Numerical methods for atomic quantum gases with applications to Bose–Einstein condensates and to ultracold fermions

2004 ◽  
Vol 395 (4-5) ◽  
pp. 223-355 ◽  
Author(s):  
A Minguzzi
Keyword(s):  
Numerical Methods ◽  
Quantum Gases ◽  
Atomic Quantum Gases ◽  
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.

scholarly journals Accurate and Efficient Numerical Methods for Computing Ground States and Dynamics of Dipolar Bose-Einstein Condensates via the Nonuniform FFT

2016 ◽  
Vol 19 (5) ◽  
pp. 1141-1166 ◽  
Author(s):  
Weizhu Bao ◽  
Qinglin Tang ◽  
Yong Zhang
Keyword(s):  
Numerical Methods ◽  
Ground State ◽  
High Efficiency ◽  
Three Dimensional ◽  
Ground States ◽  
Dipole Interaction ◽  
Polar Coordinates ◽  
Pitaevskii Equation ◽  
Nonuniform Fft ◽  
Bose Einstein

AbstractWe propose efficient and accurate numerical methods for computing the ground state and dynamics of the dipolar Bose-Einstein condensates utilising a newly developed dipole-dipole interaction (DDI) solver that is implemented with the non-uniform fast Fourier transform (NUFFT) algorithm. We begin with the three-dimensional (3D) Gross-Pitaevskii equation (GPE) with a DDI term and present the corresponding two-dimensional (2D) model under a strongly anisotropic confining potential. Different from existing methods, the NUFFT based DDI solver removes the singularity by adopting the spherical/polar coordinates in the Fourier space in 3D/2D, respectively, thus it can achieve spectral accuracy in space and simultaneously maintain high efficiency by making full use of FFT and NUFFT whenever it is necessary and/or needed. Then, we incorporate this solver into existing successful methods for computing the ground state and dynamics of GPE with a DDI for dipolar BEC. Extensive numerical comparisons with existing methods are carried out for computing the DDI, ground states and dynamics of the dipolar BEC. Numerical results show that our new methods outperform existing methods in terms of both accuracy and efficiency.

scholarly journals Atomic Quantum Gases in Kagomé Lattices

2004 ◽  
Vol 93 (3) ◽  
Author(s):  
L. Santos ◽  
M. Baranov ◽  
J. Cirac ◽  
H.-U. Everts ◽  
H. Fehrmann ◽  
...  
Keyword(s):  
Quantum Gases ◽  
Atomic Quantum Gases

scholarly journals D-DIMENSIONAL IDEAL QUANTUM GASES IN A Arn+Br-n POTENTIAL

2003 ◽  
Vol 17 (25) ◽  
pp. 1321-1330 ◽  
Author(s):  
AHMED JELLAL ◽  
MOHAMMED DAOUD
Keyword(s):  
Semiclassical Approximation ◽  
Quantum Gases ◽  
Einstein Condensation ◽  
Density Profiles ◽  
Ideal Gases ◽  
Power Law Exponent ◽  
Ideal Quantum ◽  
Bose Einstein ◽  
Physical Quantities ◽  
Number Of Particles

This paper is concerned with thermostatistics of both D-dimensional Bose and Fermi ideal gases in a confining potential of type Arn+Br-n, where A, B are strictly positive constants and n is the power-law exponent. The investigation is performed in the framework of the semiclassical approximation. Some physical quantities for such systems are derived, like the density of states, density profiles and the number of particles. Bose–Einstein condensation (BEC) is discussed in the high and low temperature limits corresponding to T→∞ and T→0, respectively.

Complex quantum gases: spinor Bose–Einstein condensates of trapped atomic vapors

2000 ◽  
Vol 280 (1-4) ◽  
pp. 27-31 ◽  
Author(s):  
H. Pu ◽  
C.K. Law ◽  
N.P. Bigelow
Keyword(s):  
Quantum Gases ◽  
Atomic Vapors ◽  
Bose Einstein
Sign in / Sign up

Export Citation Format

Share Document