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.

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 BOSE–EINSTEIN CONDENSATE IN A QUARTIC POTENTIAL: STATIC AND DYNAMIC PROPERTIES

2011 ◽  
Vol 25 (29) ◽  
pp. 3927-3940 ◽  
Author(s):  
G. K. CHAUDHARY ◽  
AMIT K. CHATTOPADHYAY ◽  
R. RAMAKUMAR
Keyword(s):  
Chemical Potential ◽  
Numerical Solutions ◽  
Dynamic Properties ◽  
Bose Condensate ◽  
Einstein Condensate ◽  
Three Dimensions ◽  
Pitaevskii Equation ◽  
Quartic Potential ◽  
Bose Einstein Condensate ◽  
Bose Einstein

In this paper, we present a theoretical study of a Bose–Einstein condensate of interacting bosons in a quartic trap in one-, two- and three-dimensions. Using Thomas–Fermi approximation, suitably complemented by numerical solutions of the Gross–Pitaevskii equation, we study the ground-state condensate density profiles, the chemical potential, the effects of cross-terms in the quartic potential, temporal evolution of various energy components of the condensate and width oscillations of the condensate. Results obtained are compared with corresponding results for a bose condensate in a harmonic confinement.

Effect of optical lattice on rotating Bose–Einstein condensates in synthetic magnetic field

2018 ◽  
Vol 32 (20) ◽  
pp. 1850212 ◽  
Author(s):  
Jingmin Hua ◽  
Bing Wang ◽  
Genwang Fan ◽  
Yu Lan ◽  
Qiang Zhao
Keyword(s):  
Magnetic Field ◽  
Optical Lattice ◽  
Chemical Potential ◽  
Dynamic Properties ◽  
Rotational Frequency ◽  
Einstein Condensate ◽  
Two Dimensions ◽  
Pitaevskii Equation ◽  
Bose Einstein ◽  
Synthetic Magnetic Field

In this paper, we study the static and dynamic properties of vortices formation in a rotating Bose–Einstein condensate in synthetic magnetic field. The condensate is confined in a harmonic potential and an optical lattice potential. We numerically solve the time-dependent Gross–Pitaevskii equation in two dimensions and compare the vortices formation process with rotating frame method. We derive the two expressions about vortex number N[Formula: see text] and chemical potential [Formula: see text] as a function of rotational frequency [Formula: see text], which show that the number of vortices N[Formula: see text] increases linearly with [Formula: see text], while the chemical potential [Formula: see text] remains nearly unchanged with increasing [Formula: see text]. The analytical results are in qualitative agreement with the numerical ones. Moreover, we also investigate the vortex dynamics. Numerical results indicate that the time spent for the formation of steady state vortices is reduced drastically if the optical lattice is considered. Nevertheless, the synthetic magnetic field approach is still low efficient to generate more vortices.

scholarly journals Derivation of the Landau–Pekar Equations in a Many-Body Mean-Field Limit

2021 ◽  
Vol 240 (1) ◽  
pp. 383-417
Author(s):  
Nikolai Leopold ◽  
David Mitrouskas ◽  
Robert Seiringer
Keyword(s):  
Mean Field ◽  
Einstein Condensate ◽  
Back Reaction ◽  
Many Body ◽  
Field Limit ◽  
Mean Field Limit ◽  
Phonon Field ◽  
Bose Einstein Condensate ◽  
Weakly Couple ◽  
Bose Einstein

AbstractWe consider the Fröhlich Hamiltonian in a mean-field limit where many bosonic particles weakly couple to the quantized phonon field. For large particle numbers and a suitably small coupling, we show that the dynamics of the system is approximately described by the Landau–Pekar equations. These describe a Bose–Einstein condensate interacting with a classical polarization field, whose dynamics is effected by the condensate, i.e., the back-reaction of the phonons that are created by the particles during the time evolution is of leading order.

scholarly journals Two-component axionic dark matter halos

2020 ◽  
Vol 35 (26) ◽  
pp. 2050227 ◽  
Author(s):  
Gennady P. Berman ◽  
Vyacheslav N. Gorshkov ◽  
Vladimir I. Tsifrinovich ◽  
Marco Merkli ◽  
Vladimir V. Tereshchuk
Keyword(s):  
Dark Matter ◽  
Ground State ◽  
Mass Density ◽  
Mean Field ◽  
Einstein Condensate ◽  
Dark Matter Halo ◽  
Bose Einstein Condensate ◽  
Interesting Connection ◽  
Two Component ◽  
Bose Einstein

We consider a two-component dark matter halo (DMH) of a galaxy containing ultra-light axions (ULA) of different mass. The DMH is described as a Bose–Einstein condensate (BEC) in its ground state. In the mean-field (MF) limit, we have derived the integro-differential equations for the spherically symmetrical wave functions of the two DMH components. We studied, numerically, the radial distribution of the mass density of ULA and constructed the parameters which could be used to distinguish between the two- and one-component DMH. We also discuss an interesting connection between the BEC ground state of a one-component DMH and Black Hole temperature and entropy, and Unruh temperature.

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.

scholarly journals Bose-Einstein Condensation of Confined Atomic Gases at Ultra Low Temperatures

2017 ◽  
Vol 9 (5) ◽  
pp. 96
Author(s):  
M. Serhan
Keyword(s):  
Low Temperatures ◽  
Chemical Potential ◽  
Scattering Length ◽  
Einstein Condensation ◽  
Pitaevskii Equation ◽  
Atomic Gases ◽  
Bose Einstein Condensation ◽  
Gaussian Type ◽  
Negative Scattering Length ◽  
Bose Einstein

In this work I solve the Gross-Pitaevskii equation describing an atomic gas confined in an isotropic harmonic trap by introducing a variational wavefunction of Gaussian type. The chemical potential of the system is calculated and the solutions are discussed in the weakly and strongly interacting regimes. For the attractive system with negative scattering length the maximum number of atoms that can be put in the condensate without collapse begins is calculated.

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