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arXiv:cond-mat/0212376 · Physical Review A

Dynamics of a period-3 pattern-loaded Bose-Einstein condensate in an optical lattice

Ana María Rey, P. B. Blakie, Charles W. Clark

Published May 27, 2003• 11 citations
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Abstract

We discuss the dynamics of a Bose-Einstein condensate initially loaded into every third site of an optical lattice using a description based upon the discrete nonlinear Schr\"odinger equation. An analytic solution is developed for the case of a periodic initial condition and is compared with numerical simulations for more general initial configurations. We show that mean field effects in this system can cause macroscopic quantum self-trapping, a phenomenon already predicted for double-well systems. In the presence of a uniform external potential, the atoms exhibit generalized Bloch oscillations which can be interpreted in terms of the interference of three different Bloch states. We also discuss how the momentum distribution of the system can be used as an experimental signature of the macroscopic self-trapping effect.

DOI
10.1103/physreva.67.053610

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We discuss the dynamics of a Bose-Einstein condensate initially loaded into every third site of an optical lattice using a description based upon the discrete nonlinear Schr"odinger equation. An analytic solution is developed for the case of a periodic initial condition and is compared with numerical simulations for more general initial configurations. We show that mean field effects in this system can cause macroscopic quantum self-trapping, a phenomenon already predicted for double-well systems. In the presence of a uniform external potential, the atoms exhibit generalized Bloch oscillations which can be interpreted in terms of the interference of three different Bloch states. We also discuss how the momentum distribution of the system can be used as an experimental signature of the macroscopic self-trapping effect.
We study the dynamic behaviour of Bose–Einstein condensates with two- and three-atom interactions in optical lattices with analytical and numerical methods. It is found that the steady-state relative population displays tuning-fork bifurcation when the system parameters are changed to certain critical values. In particular, the existence of the three-body interaction not only transforms the bifurcation point of the system but also greatly affects the macroscopic quantum self-trapping behaviours associated with the critically stable steady-state solution. In addition, we investigated the influence of the initial conditions, three-body interaction, and the energy bias on the macroscopic quantum self-trapping. Finally, by applying the periodic modulation on the energy bias, we observed that the relative population oscillation exhibits a process from order to chaos, via a series of period-doubling bifurcations.
We study the dynamics of ultracold atoms in an optical lattice under constant bias. After recapitulating the ideas underlying Bloch oscillations and Zener's formula for interband transitions, the Bloch-Zener scenario is tested by means of accurate numerical solutions to the time-dependent Schrödinger equation. It is shown how two shortcomings of the traditional Zener formula can be removed: the common weak-binding approximation can be circumvented by combining Kohn's insight into the structure of complex energy bands with the Dykhne-Davis-Pechukas description of transitions in terms of adiabatic excursions on analytically continued eigenvalue surfaces, and a usually neglected Stokes phenomenon comes into play when accounting for the finite width of the Brillouin zone. Treating Bose-Einstein condensates in optical lattices within the standard mean-field approximation at zero temperature, the ideal Bloch-Zener scenario turns out to be remarkably stable against the condensate's nonlinear self-interaction. Yet, under appropriate conditions a Bloch-oscillating Gross-Pitaevskii wavepacket reveals characteristic signatures of that nonlinearity, such as sudden phase jumps, slight shifts of the oscillation frequency or non-classical breathing modes. It is suggested that such experimentally detectable signatures will play an important role in future high-precision experiments aiming at the exploration of many-body dynamics in periodic potentials with condensates in optical lattices.
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.
We present the results of experimental work on the dynamics of a Bose-Einstein condensate (BEC) loaded in a 1D moving optical lattice. The system is studied both in the regime of low atomic density (expanding BEC) and high atomic density (trapped BEC). In the low-density regime, the stable dynamics of the system is well-described in terms of Bloch waves. In the presence of nonlinearities, as in a high-density sample, the Bloch waves are not stable solutions of the Gross-Pitaevskii equation (GPE) and dynamical instability takes place.
We study the Bloch dynamics of a quasi-one-dimensional Bose-Einstein condensate of cold atoms in a tilted optical lattice modeled by a Hamiltonian of Bose-Hubbard type. The corresponding mean-field system described by a discrete nonlinear Schr\"odinger equation can exhibit dynamical (or modulation) instability due to chaotic dynamics and equipartition over the quasimomentum modes. It is shown that these phenomena are related to Bogoliubov's depletion of the Bose-Einstein condensate and a decoherence of the condensate in the many-particle description. Three types of dynamics are distinguished: (i) decaying oscillations in the region of dynamical instability and (ii) persisting Bloch oscillations or (iii) periodic decay and revivals in the region of stability.