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arXiv:cond-mat/0701364 · Open Physics

Transport behaviour of a Bose Einstein condensate in a bichromatic optical lattice

Aranya Bhattacherjee, Monika Pietrzyk

Published Mar 1, 2008• 3 citations
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Abstract

Abstract We investigate the Bloch and dipole oscillations of a Bose Einstein condensate (BEC) in an optical superlattice. We show that, as the effective mass increases in an optical superlattice, the BEC is localized in accordance with recent experimental observations [J.E. Lye et. al. Phys. Rev. A 75, 061603 (2007)]. In addition, we find that the secondary optical lattice is a useful additional tool to manipulate the dynamics of the atoms.

DOI
10.2478/s11534-008-0036-y

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Abstract We investigate the Bloch and dipole oscillations of a Bose Einstein condensate (BEC) in an optical superlattice. We show that, as the effective mass increases in an optical superlattice, the BEC is localized in accordance with recent experimental observations [J.E. Lye et. al. Phys. Rev. A 75, 061603 (2007)]. In addition, we find that the secondary optical lattice is a useful additional tool to manipulate the dynamics of the atoms.
We derive and study the Bloch and Bogoliubov spectrum of a Bose–Einstein condensate (BEC) confined in a one-dimensional optical superlattice (created by interference between a primary optical lattice and a secondary optical lattice of small strength), using the Bogoliubov approximation and the hydrodynamic theory with mode coupling. We show that a BEC in an optical superlattice experiences two different tunnelling parameters and hence behaves like a diatomic chain. We derive expressions for the tunnelling parameters as a function of the strength of the primary and secondary lattice. This gives rise to a gapped branch in addition to the gapless acoustical branch in the Bogoliubov spectrum. The spectrum strongly depends on the strength of the secondary lattice, the interaction parameter and the number density of atoms. The effective mass is found to increase as the depth of the secondary optical lattice increases, a property that was utilized in Paraedes et al (2004 Nature 429 277) to achieve the Tonks–Girardeau regime. The coupling between the inhomogeneous density in the radial plane and the density modulation along the optical lattice gives rise to a multibranch Bogoliubov spectrum.
We report on experiments studying the transport properties of an atomic Bose-Einstein condensate in an optical lattice of spatial period $\ensuremath{\lambda}∕2n$, where nnn is an integer, realized with the dispersion of multiphoton Raman transitions. We observe Bloch oscillations, as a clear effect of quantum transport, in a subwavelength-scale periodicity lattice. An unusually large tunneling coupling between lattice sites is evident from the measured effective mass. Future prospects of the different lattice structures are expected in the search for new quantum phases in tailored lattice structures up to quantum computing in optical nanopotentials.
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.
We present theoretical and experimental studies of the dynamics of Bose-Einstein condensates in a one-dimensional optical lattice and a three-dimensional harmonic trap. For low atom densities and inertial forces, the condensate performs regular Bloch oscillations, and its center-of-mass motion closely follows semiclassical single-particle trajectories, shaped by the lowest-energy band. But in other regimes, the center-of-mass motion disrupts the internal structure of the condensate by generating solitons and vortex rings, which can trigger explosive expansion of the atom cloud. We use images of the atom cloud to provide experimental evidence for this internal disruption, and find that the process occurs most readily in high-density condensates undergoing slow Bloch oscillations.
The physics of quantum particles in periodic potentials can be described in terms of Bloch waves and indeed many effects originally predicted for electrons moving in a lattice of ions have been observed for ultracold atoms in optical lattices. Interactions among the atoms forming the BEC are responsible for the nonlinear character of the Bloch waves, resulting in the onset of different kinds of instabilities, we have performed a detailed investigation of the stability regimes of a condensate in a moving optical lattice, separately addressing the effects and the timescales of energetic and dynamic instabilities. Spin-polarized Fermi gases are free from these effects and fundamental conduction phenomena, such as the crossover from a conducting to an insulating behaviour, the latter due to a localization of the particles in the lattice, can be observed