-conjugated nuclei. Obtained results were compared with predictions of the shell-model for the deformed nuclei, with calculations based on Gross-Pitaevskii equation and with recent experimental results.

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