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Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering

DYNAMICS OF BOSE EINSTEIN CONDENSATE IN FOURIER SYNTESIZED OPTICAL LATTICE POTENTIAL

Züleyha ÖZTAŞ

Published Sep 26, 2019• 0 citations
Publisher

Abstract

In this study, we examine the dynamics of Bose Einstein condensate trapped by Fourier synthesized optical lattice potential. We use time-dependent variational approach to find the ordinary differential equations of motion. We also solve directly Gross Pitaevskii equation numerically using split step Fourier method to verify our findings. Good agreement is achieved between analytical and numerical results.

DOI
10.18038/estubtda.519725

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We suggest a pseudospectral method for solving the three-dimensional time-dependent Gross–Pitaevskii (GP) equation, and use it to study the resonance dynamics of a trapped Bose–Einstein condensate induced by a periodic variation in the atomic scattering length. When the frequency of oscillation of the scattering length is an even multiple of one of the trapping frequencies along the x , y or z direction, the corresponding size of the condensate executes resonant oscillation. Using the concept of the differentiation matrix, the partial-differential GP equation is reduced to a set of coupled ordinary differential equations, which is solved by a fourth-order adaptive step-size control Runge–Kutta method. The pseudospectral method is contrasted with the finite-difference method for the same problem, where the time evolution is performed by the Crank–Nicholson algorithm. The latter method is illustrated to be more suitable for a three-dimensional standing-wave optical-lattice trapping potential.
We investigate the dynamical instability of Bose-Einstein condensates (BECs) with higher-order interactions immersed in an optical lattice with weak driving harmonic potential. For this, we compute both analytically and numerically a modified Gross-Pitaevskii equation with higher-order nonlinearity and external potentials generated by magnetic and optical fields. Using the time-dependent variational approach, we derive the ordinary differential equations for the time evolution of the amplitude and phase of modulational perturbation. Through an effective potential, we obtain the modulational instability condition of BECs and discuss the effect of the higher-order interaction in the dynamics of the condensates in presence of optical potential. We perform direct numerical simulations to support our analytical results, and good agreement is found.
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We study dynamical behaviors of the weakly interacting Bose-Einstein condensate in the one-dimensional optical lattice with an overall double-well potential by solving the time-dependent Gross-Pitaevskii equation. It is observed that the double-well potential dominates the dynamics of such a system even if the lattice depth is several times larger than the height of the double-well potential. This result suggests that the condensate flows without resistance in the periodic lattice just like the case of a single particle moving in periodic potentials. Nevertheless, the effective mass of atoms is increased, which can be experimentally verified since it is connected to the Josephson oscillation frequency. Moreover, the periodic lattice enhances the nonlinearity of the double-well condensate, making the condensate more “self-trapped” in the π -mode self-trapping regime.