scholarly journals Faraday and Resonant Waves in Dipolar Cigar-Shaped Bose-Einstein Condensates

Symmetry ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1090 ◽  
Author(s):  
Dušan Vudragović ◽  
Antun Balaž
Keyword(s):  
Equations Of Motion ◽  
Mean Field ◽  
Dipole Interaction ◽  
Numerical Approach ◽  
Pitaevskii Equation ◽  
Density Waves ◽  
Oscillation Modes ◽  
Dipolar System ◽  
Bose Einstein ◽  
Resonant Waves

Faraday and resonant density waves emerge in Bose-Einstein condensates as a result of harmonic driving of the system. They represent nonlinear excitations and are generated due to the interaction-induced coupling of collective oscillation modes and the existence of parametric resonances. Using a mean-field variational and a full numerical approach, we studied density waves in dipolar condensates at zero temperature, where breaking of the symmetry due to anisotropy of the dipole-dipole interaction (DDI) plays an important role. We derived variational equations of motion for the dynamics of a driven dipolar system and identify the most unstable modes that correspond to the Faraday and resonant waves. Based on this, we derived the analytical expressions for spatial periods of both types of density waves as functions of the contact and the DDI strength. We compared the obtained variational results with the results of extensive numerical simulations that solve the dipolar Gross-Pitaevskii equation in 3D, and found a very good agreement.

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 STABILITY OF BOSE-EINSTEIN CONDENSATES IN A PT-SYMMETRIC DOUBLE-δ POTENTIAL CLOSE TO BRANCH POINTS

2014 ◽  
Vol 54 (2) ◽  
pp. 133-138 ◽  
Author(s):  
Andreas Löhle ◽  
Holger Cartarius ◽  
Daniel Haag ◽  
Dennis Dast ◽  
Jörg Main ◽  
...  
Keyword(s):  
Ground State ◽  
Mean Field ◽  
Einstein Condensate ◽  
Pitaevskii Equation ◽  
Branch Points ◽  
Mean Field Limit ◽  
Bose Einstein Condensate ◽  
Stability Change ◽  
The Difference ◽  
Bose Einstein

A Bose-Einstein condensate trapped in a double-well potential, where atoms are incoupled to one side and extracted from the other, can in the mean-field limit be described by the nonlinear Gross-Pitaevskii equation (GPE) with a <em>PT</em> symmetric external potential. If the strength of the in- and outcoupling is increased two <em>PT</em> broken states bifurcate from the <em>PT</em> symmetric ground state. At this bifurcation point a stability change of the ground state is expected. However, it is observed that this stability change does not occur exactly at the bifurcation but at a slightly different strength of the in-/outcoupling effect. We investigate a Bose-Einstein condensate in a <em>PT</em> symmetric double-δ potential and calculate the stationary states. The ground state’s stability is analysed by means of the Bogoliubov-de Gennes equations and it is shown that the difference in the strength of the in-/outcoupling between the bifurcation and the stability change can be completely explained by the norm-dependency of the nonlinear term in the Gross-Pitaevskii equation.

scholarly journals PATTERN FORMING DYNAMICAL INSTABILITIES OF BOSE–EINSTEIN CONDENSATES

2004 ◽  
Vol 18 (05n06) ◽  
pp. 173-202 ◽  
Author(s):  
P. G. KEVREKIDIS ◽  
D. J. FRANTZESKAKIS
Keyword(s):  
Modulational Instability ◽  
Mean Field ◽  
Three Dimensional ◽  
Two Dimensions ◽  
One Dimension ◽  
Pitaevskii Equation ◽  
Long Wavelength ◽  
Pattern Forming ◽  
Bose Einstein ◽  
Dynamical Instabilities

In this short topical review, we revisit a number of works on the pattern-forming dynamical instabilities of Bose–Einstein condensates in one- and two-dimensional settings. In particular, we illustrate the trapping conditions that allow the reduction of the three-dimensional, mean field description of the condensates (through the Gross–Pitaevskii equation) to such lower dimensional settings, as well as to lattice settings. We then go on to study the modulational instability in one dimension and the snaking/transverse instability in two dimensions as typical examples of long-wavelength perturbations that can destabilize the condensates and lead to the formation of patterns of coherent structures in them. Trains of solitons in one dimension and vortex arrays in two dimensions are prototypical examples of the resulting nonlinear waveforms, upon which we briefly touch at the end of this review.

Effects of three-body interactions on the instabilities and self-oscillations of the four-wave mixing in Bose–Einstein condensates

2017 ◽  
Vol 31 (21) ◽  
pp. 1750150 ◽  
Author(s):  
G. J. Ngounga Makoundit ◽  
T. B. Ekogo ◽  
A. B. Moubissi ◽  
G. H. Ben-Bolie ◽  
T. C. Kofane
Keyword(s):  
Probe Beam ◽  
Mean Field ◽  
Field Approximation ◽  
Four Wave Mixing ◽  
Signal Beam ◽  
Mean Field Approximation ◽  
Pitaevskii Equation ◽  
Wave Mixing ◽  
Three Body ◽  
Bose Einstein

In this paper, we analyze and discuss instabilities and self-oscillations of four-wave mixing in two-component Bose–Einstein condensates with two- and three-body interatomic interactions. The model is very accurately described in the mean-field approximation by the cubic–quintic Gross–Pitaevskii equation. The relation between the input and output field intensities is multivalued and the effects of the quintic nonlinearity on the self-oscillations of the system are studied. We have also found that the magnitude of the signal beam increases with the increase of the intensity of the probe beam, up to a saturated value, then it decreases with the increase of the intensity of the probe beam. We have shown that the three-body interatomic interactions enhance this saturated value.

scholarly journals Self-Consistent Derivation of the Modified Gross-Pitaevskii Equation with Lee-Huang-Yang Correction

2018 ◽  
Vol 8 (10) ◽  
pp. 1998 ◽  
Author(s):  
Luca Salasnich
Keyword(s):  
Order Parameter ◽  
Semiclassical Approximation ◽  
Mean Field ◽  
Field Operator ◽  
Pitaevskii Equation ◽  
Small Quantum ◽  
External Trapping Potential ◽  
Key Steps ◽  
Interacting Atoms ◽  
Bose Einstein

We consider a dilute and ultracold bosonic gas of weakly-interacting atoms. Within the framework of quantum field theory, we derive a zero-temperature modified Gross–Pitaevskii equation with beyond-mean-field corrections due to quantum depletion and anomalous density. This result is obtained from the stationary equation of the Bose–Einstein order parameter coupled to the Bogoliubov–de Gennes equations of the out-of-condensate field operator. We show that, in the presence of a generic external trapping potential, the key steps to get the modified Gross–Pitaevskii equation are the semiclassical approximation for the Bogoliubov–de Gennes equations, a slowly-varying order parameter and a small quantum depletion. In the uniform case, from the modified Gross–Pitaevskii equation, we get the familiar equation of state with Lee–Huang–Yang correction.

scholarly journals Dynamics of Bose–Einstein Condensates Subject to the Pöschl–Teller Potential through Numerical and Variational Solutions of the Gross–Pitaevskii Equation

Materials ◽  
2020 ◽  
Vol 13 (10) ◽  
pp. 2236
Author(s):  
Lucas Carvalho Pereira ◽  
Valter Aragão do Nascimento
Keyword(s):  
Chemical Potential ◽  
Mean Field ◽  
Interatomic Interaction ◽  
Einstein Condensate ◽  
Point Of View ◽  
Pitaevskii Equation ◽  
Theoretical Point ◽  
Solid State Physics ◽  
Atomic And Molecular Physics ◽  
Bose Einstein

We present for the first time an approach about Bose–Einstein condensates made up of atoms with attractive interatomic interactions confined to the Pöschl–Teller hyperbolic potential. In this paper, we consider a Bose–Einstein condensate confined in a cigar-shaped, and it was modeled by the mean field equation known as the Gross–Pitaevskii equation. An analytical (variational method) and numerical (two-step Crank–Nicolson) approach is proposed to study the proposed model of interatomic interaction. The solutions of the one-dimensional Gross–Pitaevskii equation obtained in this paper confirmed, from a theoretical point of view, the possibility of the Pöschl–Teller potential to confine Bose–Einstein condensates. The chemical potential as a function of the depth of the Pöschl–Teller potential showed a behavior very similar to the cases of Bose–Einstein condensates and superfluid Fermi gases in optical lattices and optical superlattices. The results presented in this paper can open the way for several applications in atomic and molecular physics, solid state physics, condensed matter physics, and material sciences.

Stability of binary condensates with spatial modulations of quintic nonlinearities in optical lattices

2015 ◽  
Vol 29 (03) ◽  
pp. 1550008 ◽  
Author(s):  
M. D. Mboumba ◽  
A. B. Moubissi ◽  
T. B. Ekogo ◽  
D. Belobo Belobo ◽  
G. H. Ben-Bolie ◽  
...  
Keyword(s):  
Optical Lattice ◽  
Optical Lattices ◽  
Mean Field ◽  
Collective Excitations ◽  
Pitaevskii Equation ◽  
Dependent Potential ◽  
The Mean ◽  
The Stability ◽  
Bose Einstein ◽  
Spatial Modulations

The stability and collective excitations of binary Bose–Einstein condensates with cubic and quintic nonlinearities in variable anharmonic optical lattices are investigated. By using the variational approach, the influences of the quintic nonlinearities and the shape of the external potential on the stability are discussed in details. It is found that the quintic intraspecies and interspecies interatomic interactions profoundly affect the stability criterion and collective excitations of the system. The shape dependent potential form that characterizes the optical lattice deeply alters the stability regions. Direct numerical simulations of the mean-field coupled Gross–Pitaevskii equation describing the system agree well with the analytical predictions.

THREE-BODY INTERACTIONS BEYOND THE GROSS–PITAEVSKII EQUATION AND MODULATIONAL INSTABILITY OF BOSE–EINSTEIN CONDENSATES

2012 ◽  
Vol 26 (32) ◽  
pp. 1250202 ◽  
Author(s):  
DIDIER BELOBO BELOBO ◽  
GERMAIN HUBERT BEN-BOLIE ◽  
TIMOLEON CREPIN KOFANE
Keyword(s):  
Modulational Instability ◽  
Mean Field Theory ◽  
Mean Field ◽  
External Potential ◽  
Pitaevskii Equation ◽  
Theoretical Predictions ◽  
The Mean ◽  
Three Body ◽  
Bose Einstein ◽  
Condensate System

Beyond the mean-field theory, a new model of the Gross–Pitaevskii equation (GPE) that describes the dynamics of Bose–Einstein condensates (BECs) is derived using an appropriate phase-imprint on the old wavefunction. This modified version of the GPE in addition to the two-body interactions term, also takes into account effects of the three-body interactions. The three-body interactions consist of a quintic term and the delayed nonlinear response of the condensate system term. Then, the modulational instability (MI) of the new GPE confined in an attractive harmonic potential is investigated. The analytical study shows that the three-body interactions destabilize more the condensate system while the external potential alleviates the instability. Numerical results confirm the theoretical predictions. Further numerical investigations of the behavior of solitons reveal that the three-body interactions enhance the appearance of solitons, increase the number of solitons generated and deeply change the lifetime of solitons. Moreover, the external potential delays the appearance of solitons. Besides, a new initial condition is introduced which enables to increase the number of solitons created and deeply affects the trail of chains of solitons generated. Moreover, the MI of a condensate without the external potential, and in a repulsive potential is also investigated.

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