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Dynamical self-trapping of Bose-Einstein condensates in shallow optical lattices

Matthias Rosenkranz, Dieter Jaksch, Fong Yin Lim, Weizhu Bao

Published Apr 13, 2008• 1 citation
OpenAlex

Abstract

We observe a sudden breakdown of the transport of a strongly repulsive Bose-Einstein condensate through a shallow optical lattice of finite width. By using accurate numerical methods and an analytical description in terms of nonlinear Bloch waves, we attribute this behavior to the development of a self-trapped state. The dependence of this drop on the lattice depth and the interaction strength is investigated. We show that by applying a constant offset potential to the lattice region it is possible to prohibit this self-trapping. We also observe the disappearance of the self-trapped state after a finite time as a result of the finiteness of the lattice.

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We observe a sudden breakdown of the transport of a strongly repulsive Bose-Einstein condensate through a shallow optical lattice of finite width. By using accurate numerical methods and an analytical description in terms of nonlinear Bloch waves, we attribute this behavior to the development of a self-trapped state. The dependence of this drop on the lattice depth and the interaction strength is investigated. We show that by applying a constant offset potential to the lattice region it is possible to prohibit this self-trapping. We also observe the disappearance of the self-trapped state after a finite time as a result of the finiteness of the lattice.
We observe a sudden breakdown of the transport of a strongly repulsive Bose-Einstein condensate through a shallow optical lattice of finite width. We are able to attribute this behavior to the development of a self-trapped state by using accurate numerical methods and an analytical description in terms of nonlinear Bloch waves. The dependence of the breakdown on the lattice depth and the interaction strength is investigated. We show that it is possible to prohibit the self-trapping by applying a constant offset potential to the lattice region. Furthermore, we observe the disappearance of the self-trapped state after a finite time as a result of the revived expansion of the condensate through the lattice. This revived expansion is due to the finite width of the lattice.
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 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 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.
In the present paper, we analytically and numerically investigate the dynamics of Bose-Einstein condensates (BECs) loaded into deep optical lattices of one dimension (1D), 2D, and 3D. We focus on the self-trapped state and the effect of the lattice dimension. Under the tight-binding approximation, we obtain an analytical criterion for the self-trapped state of BEC using the time-dependent variational method. The phase diagram for self-trapping, soliton, breather, or diffusion of a BEC cloud is obtained accordingly and verified by directly solving a discrete Gross-Pitaevskii equation numerically. In particular, we find that the criterion and the phase diagrams are modified dramatically by the dimension of the optical lattices.