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arXiv:cond-mat/0611227 · New Journal of Physics

Localization and anomalous transport in a 1D soft boson optical lattice

Ari K. Tuchman, W Li, H Chien, S Dettmer, Mark A. Kasevich

Published Dec 11, 2006• 14 citations
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Abstract

We study the dynamics of Bose–Einstein condensed atoms in a one-dimensional (1D) optical lattice potential in a regime where the collective (Josephson) tunnelling energy is comparable with the on-site interaction energy, and the number of particles per lattice site is mesoscopically large. By directly imaging the motion of atoms in the lattice, we observe an abrupt suppression of atom transport through the array for a critical ratio of these energies, consistent with quantum fluctuation induced localization. Directly below the onset of localization, the frequency of the observed superfluid transport can be explained by a phonon excitation but deviates substantially from that predicted by the hydrodynamic/Gross–Pitaevskii equations.

DOI
10.1088/1367-2630/8/12/311

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We study the dynamics of Bose–Einstein condensed atoms in a one-dimensional (1D) optical lattice potential in a regime where the collective (Josephson) tunnelling energy is comparable with the on-site interaction energy, and the number of particles per lattice site is mesoscopically large. By directly imaging the motion of atoms in the lattice, we observe an abrupt suppression of atom transport through the array for a critical ratio of these energies, consistent with quantum fluctuation induced localization. Directly below the onset of localization, the frequency of the observed superfluid transport can be explained by a phonon excitation but deviates substantially from that predicted by the hydrodynamic/Gross–Pitaevskii equations.
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We analyze the localization of a Bose-Einstein condensate in a one-dimensional bichromatic quasi-periodic optical-lattice potential by numerically solving the 1D Gross-Pitaevskii equation (1D GPE).We first derive the 1D Gross-Pitaevskii equation from the dimensional reduction of the 3D quantum field theory of interacting bosons obtaining two coupled differential equations (for axial wave fuction and space-time dependent transverse width) which reduce to the 1D Gross-Pitaevskii equation under strict conditions.Then, by using the 1D Gross-Pitaevskii equation we report the suppression of localization in the interacting Bose-Einstein condensate when the repulsive scattering length between bosonic atoms is sufficiently large.
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.