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arXiv:0904.4810 · Physical Review A

Instabilities of a matter wave in a matter grating

Giovanni Barontini, Michele Modugno

Published Dec 7, 2009• 7 citations
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Abstract

We investigate the stability of Bloch waves for a Bose-Einstein condensate moving through a periodic lattice which is created by another condensate modulated by an optical lattice. We show that the coupling of phonon-antiphonon modes of the two species gives rise to a very rich structure of the regimes for dynamical instability, with significant differences with respect to the case of a single condensate in an optical lattice. We characterize the relative weight of each condensate in the mixing and discuss an analytic limit that accounts for the bare structure of the instability diagrams.

DOI
10.1103/physreva.80.063613

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We study dynamical and energetic instabilities in the transport properties of Bloch waves for atomic multicomponent Bose-Einstein condensates in optical lattices in the tight-binding limit. We obtain stability criteria analytically, as a function of superfluid velocities and interaction parameters, in several cases, for two-component and spinor condensates. In the two-species case we find that the presence of the other condensate component can stabilize the superfluid flow of an otherwise unstable condensate and that the free space dynamical miscibility condition of the two species can be reversed by tuning the superfluid flow velocities. In spin-1 condensates, we find the steady-state Bloch wave solutions and characterize their stability criteria. We find that generally more regions of dynamical instability arise for the polar than for the ferromagnetic solutions. In the presence of magnetic Zeeman shifts, we find a richer variety of condensate solutions and find that the linear Zeeman shift can stabilize the superfluid flow in several cases of interest.
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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 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.