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arXiv:cond-mat/0111308 · Physical Review A

Nonlinear atom optics and bright-gap-soliton generation in finite optical lattices

Iacopo Carusotto, Davide Embriaco, Giuseppe Carlo La Rocca

Published May 7, 2002• 82 citations
arXivHTMLPDF

Abstract

We theoretically investigate the transmission dynamics of coherent matter wave pulses across finite optical lattices in both the linear and the nonlinear regimes. The shape and the intensity of the transmitted pulse are found to strongly depend on the parameters of the incident pulse, in particular its velocity and density: a clear physical picture of the main features observed in the numerical simulations is given in terms of the atomic band dispersion in the periodic potential of the optical lattice. Signatures of nonlinear effects due to the atom-atom interaction are discussed in detail, such as atom-optical limiting and atom-optical bistability. For positive scattering lengths, matter waves propagating close to the top of the valence band are shown to be subject to modulational instability. A scheme for the experimental generation of narrow bright gap solitons from a wide Bose-Einstein condensate is proposed: the modulational instability is seeded starting from the strongly modulated density profile of a standing matter wave and the solitonic nature of the generated pulses is checked from their shape and their collisional properties.

DOI
10.1103/physreva.65.053611

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We theoretically investigate the transmission dynamics of coherent matter wave pulses across finite optical lattices in both the linear and the nonlinear regimes. The shape and the intensity of the transmitted pulse are found to strongly depend on the parameters of the incident pulse, in particular its velocity and density: a clear physical picture of the main features observed in the numerical simulations is given in terms of the atomic band dispersion in the periodic potential of the optical lattice. Signatures of nonlinear effects due to the atom-atom interaction are discussed in detail, such as atom-optical limiting and atom-optical bistability. For positive scattering lengths, matter waves propagating close to the top of the valence band are shown to be subject to modulational instability. A scheme for the experimental generation of narrow bright gap solitons from a wide Bose-Einstein condensate is proposed: the modulational instability is seeded starting from the strongly modulated density profile of a standing matter wave and the solitonic nature of the generated pulses is checked from their shape and their collisional properties.
Optical lattices have been used as a versatile toolbox to control Bose-Einstein condensates (BECs) in recent years, and a wealth of emergent nonlinear phenomena have been found, including bright gap solitons and dark ones, among which the former has been realized in experiments. The latter, however, has only theoretical results and its fundamental properties are still not well understood. Here we theoretically and numerically explore an open issue of creating stable matter-wave dark gap solitons in a one-dimensional optical lattice, onto which the BECs with self-defocusing quintic nonlinearity are loaded. Using linear-stability analysis and direct simulations, the formation, structures, and properties of dark gap solitons in quintic nonlinearity have been compared to those upheld by cubic Kerr nonlinearity. In particular, we uncover that the dark gap solitons and soliton clusters are robustly stable in the first finite band gap of the underlying linear spectrum, and are hard to be stabilized in the second gap. The predicted dark gap solitons are observable in current experiments on dense ultracold atoms, using an optical lattice technique, and in the optics domain for nonlinear light propagation in periodic optical media with quintic nonlinearity.
We consider several effects of the matter wave dynamics which can be observed in Bose–Einstein condensates embedded into optical lattices. For low-density condensates, we derive approximate evolution equations, the form of which depends on relation among the main spatial scales of the system. Reduction of the Gross–Pitaevskii equation to a lattice model (the tight-binding approximation) is also presented. Within the framework of the obtained models, we consider modulational instability of the condensate, solitary and periodic matter waves, paying special attention to different limits of the solutions, i.e. to smooth movable gap solitons and to strongly localized discrete modes. We also discuss how the Feshbach resonance, a linear force and lattice defects affect the nonlinear matter waves.
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 overview our recent theoretical studies on nonlinear atom optics of the Bose-Einstein condensates (BECs) loaded into optical lattices. In particular, we describe the band-gap spectrum and nonlinear localization of BECs in one- and two-dimensional optical lattices. We discuss the structure and stability properties of spatially localized states (matter-wave solitons) in 1D lattices, as well as trivial and vortex-like bound states of 2D gap solitons. To highlight similarities between the behavior of coherent light and matter waves in periodic potentials, we draw useful parallels with the physics of coherent light waves in nonlinear photonic crystals and optically-induced photonic lattices.
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.
Solitons, nonlinear particle-like excitations with inalterable properties (amplitude, shape, and velocity) as they propagate, are omnipresent in many branches of science—and in physics in particular. Flat-top solitons are a novel type of bright solitons that have not been well explored in pure nonlinear media. Here, a model of nonlinear Kerr (cubic) media of ultracold atoms with spatially modulated repulsive interactions is proposed and shown to support a vast variety of stable flat-top matter-wave solitons, including one-dimensional flat-top fundamental and multipole solitons, and two-dimensional flat-top fundamental and vortex solitons. We demonstrate that by varying the relevant physical parameters (nonlinearity coefficient and chemical potential), the ordinary bright (Gaussian) solitons can transform into the novel flat-top solitons. The (in)stability domains of the flat-top soliton families are checked by means of linear stability analysis and reconfirmed by direct numerical simulations. This model is generic in the contexts of nonlinear optics and Bose–Einstein condensates, which provides direct experimental access to observe the predicted solutions.