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.

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.

Two-dimensional quantum turbulence in a nonuniform Bose-Einstein condensate

2009 ◽  
Vol 80 (2) ◽  
Author(s):  
T.-L. Horng ◽  
C.-H. Hsueh ◽  
S.-W. Su ◽  
Y.-M. Kao ◽  
S.-C. Gou
Keyword(s):  
Quantum Turbulence ◽  
Einstein Condensate ◽  
Two Dimensional ◽  
Bose Einstein Condensate ◽  
Bose Einstein

scholarly journals Schemes for loading a Bose Einstein condensate into a two-dimensional dipole trap

2003 ◽  
Vol 5 (2) ◽  
pp. S155-S163 ◽  
Author(s):  
Yves Colombe ◽  
Demascoth Kadio ◽  
Maxim Olshanii ◽  
Brigitte Mercier ◽  
Vincent Lorent ◽  
...  
Keyword(s):  
Einstein Condensate ◽  
Two Dimensional ◽  
Dipole Trap ◽  
Bose Einstein Condensate ◽  
Bose Einstein

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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