Emulation of the evolution of a Bose–Einstein condensate in a time-dependent harmonic trap

2007 ◽  
Vol 364 (6) ◽  
pp. 497-504 ◽  
Author(s):  
Stavros Theodorakis ◽  
Yiannis Constantinou
Keyword(s):  
Einstein Condensate ◽  
Harmonic Trap ◽  
Time Dependent ◽  
Bose Einstein Condensate ◽  
Bose Einstein

scholarly journals Oscillations in a parametrically excited Bose-Einstein condensate in combined harmonic and optical lattice trap

Open Physics ◽  
2012 ◽  
Vol 10 (2) ◽  
Author(s):  
Priyanka Verma ◽  
Aranya Bhattacherjee ◽  
Man Mohan
Keyword(s):  
Optical Lattice ◽  
Chaotic Dynamics ◽  
Einstein Condensate ◽  
Harmonic Trap ◽  
Time Dependent ◽  
Time Varying ◽  
Numerical Techniques ◽  
Bose Einstein Condensate ◽  
Parametric Instabilities ◽  
Bose Einstein

AbstractIn this work, we study parametric excitations in an elongated cigar-shaped BEC in a combined harmonic trap and a time dependent optical lattice by using numerical techniques. We show that there exists a relative competition between the harmonic trap which tries to spatially localize the BEC and the time varying optical lattice which tries to delocalize the BEC. This competition gives rise to parametric excitations (oscillations of the BEC width). Regular oscillations disappear when one of the competing factors, i.e. the strength of harmonic trap or the strength of optical lattice, dominates. Parametric instabilities (chaotic dynamics) arise for large variations in the strength of the optical lattice.

scholarly journals A BOSE-EINSTEIN CONDENSATE WITH PT-SYMMETRIC DOUBLE-DELTA FUNCTION LOSS AND GAIN IN A HARMONIC TRAP: A TEST OF RIGOROUS ESTIMATES

2014 ◽  
Vol 54 (2) ◽  
pp. 116-121 ◽  
Author(s):  
Daniel Haag ◽  
Holger Cartarius ◽  
Günter Wunner
Keyword(s):  
Delta Function ◽  
Einstein Condensate ◽  
Harmonic Trap ◽  
Bose Einstein Condensate ◽  
Quantum Numbers ◽  
Recent Estimate ◽  
Function Loss ◽  
Linear And Nonlinear ◽  
Adjoint Operators ◽  
Bose Einstein

We consider the linear and nonlinear Schrödinger equation for a Bose-Einstein condensate in a harmonic trap with <em>PT</em>-symmetric double-delta function loss and gain terms. We verify that the conditions for the applicability of a recent proposition by Mityagin and Siegl on singular perturbations of harmonic oscillator type self-adjoint operators are fulfilled. In both the linear and nonlinear case we calculate numerically the shifts of the unperturbed levels with quantum numbers n of up to 89 in dependence on the strength of the non-Hermiticity and compare with rigorous estimates derived by those authors. We confirm that the predicted 1/<em>n</em><sup>1/2</sup> estimate provides a valid upper bound on the shrink rate of the numerical eigenvalues. Moreover, we find that a more recent estimate of log(<em>n</em>)/<em>n</em><sup>3/2</sup> is in excellent agreement with the numerical results. With nonlinearity the shrink rates are found to be smaller than without nonlinearity, and the rigorous estimates, derived only for the linear case, are no longer applicable.

Analytical solutions for the spin-1 Bose-Einstein condensate in a harmonic trap

2013 ◽  
Vol 8 (3) ◽  
pp. 319-327
Author(s):  
Yu-Ren Shi ◽  
Xue-Ling Wang ◽  
Guang-Hui Wang ◽  
Cong-Bo Liu ◽  
Zhi-Gang Zhou ◽  
...  
Keyword(s):  
Analytical Solutions ◽  
Einstein Condensate ◽  
Harmonic Trap ◽  
Bose Einstein Condensate ◽  
Bose Einstein

scholarly journals Role of Excited States in the Splitting of a Trapped Interacting Bose-Einstein Condensate by a Time-Dependent Barrier

2007 ◽  
Vol 99 (3) ◽  
Author(s):  
Alexej I. Streltsov ◽  
Ofir E. Alon ◽  
Lorenz S. Cederbaum
Keyword(s):  
Excited States ◽  
Einstein Condensate ◽  
Time Dependent ◽  
Bose Einstein Condensate ◽  
Bose Einstein

DYNAMICS OF NONAUTONOMOUS MATTER BREATHER WAVE IN A TIME-DEPENDENT HARMONIC TRAP WITH NONLINEAR INTERACTION MANAGEMENT

2014 ◽  
Vol 28 (04) ◽  
pp. 1450026 ◽  
Author(s):  
ZHI-GANG LIU ◽  
XIAO-XIAO MA
Keyword(s):  
Nonlinear Interaction ◽  
Complex Potential ◽  
Einstein Condensate ◽  
Time Dependent ◽  
Bose Einstein Condensate ◽  
Parabolic Potential ◽  
Bose Einstein ◽  
Condensate System ◽  
Tunneling Behavior ◽  
Interaction Management

In this paper, we study on breathers of Bose–Einstein condensate analytically in a time-dependent parabolic trap with a complex potential. It is found that the breather can be reflected by the parabolic potential or split into many humps and valleys with the time evolution. The nonlinear tunneling behavior of breather colliding on the parabolic potential is observed. The results provide many possibilities to manipulate breather experimentally in the condensate system.

scholarly journals Bose-Einstein condensate in a harmonic trap decorated with Diracδfunctions

2007 ◽  
Vol 76 (1) ◽  
Author(s):  
Haydar Uncu ◽  
Devrim Tarhan ◽  
Ersan Demiralp ◽  
Özgür E. Müstecaplıoğlu
Keyword(s):  
Einstein Condensate ◽  
Harmonic Trap ◽  
Bose Einstein Condensate ◽  
Bose Einstein

scholarly journals Exact Solutions of Bose-Einstein Condensate in Linear Magnetic Field and Time-Dependent Laser Field

2011 ◽  
Vol 119 (3) ◽  
pp. 294-297 ◽  
Author(s):  
W.H. Huang ◽  
J.W. Mao ◽  
W.G. Qiu
Keyword(s):  
Magnetic Field ◽  
Exact Solutions ◽  
Laser Field ◽  
Einstein Condensate ◽  
Time Dependent ◽  
Bose Einstein Condensate ◽  
Bose Einstein

Quantum fluctuations in the time-dependent BCS–BEC crossover

2008 ◽  
Vol 366 (1877) ◽  
pp. 2813-2820 ◽  
Author(s):  
B.M Breid ◽  
J.R Anglin
Keyword(s):  
Landau Theory ◽  
Einstein Condensate ◽  
Time Dependent ◽  
Integral Approach ◽  
Saddle Point Approximation ◽  
Ginzburg Landau ◽  
Bose Einstein Condensate ◽  
Fermionic Atoms ◽  
Molecular Fields ◽  
Bose Einstein

We describe the time-dependent formation of a molecular Bose–Einstein condensate from a BCS state of fermionic atoms as a result of slow sweeping through a Feshbach resonance. We apply a path integral approach for the molecules, and use two-body adiabatic approximations to solve the atomic evolution in the presence of the classical molecular fields, obtaining an effective action for the molecules. In the narrow resonance limit, the problem becomes semiclassical, and we discuss the growth of the molecular condensate in the saddle point approximation. Considering this time-dependent process as an analogue of the cosmological Zurek scenario, we compare the way condensate growth is driven in this rigorous theory with its phenomenological description via time-dependent Ginzburg–Landau theory.

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