Explicit solutions to an effective Gross–Pitaevskii equation: One-dimensional Bose–Einstein condensate in specific traps

2008 ◽  
Vol 49 (2) ◽  
pp. 023503 ◽  
Author(s):  
E. Kengne ◽  
X. X. Liu ◽  
B. A. Malomed ◽  
S. T. Chui ◽  
W. M. Liu
Keyword(s):  
Einstein Condensate ◽  
Pitaevskii Equation ◽  
Explicit Solutions ◽  
One Dimensional ◽  
Bose Einstein Condensate ◽  
Bose Einstein

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.

Exact Chirped Soliton Solutions for the One-Dimensional Gross– Pitaevskii Equation with Time-Dependent Parameters

2012 ◽  
Vol 67 (3-4) ◽  
pp. 141-146 ◽  
Author(s):  
Zhenyun Qina ◽  
Gui Mu
Keyword(s):  
Soliton Solution ◽  
Soliton Solutions ◽  
Einstein Condensate ◽  
Time Dependent ◽  
Pitaevskii Equation ◽  
Zero Temperature ◽  
One Dimensional ◽  
Bose Einstein Condensate ◽  
The One ◽  
Bose Einstein

The Gross-Pitaevskii equation (GPE) describing the dynamics of a Bose-Einstein condensate at absolute zero temperature, is a generalized form of the nonlinear Schr¨odinger equation. In this work, the exact bright one-soliton solution of the one-dimensional GPE with time-dependent parameters is directly obtained by using the well-known Hirota method under the same conditions as in S. Rajendran et al., Physica D 239, 366 (2010). In addition, the two-soliton solution is also constructed effectively

scholarly journals Parafermionic behavior of Bose-Einstein condensates

2019 ◽  
Vol 21 ◽  
pp. 71
Author(s):  
A. Martinou ◽  
D. Bonatsos
Keyword(s):  
Optical Potential ◽  
Optical Trap ◽  
Einstein Condensate ◽  
Pitaevskii Equation ◽  
One Dimensional ◽  
Bright Solitons ◽  
Bose Einstein Condensate ◽  
Repulsive Interactions ◽  
Bose Einstein

Bright solitons of 7Li atoms in a quasi one-dimensional optical trap, formed in a stable Bose–Einstein condensate in which the interactions have been magnetically tuned from repulsive to attractive, have been seen to exhibit repulsive interactions among them when set in motion by offsetting the optical potential. Solving first the Gross–Pitaevskii equation for the special conditions corresponding to the experiment, we show then that this system can be described in terms of generalized parafermionic oscillators, the order of the parafermions being related to the strength of the interaction among the atoms and being a measure of the bosonic behavior vs. the fermionic behavior of the system.

scholarly journals Emission of Solitons From an Obstacle Moving in the Bose-Einstein Condensate

2021 ◽  
Vol 9 ◽  
Author(s):  
Yu Song ◽  
Yu Mo ◽  
Shiping Feng ◽  
Shi-Jie Yang
Keyword(s):  
Numerical Simulations ◽  
Einstein Condensate ◽  
Pitaevskii Equation ◽  
Nonlinear Interactions ◽  
One Dimensional ◽  
System Parameters ◽  
Dark Solitons ◽  
Bose Einstein Condensate ◽  
Bose Einstein ◽  
Moving Obstacle

Dark solitons dynamically generated from a potential moving in a one-dimensional Bose-Einstein condensate are displayed. Based on numerical simulations of the Gross-Pitaevskii equation, we find that the moving obstacle successively emits a series of solitons which propagate at constant speeds. The dependence of soliton emission on the system parameters is examined. The formation mechanism of solitons is interpreted as interference between a diffusing wavepacket and the condensate background, enhanced by the nonlinear interactions.PACS numbers: 03.75.Mn, 03.75.Lm, 05.30.Jp

scholarly journals Stationary and Dynamical Solutions of the Gross-Pitaevskii Equation for a Bose-Einstein Condensate in a PT symmetric Double Well

10.14311/1797 ◽  
2013 ◽  
Vol 53 (3) ◽  
Author(s):  
Holger Cartarius ◽  
Dennis Dast ◽  
Daniel Haag ◽  
Günter Wunner ◽  
Rüdiger Eichler ◽  
...  
Keyword(s):  
Wave Function ◽  
Three Dimensional ◽  
Stationary Solutions ◽  
Einstein Condensate ◽  
Time Dependent ◽  
Pitaevskii Equation ◽  
One Dimensional ◽  
Bose Einstein Condensate ◽  
Bose Einstein ◽  
Double Well Potential

We investigate the Gross-Pitaevskii equation for a Bose-Einstein condensate in a PT symmetric double-well potential by means of the time-dependent variational principle and numerically exact solutions. A one-dimensional and a fully three-dimensional setup are used. Stationary states are determined and the propagation of wave function is investigated using the time-dependent Gross-Pitaevskii equation. Due to the nonlinearity of the Gross-Pitaevskii equation the potential dependson the wave function and its solutions decide whether or not the Hamiltonian itself is PT symmetric. Stationary solutions with real energy eigenvalues fulfilling exact PT symmetry are found as well as PT broken eigenstates with complex energies. The latter describe decaying or growing probability amplitudes and are not true stationary solutions of the time-dependent Gross-Pitaevskii equation. However, they still provide qualitative information about the time evolution of the wave functions.

scholarly journals Momentum correlations as signature of sonic Hawking radiation in Bose-Einstein condensates

2018 ◽  
Vol 4 (4) ◽  
Author(s):  
Alessandro Fabbri ◽  
Nicolas Pavloff
Keyword(s):  
Hawking Radiation ◽  
Momentum Space ◽  
Einstein Condensate ◽  
Measuring Process ◽  
One Dimensional ◽  
Bose Einstein Condensate ◽  
Momentum Correlation ◽  
Quantum Quenches ◽  
Effects Of Temperature ◽  
Bose Einstein

We study the two-body momentum correlation signal in a quasi one dimensional Bose-Einstein condensate in the presence of a sonic horizon. We identify the relevant correlation lines in momentum space and compute the intensity of the corresponding signal. We consider a set of different experimental procedures and identify the specific issues of each measuring process. We show that some inter-channel correlations, in particular the Hawking quantum-partner one, are particularly well adapted for witnessing quantum non-separability, being resilient to the effects of temperature and/or quantum quenches.

scholarly journals Do we need a non-perturbative theory of Bose-Einstein condensation?

2021 ◽  
Vol 2103 (1) ◽  
pp. 012200
Author(s):  
K G Zloshchastiev
Keyword(s):  
Phase Contrast ◽  
Einstein Condensate ◽  
Einstein Condensation ◽  
One Dimensional ◽  
Quantum Fluid ◽  
Bose Einstein Condensate ◽  
Dipole Force ◽  
Theoretical Assumptions ◽  
Bose Einstein ◽  
Best Fit

Abstract We recall the experimental data of one-dimensional axial propagation of sound near the center of the Bose-Einstein condensate cloud, which used the optical dipole force method of a focused laser beam and rapid sequencing of nondestructive phase-contrast images. We reanalyze these data within the general quantum fluid framework but without model-specific theoretical assumptions; using the standard best fit techniques. We demonstrate that some of their features cannot be explained by means of the perturbative two-body approximation and Gross-Pitaevskii model, and conjecture possible solutions.

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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