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

Abstract

Abstract:In 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. PACS

Generation of higher harmonics in dipolar Bose–Einstein condensates trapped in periodically modulated potentials

“…The application of the modulation to both the HO and OL potentials makes the results more complex; nevertheless, in all cases, the VA predicts quasi-periodic dynamics, rather than dynamical chaos. The comparison to the direct simulations corroborates the validity of a majority of spectral peaks predicted by the VA. A quasi-one-dimensional BEC under the action of time-modulated potentials, such as harmonic-oscillator traps and optical lattices, may find various applications [56][57][58][59][60][61]116]. A comprehensive review of the respective technique of the spatiotemporal engineering in BEC is given in ref.…”

“…It has also been found, in the experiment and the theory alike, that temporal modulation of the external trap or s-wave scattering length induces a variety of collective excitations in BEC [14,21,[43][44][45][46][47][48][49][50][51][52][53][54][55]. In particular, a quasi-one-dimensional BEC under the action of the HO potential combined with a temporally modulated OL is a relevant setting [56][57][58][59][60][61]. However, exact solutions of the GPE in the presence of a complex trap are not available even in lower dimensions, with the exception of models specially engineered so that to make them equivalent to the one-dimensional integrable NLSE [62].…”

“…Relevant numerical methods are based on the direct and inverse fast Fourier transforms (FFTs) for the imaginary-and real-time propagation and the Crank-Nicolson discretization [88][89][90][91]. Apart from the numerical approaches, the variational approximation (VA) is a powerful method for the semi-analytical study of the dynamics of BEC, such as investigating oscillation modes, frequency shift, stability, Faraday patterns, coupled modes, parametric and geometric resonances, temporal modulation of the s-wave scattering length, and localization in OL potentials [22,59,60,73,[92][93][94][95][96][97][98][99][100]. In particular, the VA was used to predict stable solitons with the strongly anisotropic structure in the plane including the direction of the polarizing magnetic field, which is combined with a trapping HO potential acting in the direction perpendicular to the plane [73,75].…”

Controlled generation of nonlinear resonances through sinusoidal lattice modes in Bose–Einstein condensate

“…These authors also showed the possibility of suppression of chaos and its control through the intensity of the lattice potential. Recently, nonlinear resonance phenomenon has been studied in BEC, where the occurrence of resonances has been investigated through periodic modulation of the scattering length [28][29][30]. Unlike the methods opted in these studies, we take a different approach by introducing a lattice potential and show that it is possible to generate the nonlinear resonances in BEC, through controlled chirp management.…”