Ansatz from nonlinear optics applied to trapped Bose-Einstein condensates (original) (raw)
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We investigate a quasi one-dimensional 87 Rb Bose-Einstein condensate in a harmonic trap with an additional dimple trap (dT) in the center. Within a zero-temperature Gross-Pitaevskii mean-field description we provide a one-dimensional physical intuitive model, which we solve by both a time-independent variational approach and numerical calculations. With this we obtain at first equilibrium results for the emerging condensate wave function which reveal that a dimple trap potential induces a bump or a dip in case of a red-or a blue-detuned Gaussian laser beam, respectively. Afterwards, we investigate how this dT induced bump/dip-imprint upon the condensate wave function evolves for two quench scenarios. At first we consider the generic case that the harmonic confinement is released. During the resulting time-of-flight expansion it turns out that the dT induced bump in the condensate wave function remains present, whereas the dip starts decaying after a characteristic time scale which decreases with increasing blue-detuned dT depth. Secondly, once the red-or blue-detuned dT is switched off, we find that bright shock-waves or gray/dark bi-soliton trains emerge which oscillate within the harmonic confinement with a characteristic frequency.
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Journal of Physics A: Mathematical and Theoretical, 2016
Employing a general variational method and perturbation theory, we derived explicit solutions for the description of one-dimensional two species Bose-Einstein condensates confined by a harmonic trap potential in an optical lattice. We consider the system of two coupled Gross-Pitaevkii equations (GPE) and derive explicit expressions for the chemical potentials and wavefunctions in terms of the atom-atom interaction parameters and laser intensity. We have compared our results with the numerical solutions of the GPE and performed a quantitative analysis for the both considered methods. We underline the importance of the obtained explicit solutions to characterize the density profile or degree of miscibility of the two components.
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Autosolitons in trapped Bose-Einstein condensates with two- and three-body inelastic processes
Physical Review A, 2001
In this work, we consider the conditions for the existence of autosolitons, in trapped Bose-Einstein condensates with attractive atomic interactions. First, the variational approach is employed to estimate the stationary solutions for the three-dimensional Gross-Pitaevskii equation with trap potential, linear atomic feeding from the thermal cloud and two- and three-body inelastic processes. Next, by using exact numerical calculations, we show that the variational approach gives reliable analytical results. We also discuss the possible observation of autosolitons in experiments with Lithium-7.
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The stationary solutions of the Gross-Pitaevskii equation can be divided in two classes: those which reduce, in the limit of vanishing nonlinearity, to the eigenfunctions of the associated Schr\"odinger equation and those which do not have linear counterpart. Analytical and numerical results support an existence condition for the solutions of the first class in terms of the ratio between their proper frequency and the corresponding linear eigenvalue. For one-dimensional confined systems, we show that solutions without linear counterpart do exist in presence of a multi-well external potential. These solutions, which in the limit of strong nonlinearity have the form of chains of dark or bright solitons located near the extrema of the potential, represent macroscopically excited states of a Bose-Einstein condensate and are in principle experimentally observable.
Dark-soliton states of Bose-Einstein condensates in anisotropic traps
Physical Review A, 2000
Dark soliton states of Bose-Einstein condensates in harmonic traps are studied both analytically and computationally by the direct solution of the Gross-Pitaevskii equation in three dimensions. The ground and self-consistent excited states are found numerically by relaxation in imaginary time. The energy of a stationary soliton in a harmonic trap is shown to be independent of density and geometry for large numbers of atoms. Large amplitude field modulation at a frequency resonant with the energy of a dark soliton is found to give rise to a state with multiple vortices. The Bogoliubov excitation spectrum of the soliton state contains complex frequencies, which disappear for sufficiently small numbers of atoms or large transverse confinement. The relationship between these complex modes and the snake instability is investigated numerically by propagation in real time. 03.75.Fi, 05.45.Yv,