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arXiv:cond-mat/0306184

Intrinsic self-rotation of BEC Bloch wave packets

Roberto B. Diener, Artem M. Dudarev, Ganesh M. Sundaram, Niu, Qian

Published Jun 6, 2003• 2 citations
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Abstract

The semiclassical theory of Bloch wave packet dynamics predicts a self-rotation angular momentum in asymmetric periodic potentials, which has never been observed. We show how this is manifested in Bose-Einstein condensed atoms in optical lattices. Displacing the wave packet to a corner of the Brillouin zone we obtain a current distribution with a non-quantized angular momentum, independent of the size of the distribution. A weak interatomic interaction does not modify the results, affecting only the rate of spreading in the lattice. A strong repulsive interaction results in a collapse of the wavefunction into matter-wave lattice solitons.

DOI
10.48550/arxiv.cond-mat/0306184

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The semiclassical theory of Bloch wave packet dynamics predicts a self-rotation angular momentum in asymmetric periodic potentials, which has never been observed. We show how this is manifested in Bose-Einstein condensed atoms in optical lattices. Displacing the wave packet to a corner of the Brillouin zone we obtain a current distribution with a non-quantized angular momentum, independent of the size of the distribution. A weak interatomic interaction does not modify the results, affecting only the rate of spreading in the lattice. A strong repulsive interaction results in a collapse of the wavefunction into matter-wave lattice solitons.
We study systematically the period-doubled Bloch states for a weakly interacting Bose–Einstein condensate in a one-dimensional optical lattice. This kind of state is of form ψ k = e ikx ϕ k ( x ) , where ϕ k ( x ) is of a period twice the optical lattice constant. Our numerical results show how these nonlinear period-doubled states grow out of linear period-doubled states at a quarter away from the Brillouin zone center as the repulsive interatomic interaction increases. This is corroborated by our analytical results. We find that all nonlinear period-doubled Bloch states have both Landau instability and dynamical instability .
We suggest a method to experimentally obtain two-dimensional matter-wave discrete solitons with a self-repulsive Bose–Einstein condensate in optical lattices. At the edge of the Brillouin zone, a wavepacket effective mass is negative, which could be treated as an inversion of the nonlinearity sign. Above critical nonlinearity this makes the wavepackets collapse partially into localized modes with a chemical potential located in the gap between the first and the second bands. This critical nonlinearity is also associated with the smallest nonlinearity for which the discrete solitons are possible in the gap. Extensive numerical simulations for square and asymmetric honeycomb lattices in the continuous model illustrate every stage of the process.
Superflow of a Bose–Einstein condensate in an optical lattice is represented by a Bloch wave, a plane wave with periodic modulation of the amplitude. We review the theoretical results of the interaction effects in the energy dispersion of the Bloch waves and in the linear stability of such waves. For sufficiently strong repulsion between the atoms, the lowest Bloch band develops a loop at the edge of the Brillouin zone, with the dramatic consequence of a finite probability of Landau–Zener tunnelling even in the limit of a vanishing external force. Superfluidity can exist in the central region of the Brillouin zone in the presence of a repulsive interaction, beyond which Landau instability takes place where the system can lower its energy by making a transition into states with smaller Bloch wavenumbers. In the outer part of the region of Landau instability, the Bloch waves are also dynamically unstable in the sense that a small initial deviation grows exponentially in time. In the inner region of Landau instability, a Bloch wave is dynamically stable in the absence of persistent external perturbations. Experimental implications of our findings will be discussed.
We discuss a method for creating bright matter solitons by loading a Bose-Einstein condensate of atoms in a driven tilted optical lattice. It is shown that one can realize the self-focusing regime for the wave-packet dynamics by properly adjusting the phase of the driving field with respect to the phase of Bloch oscillations. If atom-atom interactions are larger than some critical value gmin{g}_{\mathrm{min}}gmin​, this self-focusing regime is followed by the formation of bright solitons. Increasing the interactions above another critical value gmax{g}_{\mathrm{max}}gmax​ makes this process unstable. Instead of soliton formation one now meets the phenomenon of incoherent self-trapping. In this regime a fraction of atoms is trapped in incoherent localized wave packets, while the remaining atoms spread ballistically.
In this thesis I report on experiments on the quantum dynamics of matter waves in a onedimensional lattice potential. A 87Rb Bose-Einstein condensates is prepared in a one-dimensional waveguide in the lowest band of a superimposed optical lattice potential. The action of a weak lattice potential allows to modify the linear wave dispersion. We realized dispersion management by switching from normal to anomalous dispersion during the evolution. In this way the initial expansion of a wave packet is reversed to a compression and thus the effective spreading can be suppressed. By preparing a BEC at the Brillouin zone edge, we observed bright atomic gap solitons – non-spreading wave packets. They form, if the atom number and the lattice potential depth is tuned such that the effect of the repulsive atomic interaction and the anomalous dispersion cancel. For deep lattice potentials our system is described by a discrete nonlinear Schrödinger equation, whose dynamics is determined by the tunneling between adjacent lattice sites and the nonlinear phase evolution. In the main part of this thesis I report on the first experimental observation of nonlinear self-trapping for matter waves. The transition from the diffusive regime, characterized by an continuous expansion of the condensate, to the self-trapping regime is accomplished by increasing the atomic density. Due to the corresponding increase of the repulsive atomic interaction the initial expansion stops and the width of the wave packet remains finite. The comparison with a numerical analysis reveals that the effect is due to an inhibition of the site-to-site tunneling induced by the nonlinear phase evolution.