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arXiv:cond-mat/0306656 · Journal of Physics B Atomic Molecular and Optical Physics

Regular spatial structures in arrays of Bose Einstein condensates induced by modulational instability

B B Baizakov, V V Konotop, M Salerno

Published Dec 4, 2002• 158 citations
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Abstract

We show that the phenomenon of modulational instability in arrays of Bose–Einstein condensates confined to optical lattices gives rise to coherent spatial structures of localized excitations. These excitations represent thin discs in 1D, narrow tubes in 2D, and small hollows in 3D arrays, filled in with condensed atoms of much greater density compared to surrounding array sites. Aspects of the developed pattern depend on the initial distribution function of the condensate over the optical lattice, corresponding to particular points of the Brillouin zone. The long-time behaviour of the spatial structures emerging due to modulational instability is characterized by the periodic recurrence to the initial low-density state in a finite optical lattice. We propose a simple way to retain the localized spatial structures with high atomic concentration, which may be of interest for applications. A theoretical model, based on the multiple-scale expansion, describes the basic features of the phenomenon. Results of numerical simulations confirm the analytical predictions.

DOI
10.1088/0953-4075/35/24/312

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We show that the phenomenon of modulational instability in arrays of Bose–Einstein condensates confined to optical lattices gives rise to coherent spatial structures of localized excitations. These excitations represent thin discs in 1D, narrow tubes in 2D, and small hollows in 3D arrays, filled in with condensed atoms of much greater density compared to surrounding array sites. Aspects of the developed pattern depend on the initial distribution function of the condensate over the optical lattice, corresponding to particular points of the Brillouin zone. The long-time behaviour of the spatial structures emerging due to modulational instability is characterized by the periodic recurrence to the initial low-density state in a finite optical lattice. We propose a simple way to retain the localized spatial structures with high atomic concentration, which may be of interest for applications. A theoretical model, based on the multiple-scale expansion, describes the basic features of the phenomenon. Results of numerical simulations confirm the analytical predictions.
Abstract. We show that the phenomenon of modulational instability in arrays of Bose-Einstein condensates confined to optical lattices gives rise to coherent spatial structures of localized excitations. These excitations represent thin disks in 1D, narrow tubes in 2D, and small hollows in 3D arrays, filled in with condensed atoms of much greater density compared to surrounding array sites. Aspects of the developed pattern depend on the initial distribution function of the condensate over the optical lattice, corresponding to particular points of the Brillouin zone. The long-time behavior of the spatial structures emerging due to modulational instability is characterized by the periodic recurrence to the initial low-density state in a finite optical lattice. We propose a simple way to retain the localized spatial structures with high atomic concentration, which may be of interest for applications. Theoretical model, based on the multiple scale expansion, describes the basic features of the phenomenon. Results of numerical simulations confirm the analytical predictions.
We propose to employ the phenomenon of modulational instability in order to create regularly arranged localized excitations in arrays of Bose‐Einstein condensates. These excitations are narrow tubes in 2D and small hollows in 3D arrays filled in with the condensed atoms of much greater density compared to surrounding array sites. As the regions with high atomic concentration develop due to the modulational instability, they can be preserved by increasing the strength of the optical lattice. Theoretical model, based on the multiple scale expansion, describes the main features of the phenomenon. Analytical predictions are confirmed by numerical simulations of the Gross‐Pitaevskii equation.
We consider the problem of formation of small-amplitude spatially localized oscillatory structures for atomic Bose-Einstein condensates confined in two- and three-dimensional optical lattices, respectively. Our approach is based on applying the regions with different signs of atomic effective masses where an atomic system exhibits effective hyperbolic dispersion within the first Brillouin zone. By using the kp\mathbf{kp}kp method we have demonstrated mapping of the initial Gross-Pitaevskii equation on nonlinear Klein-Gordon and/or Ginzburg-Landau-Higgs equations, which is inherent in matter fields within ${\ensuremath{\phi}}^{4}$-field theories. Formation of breatherlike oscillating localized states---atomic oscillons---as well as kink-shaped states have been predicted in this case. Apart from classical field theories atomic field oscillons occurring in finite lattice structures possess a critical number of particles for their formation. The obtained results pave the way to simulating some analogues of fundamental cosmological processes occurring during our Universe's evolution and to modeling nonlinear hyperbolic metamaterials with condensed matter (atomic) systems.
Abstract We investigate the chaotic and regular spatial structures of Bose–Einstein condensates (BECs) with a spatially modulated atom-atom interaction and without an external trapping potential. A BEC with a spatially modulated atom-atom interaction is equivalent to being constrained by a nonlinear optical lattice. Theoretical analyses show the existence of a steady atomic current in the BEC with a spatially varying phase. Under perturbative conditions, the Melnikov chaos criteria of BECs with a spatially varying phase and a constant one are theoretically obtained, respectively. When the perturbative conditions cannot be satisfied, for a repulsive BEC with a spatially varying phase, numerical simulations demonstrate that changing the initial condition can eliminate the chaotic spatial structure and then the system transitions into a biperiodic spatial structure. Increasing the chemical potential can result in a transition from the biperiodic spatial structure to a single-periodic spatial structure. For an attractive BEC with a spatially varying phase, numerical simulations show that decreasing the chemical potential can lead to a high atomic density, but when the wave number of the laser inducing the optical Feshbach resonance exceeds a critical value, the atomic density falls back to a finite range. Regardless of whether the BEC has a spatially varying phase or a constant one, modulating the laser wave number can effectively suppress the chaotic spatial structure in the BEC and then force it into a regular spatial structure.
We study quantum effects in the dynamics of a Bose-Einstein condensate loaded onto the edge of a Brillouin zone of a one-dimensional periodic potential created by an optical lattice. We show that quantum fluctuations trigger the dynamical instability of the Bloch states of the condensate and can lead to the generation of arrays of matter-wave gap solitons. Our approach also allows us to study the instability-induced anomalous heating of the condensate at the edge of the Brillouin zone and growth of the uncondensed atomic fraction. We demonstrate that there are regimes in which the heating effects do not suppress the formation of the localised states. We show that a phase imprinting technique can ensure the formation of gap soliton trains after short evolution times and at fixed positions.