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Physical Review A

Strong-field driving of a dilute atomic Bose-Einstein condensate

Mirosław Brewczyk, Kazimierz Rza̧żewski, Charles W. Clark

Published Jan 1, 1998• 4 citations
Publisher

Abstract

A hydrodynamical version of the time-dependent Gross-Pitaevskii equation has been formulated and applied to the description of a Bose-Einstein condensate (BEC) of ${}^{87}$Rb atoms in the JILA time-averaged orbiting potential (TOP) trap. The response of the BEC to time-dependent modulations of the trap potential is computed and the characteristic frequencies of a BEC oscillation agree well with those observed in recent experiments. For the axially symmetric $m=0$ mode of the TOP trap, we find a weak dependence of the oscillatory frequency on the strength of the driving amplitude under conditions comparable to those of current experiments. The free ringing of the BEC that is induced by a transient change in the potential is found to be periodic, in agreement with the predictions of Thomas-Fermi theory. We analyze the harmonic content of the spectral response and consider possibilities for high-harmonic generation in the context of nonlinear atom optics.

DOI
10.1103/physreva.57.488

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A hydrodynamical version of the time-dependent Gross-Pitaevskii equation has been formulated and applied to the description of a Bose-Einstein condensate (BEC) of 87{}^{87}87Rb atoms in the JILA time-averaged orbiting potential (TOP) trap. The response of the BEC to time-dependent modulations of the trap potential is computed and the characteristic frequencies of a BEC oscillation agree well with those observed in recent experiments. For the axially symmetric m=0m=0m=0 mode of the TOP trap, we find a weak dependence of the oscillatory frequency on the strength of the driving amplitude under conditions comparable to those of current experiments. The free ringing of the BEC that is induced by a transient change in the potential is found to be periodic, in agreement with the predictions of Thomas-Fermi theory. We analyze the harmonic content of the spectral response and consider possibilities for high-harmonic generation in the context of nonlinear atom optics.
We investigate the response of a Bose-Einstein condensate of trapped, neutral atoms to weak and strong sinusoidal perturbation of the trapping potential both by solving the Bogoliubov equations and by direct integration of the time-dependent, driven Ginzburg-Pitaevskii-Gross equation. We find that the distortion of the condensate is maximal when the frequency of the perturbation equals one of the mode positions of the condensate's excitation spectrum. On resonance, the condensate exhibits a strong nonlinear response that can be used as a clear signature of the mode frequency in an experiment where the trap potential is weakly perturbed. For strong driving, we find evidence for an array of nonlinear effects such as harmonic generation and frequency mixing. These phenomena are the matter-wave analogs of conventional nonlinear optics and should be straightforward to study in evaporatively cooled samples of alkali-metal atoms. \textcopyright{} 1996 The American Physical Society.
A hydrodynamical version of the time-dependent Gross-Pitaevskii equation is used to describe driven vibrations of a Bose-Einstein condensate of 87 Rb atoms in a magnetic trap. If the trap frequency is suddenly decreased, and later is suddenly returned to its initial value, the response of the condensate departs from the self-similar character that is obtained in the Thomas-Fermi approach. We show that the self-similar Thomas-Fermi modes are, in fact, unstable. Thus, the `quantum pressure' term in the hydrodynamic equations of motion can play a significant role in condensate excitation dynamics, even when its effect on ground-state properties is negligible.
The response of a trapped Bose-Einstein condensed gas to a periodic driving force is studied theoretically in the framework of the nonlinear Gross-Pitaevskii equation. The monopole mode is driven by periodical modulation of the frequency of the isotropic harmonic trapping potential. Period-doubled motion is shown to occur when the driving is strong and close to resonance with the monopole mode. A variational model predicts chaotic oscillations but is found to disagree with the full solutions to the Gross-Pitaevskii equation.
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.
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.