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Europhysics Letters (EPL)

Josephson-type oscillations of a driven Bose-Einstein condensate in an optical lattice

Maria Luisa Chiofalo, M. P. Tosi

Published Nov 1, 2001• 15 citations
Publisher

Abstract

Coherent transport behaviour has been demonstrated in experiments on atomic Bose-Einstein condensates driven by an external force through a quasi-one-dimensional optical lattice. We exploit the Wannier-function representation of band states to elucidate the relationship of such coherent transport with the weak-link Josephson effect and test the observability of multimode behaviour in condensates by numerical solution of the Gross-Pitaevskii equation.

DOI
10.1209/epl/i2001-00523-2

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Coherent transport behaviour has been demonstrated in experiments on atomic Bose-Einstein condensates driven by an external force through a quasi-one-dimensional optical lattice. We exploit the Wannier-function representation of band states to elucidate the relationship of such coherent transport with the weak-link Josephson effect and test the observability of multimode behaviour in condensates by numerical solution of the Gross-Pitaevskii equation.
Experiments on atomic Bose-Einstein condensates inside quasi-one-dimensional optical lattices and related developments in the realization of atom lasers are currently at the frontiers in atomic physics. We give a short review of theoretical progress in evaluating the coherent transport of matter in such configurations, which has been based on an adaptation of the Wannier function representation of quasi-particle states in periodic potentials and on the use of advanced numerical methods for the solution of the time-dependent Gross-Pitaevskii equation. We present various methods by which the band structure of the elementary excitations of a periodic condensate may be probed and describe in terms of Bloch oscillations the coherent emission of matter pulses from a condensate inside an optical lattice under the force of gravity. A harmonic force can be applied to a condensate inside a magnetic trap by a rapid displacement of the center of the trap and a transition of the condensate from superfluid to dissipative behavior is driven by superposing an optical lattice. Finally, in the superfluid regime the combination of a constant force and a harmonic force in the presence of an optical lattice drives Josephson-type oscillations of the condensate, leading to observable resonances and multimode behavior.
Bose-Einstein condensates of alkali atoms inside an optical lattice provide a unique opportunity to investigate such issues as coherent transport of matter, Josephson-type phenomena, and dissipation of superfluidity under highly controllable experimental conditions. We give a short review of theoretical progress in evaluating the collective excitations of a periodic condensate and the coherent transport of matter in different configurations, which has been based on an adaptation of the Wannier function representation of quasi-particle states in periodic potentials and on the use of advanced numerical methods for the solution of the Gross-Pitaevskii equation. We present various methods by which the band structure of the elementary excitations may be probed and show that in the superfluid regime the combination of a constant force and a harmonic force in the presence of the optical lattice drives Josephson-type oscillations of the condensate, leading to observable resonances and multimode behaviour. Finally, we discuss decoherence of the condensate and dissipation via sound wave emission above a local velocity threshold.
A Bose-Einstein condensate loaded in a one-dimensional bichromatic optical lattice with constituent sublattices having incommensurate periods is considered. Using the rational approximations for the incommensurate periods, we show that below the mobility edge the localized states are distributed nearly homogeneously in the space and explore the versatility of such potentials. We show that superposition of symmetric and antisymmetric localized states can be used to simulate various physical dynamical regimes, known to occur in double-well and multiwell traps. As examples, we obtain an alternative realization of a bosonic Josephson junction, whose coherent oscillations display beatings or switching in the weakly nonlinear regime, and describe self-trapping and four-mode dynamics, mimicking coherent oscillations and self-trapping in four-well potentials. These phenomena can be observed for different pairs of modes, which are localized due to the interference rather than due to a confining trap. The results obtained using few-mode approximations are compared with the direct numerical simulations of the one-dimensional Gross-Pitaevskii equation. The localized states and the related dynamics are found to persist for long times even in the repulsive condensates. We also described bifurcations of the families of nonlinear modes, the symmetry breaking, and stable minigap solitons.
We study dynamical behaviors of the weakly interacting Bose-Einstein condensate in the one-dimensional optical lattice with an overall double-well potential by solving the time-dependent Gross-Pitaevskii equation. It is observed that the double-well potential dominates the dynamics of such a system even if the lattice depth is several times larger than the height of the double-well potential. This result suggests that the condensate flows without resistance in the periodic lattice just like the case of a single particle moving in periodic potentials. Nevertheless, the effective mass of atoms is increased, which can be experimentally verified since it is connected to the Josephson oscillation frequency. Moreover, the periodic lattice enhances the nonlinearity of the double-well condensate, making the condensate more “self-trapped” in the π -mode self-trapping regime.
We study defect modes of a Bose-Einstein condensate in an optical lattice with a localized defect within the framework of the one-dimensional Gross-Pitaevskii equation. It is shown that for a significant range of parameters the defect modes can be accurately described by an expansion over Wannier functions, whose envelope is governed by the coupled nonlinear Schr\"odinger equations with a $\ensuremath{\delta}$ impurity. The stability of the defect modes is verified by direct numerical simulations of the underlying Gross-Pitaevskii equation with a periodic and defect potentials. We also discuss possibilities of driving defect modes through the lattice and suggest ideas for their experimental generation.
We investigate a Bose-Einstein condensate (BEC) held in a quasi-one-dimensional Wannier-Stark lattice which is a combination of linear potential with an accelerating optical lattice. It is demonstrated that the system can be reduced to a periodically driven Gross-Pitaevskii one, in which we find the exact analytical solution and the regular and chaotic numerical solutions with accelerated atomic flow densities. The higher instabilities in the transport of BEC are predicted for the positive interatomic interaction. The results suggest an experimental scheme to generate and control the accelerated regular and chaotic matter waves.