Excitations of a Bose-Einstein condensate in a one-dimensional optical lattice (original) (raw)
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Parametric excitation of a Bose-Einstein condensate in a one-dimensional optical lattice
Physical Review A, 2005
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 Ω drives the parametric excitation of Bogoliubov modes with frequency Ω/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 Stöferle et al.,
Coherent Dynamics of Bose-Einstein Condensates in a 1d Optical Lattice
2002
We study the mutual interaction of a Bose-Einstein condensed gas with a single mode of a high-finesse optical cavity. We show how the cavity transmission reflects condensate properties and calculate the self-consistent intra-cavity light field and condensate evolution. Solving the coupled condensate-cavity equations we find that while falling through the cavity, the condensate is adiabatically transfered into the ground state of the periodic optical potential. This allows time dependent non-destructive measurements on Bose-Einstein condensates with intriguing prospects for subsequent controlled manipulation.
Bose-Einstein condensates in optical lattices
We show that the GPE with cubic nonlinearity, as a model to describe the one dimensional Bose-Einstein condensates loaded into a harmonically confined optical lattice, presents a set of ground states which is orbitally stable for any value of the self-interaction (attractive and repulsive) parameter and laser intensity. We also derive a new formalism which gives explicit expressions for the minimum energy E min and the associated chemical potential µ 0 . Based on these formulas, we generalize the variational method to obtain approximate solutions, at any order of approximation, for E min , µ 0 and the ground state.
Physical Review A, 2010
We investigate the combined effects of weak disorder and a two-dimensional (2D) optical lattice on the collective excitations of a harmonically trapped Bose-Einstein condensate (BEC) at zero temperature. Accordingly, we generalize the hydrodynamic equations of superfluid for a weakly interacting Bose gas in a 2D optical lattice to include the effects of weak disorder. Our analytical results for the collective frequencies beyond the mean-field approximation reveal the peculiar role of disorder, interplaying with the 2D optical lattice and interatomic interaction, on elementary excitations along the 3D to 1D dimensional crossover. In particular, consequences of disorder on the phonon propagation and surface modes are analyzed in detail. The experimental scenario is also proposed.
Vortices in a Bose–Einstein condensate confined by an optical lattice
Journal of Physics B: Atomic, Molecular and Optical Physics, 2003
We investigate the dynamics of vortices in repulsive Bose-Einstein condensates in the presence of an optical lattice (OL) and a parabolic magnetic trap. The dynamics is sensitive to the phase of the OL potential relative to the magnetic trap, and depends less on the OL strength. For the cosinusoidal OL potential, a local minimum is generated at the trap's centre, creating a stable equilibrium for the vortex, while in the case of the sinusoidal potential, the vortex is expelled from the centre, demonstrating spiral motion. Cases where the vortex is created far from the trap's centre are also studied, revealing slow outward-spiralling drift. Numerical results are explained in an analytical form by means of a variational approximation. Finally, motivated by a discrete model (which is tantamount to the case of the strong OL lattice), we present a novel type of vortex consisting of two pairs of antiphase solitons. (Some figures in this article are in colour only in the electronic version) The experimental realization and theoretical studies of Bose-Einstein condensates (BECs) [1] have led to an explosion of interest in the field of atomic matter waves and their nonlinear excitations, including dark [2] and bright [3] solitons. More recently, two-dimensional (2D) excitations, such as vortices [4] and vortex lattices [5], were considered and realized experimentally. Other nonlinear states, such as for example Faraday waves [6], ring dark solitons and vortex necklaces [7], stable solitons and localized vortices in attractive BECs
A Bose-Einstein condensate in an optical lattice
Journal of Physics B: Atomic, Molecular and Optical Physics, 2002
We have performed a number of experiments with a Bose-Einstein condensate (BEC) in a one dimensional optical lattice. Making use of the small momentum spread of a BEC and standard atom optics techniques a high level of coherent control over an artificial solid state system is demonstrated. We are able to load the BEC into the lattice ground state with a very high efficiency by adiabatically turning on the optical lattice. We coherently transfer population between lattice states and observe their evolution. Methods are developed and used to perform band spectroscopy. We use these techniques to build a BEC accelerator and a novel, coherent, large-momentum-transfer beamsplitter.
Excitations of Bose-Einstein condensates in a one-dimensional periodic potential
Physical Review A, 2009
We report on the experimental investigation of the response of a three-dimensional Bose-Einstein condensate (BEC) in the presence of a one-dimensional (1D) optical lattice. By means of Bragg spectroscopy we probe the band structure of the excitation spectrum in the presence of the periodic potential. We selectively induce elementary excitations of the BEC choosing the transferred momentum and we observe different resonances in the energy transfer, corresponding to the transitions to different bands. The frequency, the width and the strength of these resonances are investigated as a function of the amplitude of the 1D optical lattice.