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arXiv:0901.1386 · Physical Review A

Quantum and classical dynamics of a Bose-Einstein condensate in a large-period optical lattice

J. H. Huckans, Ian B. Spielman, B. Laburthe-Tolra, William D. Phillips, J. V. Porto

Published Oct 14, 2009• 40 citations
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Abstract

Rb Bose-Einstein condensate from a one-dimensional optical lattice. We use a range of lattice periods and timescales, including those beyond the Raman-Nath limit. We compare the results to numerical solutions of the Gross-Pitaevskii equation and classical calculations, with quantitative and qualitative agreement, respectively. The classical calculations predict that the envelope of the time-evolving diffraction pattern is shaped by caustics: singularities in the phase-space density of classical trajectories. This behavior becomes increasingly clear as the lattice period grows.

DOI
10.1103/physreva.80.043609

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Rb Bose-Einstein condensate from a one-dimensional optical lattice. We use a range of lattice periods and timescales, including those beyond the Raman-Nath limit. We compare the results to numerical solutions of the Gross-Pitaevskii equation and classical calculations, with quantitative and qualitative agreement, respectively. The classical calculations predict that the envelope of the time-evolving diffraction pattern is shaped by caustics: singularities in the phase-space density of classical trajectories. This behavior becomes increasingly clear as the lattice period grows.
[[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.
An investigation of Bose-Einstein condensate in two-dimensional optical lattice potentials, formed by laser beams, is carried out.We are interested in the dynamics of Bose-Einstein condensate in a square optical lattice, where the periodic potential can lead to the stabilization of an otherwise unstable Bose-Einstein condensate.The behavior of Bose-Einstein condensate in optical lattices is described by the nonlinear Gross-Pitaevskii equation, which we treat numerically.By applying the Petviashvili iteration method, we demonstrate the existence of solitonic solutions in the case of counterpropagating matter waves, and analyze their stability.
We investigate in detail the effects of nonlinearity on optical diffraction of Bose-Einstein condensates (BECs). By directly integrating the optically coupled two-component Gross-Pitaevskii equation in real space-time, comprehensive analyses of BEC optical diffraction phenomena are done under various conditions of light-pulse irradiation, total number of BEC atoms, etc., without using the adiabatic elimination approximation for an atomic excited state. Calculation results for the optical diffraction of 87Rb{}^{87}\text{Rb}87Rb BECs revealed that (1) the effect of nonlinearity on the atomic states causes the ``nonkinetic'' nonlinear effect in the Raman-Nath regime of diffraction, while the dynamics of BEC atoms due to the nonlinearity-induced repulsive forces works dominantly to produce the ``kinetic'' nonlinear effect in the Bragg regime of diffraction; (2) nonlinearity reduces the amplitude and frequency of the two-photon Rabi oscillation between BEC stationary and moving states, suggesting limitations in implementing the BEC Mach-Zehnder interferometer; and (3) the observed nonlinear effects are free from kinetic effects of the atomic excited state and not responsible for the optical transition process.
We consider quantum droplets in dipolar Bose-Einstein condensates embedded in optical lattices within the framework of Gross-Pitaevskii equations. In dipolar BECs, the long-range and isotropic dipole-dipole interaction provides an additional mechanism for self-binding. We analyze the linear stability as well dynamics of quantum droplets. We find an effective potential for the width and show that the optimum width for formation of quantum droplet increases as the dipole-dipole interaction increases. We study dynamics of the stable droplets and see that its width oscillates with time, and the amplitude of oscillation increases with the increase of dipole-dipole interaction. In presence of optical lattices, width of a stable droplet changes quasi-periodically while the location of density profile changes periodically in space. The frequency of oscillation depends sensitively on the lattice parameters. We check dynamical stability of a quantum droplet through numerical simulation.
An atomic Bose-Einstein condensate (BEC) is often described as a macroscopic object which can be approximated by a coherent state. This, on the surface, would appear to indicate that its behavior should be close to being classical. In this paper, we clarify the extent of how "classical" a BEC is by exploring the semiclassical equations for BECs under the mean field Gaussian approximation. Such equations describe the dynamics of a condensate in the classical limit in terms of the variables < x > and < p > as well as their respective variances. We compare the semiclassical solution with the full quantum solution based on the Gross-Pitaevskii Equation (GPE) and find that the interatomic interactions which generate nonlinearity make the system less "classical." On the other hand, many qualitative features are captured by the semiclassical equations, and the equations to be solved are far less computationally intensive than solving the GPE which make them ideal for providing quick diagnostics, and for obtaining new intuitive insight.
We study dynamical behaviors of the weakly interacting Bose-Einstein condensate in the one-dimensional optical lattice with an overall double-well potential by solving the time-dependent Gross-Pitaevskii equation. It is observed that the double-well potential dominates the dynamics of such a system even if the lattice depth is several times larger than the height of the double-well potential. This result suggests that the condensate flows without resistance in the periodic lattice just like the case of a single particle moving in periodic potentials. Nevertheless, the effective mass of atoms is increased, which can be experimentally verified since it is connected to the Josephson oscillation frequency. Moreover, the periodic lattice enhances the nonlinearity of the double-well condensate, making the condensate more “self-trapped” in the π -mode self-trapping regime.