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Journal of the Physical Society of Japan

Excitation Spectra of Bose–Einstein Condensates in Optical Lattice

Masanori Ichioka, Kazushige Machida

Published Sep 15, 2003• 4 citations
Publisher

Abstract

The excitation spectra of Bose–Einstein condensates are investigated in a three-dimensional optical lattice by the Bogoliubov theory considering the original sinusoidal potential for the optical lattice. When the lattice potential becomes high, the excitations show softening at large wavelengths, suggesting the breakdown of superfluidity. We also study the filling and interaction dependences of the properties of the excitation spectra and one-dimensional lattice case.

DOI
10.1143/jpsj.72.2137

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The excitation spectra of Bose–Einstein condensates are investigated in a three-dimensional optical lattice by the Bogoliubov theory considering the original sinusoidal potential for the optical lattice. When the lattice potential becomes high, the excitations show softening at large wavelengths, suggesting the breakdown of superfluidity. We also study the filling and interaction dependences of the properties of the excitation spectra and one-dimensional lattice case.
[[abstract]]We study the instabilities, Landau and dynamical instabilities, that are two mechanisms responsible for the breakdown of superfluidity in Bose-Einstein condensates interacting with a one-dimensional optical lattice. An effective-mass Gross-Pitaevskii equation was used to calculate the excitation spectrum and the condensate density of Bose-Einstein condensates in a weak periodic potential. After the condensate velocities greater than the speed of sound, we observe a decreasing of the condensate density, which is the onset of Landau instability. The condensate is dissipated, but not completely, from colliding with the thermal atom cloud. For even higher velocities of the condensate, we find a fast decreasing of the condensate density until full removal of the condensate. The regime of totally removing of the condensate is happened at the inverse effective mass of the condensate becoming zero or negative, where the condensate is on the dynamical instability.
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.
Bose–Einstein condensation in a finite one-dimensional atomic Bose gas trapped in an optical lattice is studied within Bogoliubov’s approximation and then beyond this approximation, within the static fluctuation approximation. A Bose–Hubbard model is used to construct the Hamiltonian of the system. The effect of the potential strength on the condensate fraction is explored at different temperatures; so is the effect of temperature on this fraction at different potential strengths. The role of the number of lattice points (the size effect) at constant number density (the filling factor) is examined; so is the effect of the number density on the condensate fraction. The results obtained are compared to other published results wherever possible.
We study the response of a Bose-Einstein condensate to a periodic modulation of the depth of an optical lattice. Using Gross-Pitaevskii theory, we show that a modulation at frequency $\ensuremath{\Omega}$ drives the parametric excitation of Bogoliubov modes with frequency $\ensuremath{\Omega}∕2$. The ensuing nonlinear dynamics leads to a rapid broadening of the momentum distribution and a consequent large increase of the condensate size after free expansion. We show that this process does not require the presence of a large condensate depletion. Our results reproduce the main features of the spectrum measured in the superfluid phase by St\"oferle et al. [Phys. Rev. Lett. 92, 130403 (2004)].
We prepare a Bose-Einstein condensed gas in a three-dimensional optical lattice and study the excitation spectrum of the superfluid phase for different interaction strengths. We probe the response of the system by modulating the depth of the optical lattice along one axis. The interactions can be controlled independently by varying the tunnel coupling along the other two lattice axes. In the weakly interacting regime we observe a small susceptibility of the superfluid to excitations, while for stronger interactions an unexpected resonance appears in the excitation spectrum. In addition we measure the coherent fraction of the atomic gas, which determines the depletion of the condensate.