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arXiv:0904.4549 · Physical Review A

Bose-Einstein condensates on tilted lattices: Coherent, chaotic, and subdiffusive dynamics

Andrey R. Kolovsky, Edgar A. Gómez, Hans Jürgen Korsch

Published Feb 18, 2010• 42 citations

Abstract

The dynamics of a (quasi-) one-dimensional interacting atomic Bose-Einstein condensate in a tilted optical lattice is studied in a discrete mean-field approximation, i.e., in terms of the discrete nonlinear Schr\"odinger equation. If the static field is varied, the system shows a plethora of dynamical phenomena. In the strong field limit, we demonstrate the existence of (almost) nonspreading states which remain localized on the lattice region populated initially and show coherent Bloch oscillations with fractional revivals in the momentum space (so-called quantum carpets). With decreasing field, the dynamics becomes irregular, however, still confined in configuration space. For even weaker fields, we find subdiffusive dynamics with a wave-packet width growing as ${t}^{1/4}$.

DOI: 10.1103/physreva.81.025603

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The dynamics of a (quasi-) one-dimensional interacting atomic Bose-Einstein condensate in a tilted optical lattice is studied in a discrete mean-field approximation, i.e., in terms of the discrete nonlinear Schr"odinger equation. If the static field is varied, the system shows a plethora of dynamical phenomena. In the strong field limit, we demonstrate the existence of (almost) nonspreading states which remain localized on the lattice region populated initially and show coherent Bloch oscillations with fractional revivals in the momentum space (so-called quantum carpets). With decreasing field, the dynamics becomes irregular, however, still confined in configuration space. For even weaker fields, we find subdiffusive dynamics with a wave-packet width growing as

{t}^{1/4}

.

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.

We investigate the dynamics of Bose-Einstein condensates in a tilted one-dimensional periodic lattice within the mean-field (Gross-Pitaevskii) description. Unlike in the linear case the Bloch oscillations decay because of nonlinear dephasing. Pronounced revival phenomena are observed. These are analyzed in detail in terms of a simple integrable model constructed by an expansion in Wannier-Stark resonance states. We also briefly discuss the pulsed output of such systems for stronger static fields.

Bloch oscillations of Bose-Einstein condensates realize sensitive matter-wave interferometers. We investigate the dynamics and stability of bright-soliton wave packets in one-dimensional tilted optical lattices with a modulated mean-field interaction

g(t)

. By means of a time-reversal argument, we prove the stability of Bloch oscillations of breathing solitons that would be quasistatically unstable. Floquet theory shows that these breathing solitons can be more stable against certain experimental perturbations than rigid solitons or even noninteracting wave packets.

We study the Bloch dynamics of a Bose-Einstein condensate of cold atoms by using the formalism of the discrete nonlinear Schroedinger equation. Depending on the static force magnitudes the system is shown to exhibit two qualitatively different regimes of Bloch oscillations - exponential decay for the static force magnitude less than some critical value (defined by the condensate density) and quasiperiodic oscillations in the opposite case. The relation of these regimes to the onset of chaos in the system is discussed.

We study the dynamics of Bose-Einstein condensates in tilted and driven optical superlattices. For a bichromatic lattice, each Bloch band splits up into two minibands such that the dynamics is governed by the interplay of Bloch oscillations and transitions between the bands. Thus, bichromatic potentials provide an excellent model system for the study of nonlinear Landau-Zener tunneling, and they allow for a variety of applications in matter-wave interferometry and quantum metrology. In the present paper, we investigate the coherent dynamics of an interacting Bose-Einstein condensate as well as its stability. Different mechanisms of instability are discussed, which lead to a rapid depletion of the condensate.

The classical and quantum irregular spin dynamics of atomic spinor Bose-Einstein condensates in an optical lattice, where light-induced and static magnetic dipole-dipole interactions originate the interplay of the condensate at each site, are investigated. Classical-quantum correspondence in the large-spin limit is studied. Quantum chaotic features are studied through analysis of the irregular spectrum and time evolution of the Shannon entropy of wave packets. We show how the optical lattice strength influences the system dynamics, and is responsible for a transition from regular to irregular bahavior.