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arXiv:0706.2744 · Physical Review A

Dynamical instabilities of Bose-Einstein condensates at the band edge in one-dimensional optical lattices

Andrew J. Ferris, Matthew J. Davis, R. Geursen, P. B. Blakie, A. C. Wilson

Published Jan 18, 2008• 35 citations

Abstract

We present a joint theoretical and experimental study of the dynamical instability of a Bose---Einstein condensate at the band edge of a one-dimensional optical lattice. The instability manifests as rapid depletion of the condensate and conversion to a thermal cloud. We consider the collisional processes that can occur in such a system, and undertake a thorough theoretical study of the dynamical instability in systems of different dimensionality. We find spontaneous scattering is an important part of this process, and thus the Gross-Pitaevskii equation is unable to accurately predict the dynamics in this system. Our beyond mean-field approach, known as the truncated Wigner method, allows us to make quantitative predictions for the processes of parametric growth and heating that are observed in the laboratory, and we find good agreement with the experimental results.

DOI: 10.1103/physreva.77.012712

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We report on the experimental characterization of energetic and dynamical instability, two mechanisms responsible for the breakdown of Bloch waves in a Bose-Einstein condensate interacting with a one-dimensional (1D) optical lattice. A clear separation of these two regimes is obtained by performing measurements at different temperatures of the atomic sample. The time scales of the two processes have been determined by measuring the losses induced in the condensate. A simple phenomenological model is introduced for energetic instability while a full comparison is made between the experiment and the 3D Gross-Pitaevskii theory that accounts for dynamical instability.

We study quantum dynamics of a Bose-Einstein condensate in a one-dimensional optical lattice in the limit of weak atom-atom interactions within the truncated Wigner approximation for a system with one dynamically unstable mode. This extends previous classical studies of a pulsating dynamical instability in which atoms periodically collect together and subsequently disperse back into the initial homogeneous state. We observe that the quasiperiodic behavior still persists in the presence of quantum fluctuations for a single realization that represents a typical experimental outcome, but ensemble averages show various manifestations of quantum statistics. Quantum effects become more prominent when the effective interaction strength is increased.

The occurrence of energetic and dynamical instabilities in a Bose-Einstein condensate moving in a one-dimensional (1D) optical lattice is analyzed by means of the Gross-Pitaevskii theory. Results of full 3D calculations are compared with those of an effective 1D model, the nonpolynomial Schr\"odinger equation, pointing out the role played by transverse degrees of freedom. The instability thresholds are shown to be scarcely affected by transverse excitations, so that they can be accurately predicted by effective 1D models. Conversely, transverse excitations turn out to be important in characterizing the stability diagram and the occurrence of a complex radial dynamics above the threshold for dynamical instability. This analysis provides a realistic framework to discuss the dissipative dynamics observed in recent experiments.