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Chinese Physics B

Dynamics of Bose—Einstein condensate in a harmonic potential and a Gaussian energy barrier

Wei Hua, Bin Li, Xue‐Shen Liu

Published Jan 1, 2011• 3 citations
Publisher

Abstract

We have studied the dynamics of Bose—Einstein condensate by solving numerically the Gross-Pitaevskii (GP) equation. We examined the periodic behaviour of the condensate in a shifted harmonic potential, and further demonstrated the tunneling effect of a condensate through a Gaussian energy barrier, which is inserted after the condensate has been excited by shifting the harmonic trapping potential to a side. Moreover, it is shown that the initial condensate evolves dynamically into two separate moving condensates after the tunneling time under certain conditions.

DOI
10.1088/1674-1056/20/1/010311

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We have studied the dynamics of Bose—Einstein condensate by solving numerically the Gross-Pitaevskii (GP) equation. We examined the periodic behaviour of the condensate in a shifted harmonic potential, and further demonstrated the tunneling effect of a condensate through a Gaussian energy barrier, which is inserted after the condensate has been excited by shifting the harmonic trapping potential to a side. Moreover, it is shown that the initial condensate evolves dynamically into two separate moving condensates after the tunneling time under certain conditions.
We study certain stationary and time-evolution problems of trapped Bose-Einstein condensates using the numerical solution of the Gross-Pitaevskii (GP) equation with both spherical and axial symmetries. We consider time-evolution problems initiated by suddenly changing the interatomic scattering length or harmonic trapping potential in a stationary condensate. These changes introduce oscillations in the condensate which are studied in detail. We use a time iterative split-step method for the solution of the time-dependent GP equation, where all nonlinear and linear non-derivative terms are treated separately from the time propagation with the kinetic energy terms. Even for an arbitrarily strong nonlinear term this leads to extremely accurate and stable results after millions of time iterations of the original equation.
Using the mean-field Gross-Pitaevskii (GP) equation we study the evolution of Josephson current in a repulsive Bose-Einstein condensate in an optical-lattice potential initiated by a sudden displacement of the trapping potential. Similarly, we also study the evolution of quantum tunneling in a double-well potential in one and three dimensions initiated by a trap displacement leading to a periodic oscillation of the condensate across the barrier which could be observed experimentally. The frequencies of Josephson current found directly from the solution of the GP equation are in agreement with the experiment by Cataliotti et al. [2001 Science 293 843]. The breakdown of the Josephson current for a large trap displacement is also in agreement with another experiment by Cataliotti et al. [2003 New J. Phys. 5 71]. PACS numbers: 03.75.Lm, 03.75.KkQuantum tunneling and Josephson current in Bose-Einstein condensates 2 1.
We study certain stationary and time-evolution problems of trapped Bose-Einstein condensates of weakly interacting alkali atoms described by a nonlinear Gross-Pitaevskii (GP) equation. We suggest a pseudospectral method involving Laguerre polynomials to solve the time dependent GP for a spherically symmetric trap potential. The radial wavefunction and energy values have been calculated for different nonlinearities. Further, we study the effect of suddenly changing the interatomic scattering length or harmonic oscillator trap potential in the condensate. We also investigate the frequency of oscillation due to the variation in the strength of nonlinearity.
We investigate the quantum tunneling of a Bose-Einstein condensate confined in a optical trap. We show that periodic pulses of coherent matter are emitted from the trap by using an oscillating energy barrier. Moreover, the emitted fraction of condensed atoms strongly increases if the period of oscillation of the height of the energy barrier is in parametric resonance with the period of oscillation of the center of mass of the condensate inside the potential well. Our model is analyzed by numerically solving the nonpolynomial Schrodinger equation (NPSE), an effective one-dimensional equation which describes the macroscopic wavefunction of Bose condensates under transverse harmonic confinement. The range of validity of NPSE is discussed and compared with that of Gross-Pitaevskii equation.
The mean-field dynamics of a Bose-Einstein condensate is studied in the presence of a microscopic trapping potential from which the condensate can escape via tunneling through finite barriers. We show that the method of complex scaling can be used to obtain a quantitative description of this decay process. A real-time propagation approach that is applied to the complex-scaled Gross-Pitaevskii equation allows us to calculate the chemical potentials and lifetimes of the metastably trapped Bose-Einstein condensate. The method is applied to a one-dimensional harmonic confinement potential combined with a Gaussian envelope, for which we compute the lowest symmetric and antisymmetric quasibound states of the condensate. A comparison with alternative approaches using absorbing boundary conditions as well as complex absorbing potentials shows good agreement.