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arXiv:cond-mat/0401165 · Optics Express

Linear and nonlinear dynamics of matter wave packets in periodic potentials

Th. Anker, M. Albiez, Bernd Eiermann, M. Taglieber, Markus K Oberthaler

Published Jan 1, 2004• 16 citations
arXivHTMLPDF

Abstract

We investigate experimentally and theoretically the nonlinear propagation of 87Rb Bose Einstein condensates in a trap with cylindrical symmetry. An additional weak periodic potential which encloses an angle with the symmetry axis of the waveguide is applied. The observed complex wave packet dynamics results from the coupling of transverse and longitudinal motion. We show that the experimental observations can be understood applying the concept of effective mass, which also allows to model numerically the three dimensional problem with a one dimensional equation. Within this framework the observed slowly spreading wave packets are a consequence of the continuous change of dispersion. The observed splitting of wave packets is very well described by the developed model and results from the nonlinear effect of transient solitonic propagation.

DOI
10.1364/opex.12.000011

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We investigate experimentally and theoretically the nonlinear propagation of 87Rb Bose Einstein condensates in a trap with cylindrical symmetry. An additional weak periodic potential which encloses an angle with the symmetry axis of the waveguide is applied. The observed complex wave packet dynamics results from the coupling of transverse and longitudinal motion. We show that the experimental observations can be understood applying the concept of effective mass, which also allows to model numerically the three dimensional problem with a one dimensional equation. Within this framework the observed slowly spreading wave packets are a consequence of the continuous change of dispersion. The observed splitting of wave packets is very well described by the developed model and results from the nonlinear effect of transient solitonic propagation.
We demonstrate the control of the dispersion of matter wave packets utilizing periodic potentials. This is analogous to the technique of dispersion management known in photon optics. Matter wave packets are realized by Bose-Einstein condensates of 87Rb in an optical dipole potential acting as a one-dimensional waveguide. A weak optical lattice is used to control the dispersion relation of the matter waves during the propagation of the wave packets. The dynamics are observed in position space and interpreted using the concept of effective mass. By switching from positive to negative effective mass, the dynamics can be reversed. The breakdown of the approximation of constant, as well as experimental signatures of an infinite effective mass are studied.
The objective of this PhD thesis was the examination of the dynamical behaviour of coherent wave packets realised by Bose-Einstein condensates (BEC) out of 87Rubidium atoms. Their dynamics is mainly affected by linear dispersion due to momentum uncertainty and by nonlinear atomic interaction due to s-wave scattering. The primary objective was the realisation of bright atomic solitons, which represent density distributions with time-independent shape. They only exist if the effects of dispersion and nonlinearity cancel out each other. For 87Rb atoms with repulsive interaction this requires the dispersion of the ensemble to be anomalous. The dispersion of the wave packet can be influenced in sign and in magnitude by superimposing a periodic potential and by changing the quasi-momentum of the atoms. For that purpose an apparatus to produce Bose-Einstein condesates as source of coherent matter waves was build up and characterised. The phase transition was observed as well in magnetic as in optical dipole traps. Experiments related to the dynamic of wave packets were conducted in a twodimensional optical trap retaining the atoms against gravity and allowing them to propagate along the axis of the trap. The periodic potential to influence the dispersion results from two counterpropagating interfering laser beams superimposed to the dipole trap. A first set of experiments demonstrated the possibility to influence the linear dispersion of matter waves by changing the quasi-momentum of the atoms in a periodic potential. In particular wave packets with anomalous dispersion were prepared at the brillouin zone edge in quasi-momentum space. Their behaviour is equivalent to particles with a negative effective mass, which was be confirmed by reversing the time evolution of an expanding wave packet. This demonstration of a negative effective mass of wave packets was an essential prerequisite for the creation of atomic solitons. Their formation was observed having prepared Bose-Einstein condensates of only 1000 atoms. A further set of systematic experiments was performed confirming the solitonic behaviour of the wave packets. This was the first realisation of atomic solitons with repulsive interaction also called Gap-Solitons.
We experimentally study the dynamics of a weakly interacting Bose-Einstein condensate of cesium atoms in a 1D optical lattice with a periodic driving force. The time evolution is analysed after a quench of the driving strength which leads to an inversion of the dispersion relation in the lattice band and to a redistribution of atoms in the 1st Brillouin zone (BZ). We use the concept of a negative effective mass and the resulting changes to the effective trapping potential and interaction strength to explain the time evolution of wave packets with weak repulsive interaction. In addition, the formation of stable wave packets with a negative effective mass is observed at the center of the BZ, and we interpret these as gap solitons in a periodically driven system.
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.
We experimentally study the dynamics of weakly interacting Bose-Einstein condensates of cesium atoms in a 1D optical lattice with a periodic driving force. After a sudden start of the driving, we observe the formation of stable wave packets at the center of the first Brillouin zone (BZ) in momentum space, and we interpret these as Floquet solitons in periodically driven systems. The wave packets become unstable when we add a trapping potential along the lattice direction, leading to a redistribution of atoms within the BZ. The concept of a negative effective mass and the resulting changes to the interaction strength and effective trapping potential are used to explain the stability and the time evolution of the wave packets. We expect that similar states of matter waves exist for discrete breathers and other types of lattice solitons in periodically driven systems.
We experimentally study the dynamics of weakly interacting Bose-Einstein condensates of cesium atoms in a 1D optical lattice with a periodic driving force. After a sudden start of the driving we observe the formation of stable wave packets at the center of the first Brillouin zone (BZ) in momentum space, and we interpret these as Floquet solitons in periodically driven systems. The wave packets become unstable when we add a trapping potential along the lattice direction leading to a redistribution of atoms within the BZ. The concept of a negative effective mass and the resulting changes to the interaction strength and effective trapping potential are used to explain the stability and the time evolution of the wave packets. We expect that similar states of matter waves exist for discrete breathers and other types of lattice solitons in periodically driven systems.