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arXiv:cond-mat/0510096 · Physical Review A

Multibranch Bogoliubov-Bloch spectrum of a cigar-shaped Bose condensate in an optical lattice

Tarun Kanti Ghosh, K. Machida

Published Nov 18, 2005• 6 citations
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Abstract

We study properties of excited states of an array of weakly coupled quasi-two-dimensional Bose condensates by using the hydrodynamic theory. The spectrum of the axial excited states strongly depends on the coupling among the various discrete radial modes in a given symmetry. By including mode coupling within a given symmetry, the complete excitation spectrum of axial quasiparticles with various discrete radial nodes are presented. A single parameter which determines the strength of the mode coupling is identified. The excitation spectrum in the zero angular momentum sector can be observed by using the Bragg scattering experiments.

DOI
10.1103/physreva.72.053623

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We study properties of excited states of an array of weakly coupled quasi-two-dimensional Bose condensates by using the hydrodynamic theory. The spectrum of the axial excited states strongly depends on the coupling among the various discrete radial modes in a given symmetry. By including mode coupling within a given symmetry, the complete excitation spectrum of axial quasiparticles with various discrete radial nodes are presented. A single parameter which determines the strength of the mode coupling is identified. The excitation spectrum in the zero angular momentum sector can be observed by using the Bragg scattering experiments.
We study properties of excited states of an array of weakly coupled quasi-two-dimensional Bose condensates by using the hydrodynamic theory. We calculate multibranch Bogoliubov-Bloch spectrums and its corresponding eigenfunctions. The spectrum of the axial excited states and its eigenfunctions strongly depends on the coupling among various discrete radial modes within a given symmetry. This mode coupling is due to the presence of radial trapping potential. The multibranch nature of the Bogoliubov-Bloch spectrum and its dependence on the mode-coupling can be realized by analyzing dynamic structure factor and momentum transferred to the system in Bragg spectroscopy experiments. We also study dynamic structure factor and momentum transferred to the condensate due to the Bragg spectroscopy experiment.
We measure the response of an elongated Bose-Einstein condensate to a two-photon Bragg pulse. If the duration of the pulse is long, the total momentum transferred to the condensate exhibits a nontrivial behavior which reflects the structure of the underlying Bogoliubov spectrum. It is thus possible to perform a spectroscopic analysis in which axial phonons with a different number of radial nodes are resolved. The local density approximation is shown to fail in this regime, while the observed data agree well with the results of simulations based on the numerical solution of the Gross-Pitaevskii equation.
The behaviour of the momentum transferred to a trapped Bose-Einstein condensate by a two-photon Bragg pulse reflects the structure of the underlying Bogoliubov spectrum. In elongated condensates, axial phonons with different numbers of radial nodes give rise to a multibranch spectrum which can be resolved in Bragg spectroscopy, as shown by Steinhauer et al (2003 Phys. Rev. Lett. 90 060404). Here we present a detailed theoretical analysis of this process. We calculate the momentum transferred by numerically solving the time-dependent Gross-Pitaevskii (GP) equation. In the case of a cylindrical condensate, we compare the results with those obtained by linearizing the GP equation and using a quasiparticle projection method. This analysis shows how the axial-phonon branches affect the momentum transfer, in agreement with our previous interpretation of the observed data. We also discuss the applicability of this type of spectroscopy to typical available condensates, as well as the role of nonlinear effects.
We study the Bogoliubov spectrum of an elongated Fermi superfluid confined in an one-dimensional superfluid along the Bose-Einstein-condensate (BEC)-Bardeen-Cooper-Schrieffer (BCS) crossover. We derive analytic expressions for the sound velocity, effective mass and the Bogoliubov excitation spectrum of the axial quasiparticles long the crossover based on the hydrodynamic theory. Our investigation reveal interesting signatures of BEC-BCS crossover in an optical lattice which deserve experimental investigation.
We study properties of excited states of an elongated Fermi superfluid along the Bose-Einstein-condensate--BCS crossover including the unitarity limit. Analytic expressions for the sound velocity in an inhomogeneous as well as homogeneous Fermi superfluid along the crossover are obtained on the basis of the hydrodynamic theory. The complete excitation spectrum of axial quasiparticles with various discrete radial nodes is presented. We discuss the feasibility of measuring the sound velocity and the multibranch Bogoliubov spectrum experimentally.
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.