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 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.

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.

ON THE ENERGY OF A BOSE–EINSTEIN CONDENSATE IN AN OPTICAL LATTICE

2007 ◽  
Vol 19 (04) ◽  
pp. 371-384 ◽  
Author(s):  
AMANDINE AFTALION
Keyword(s):  
Optical Lattice ◽  
Critical Case ◽  
Periodic Potential ◽  
Einstein Condensate ◽  
Gamma Convergence ◽  
The Third ◽  
Bose Einstein Condensate ◽  
Delta Functions ◽  
Convergence Type ◽  
Bose Einstein

In this paper, we study the Gross–Pitaevskii energy of a Bose–Einstein condensate in the presence of an optical lattice, modeled by a periodic potential V(x3) in the third direction. We study a simple case where the wells of the potential V correspond to regions where V vanishes, and are separated by small intervals of size δ where V is large. According to the intensity of V, we determine the limiting energy as δ tends to 0. In the critical case, the periodic potential approaches a sum of delta functions and the limiting energy has a contribution due to the value of the wave function between the wells. The proof relies on Gamma convergence type techniques.

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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