Localization of a Bose-Einstein condensate in a bichromatic optical lattice (0907.3498v1)

Abstract: By direct numerical simulation of the time-dependent Gross-Pitaevskii equation we study different aspects of the localization of a non-interacting ideal Bose-Einstein condensate (BEC) in a one-dimensional bichromatic quasi-periodic optical-lattice potential. Such a quasi-periodic potential, used in a recent experiment on the localization of a BEC [Roati et al., Nature 453, 895 (2008)], can be formed by the superposition of two standing-wave polarized laser beams with different wavelengths. We investigate the effect of the variation of optical amplitudes and wavelengths on the localization of a non-interacting BEC. We also simulate the non-linear dynamics when a harmonically trapped BEC is suddenly released into a quasi-periodic potential, {as done experimentally in a laser speckle potential [Billy et al., Nature 453, 891 (2008)]$ We finally study the destruction of the localization in an interacting BEC due to the repulsion generated by a positive scattering length between the bosonic atoms.

• The paper demonstrates that bichromatic optical lattices induce localization in non-interacting Bose-Einstein condensates by using numerical simulations of the time-dependent Gross-Pitaevskii equation.
• The paper finds that introducing repulsive interactions shifts the system from localized to delocalized states, highlighting the sensitivity of localization to non-linearity.
• The paper validates its simulation outcomes with experimental models, reinforcing the relevance of quasi-periodic potentials in studying quantum localization phenomena.

Localization of a Bose-Einstein Condensate in a Bichromatic Optical Lattice

The paper under discussion explores the intricate paper of the localization of a Bose-Einstein Condensate (BEC) within a one-dimensional bichromatic quasi-periodic optical-lattice potential. The research focuses on the behavior of a non-interacting ideal BEC as well as the effects of inter-atomic interactions, employing the time-dependent Gross-Pitaevskii (GP) equation to describe the system dynamics.

Key Findings and Methodology

1. Model and Simulation: The paper leverages direct numerical simulations of the linear and non-linear 1D GP equation. The linear equation pertains to the non-interacting scenario equivalent to the Schrödinger equation, while the non-linear GP equation models scenarios with atomic interactions. The simulations utilize a Crank-Nicholson discretization scheme for precise time propagation.
2. Optical Lattice and Localization: The paper investigates a bichromatic optical lattice formed by superposing two standing-wave polarized laser beams with different wavelengths. This setup mimics the conditions employed by Roati et al. in experimental observations of localization in non-interacting BECs. The potential's spatial arrangement is intermediate between periodic structures and disorder, akin to the Aubry-Andre model, which elucidates a transition from extended to localized states.
3. Non-Linearity and Destruction of Localization: The research underscores the sensitivity of the localization phenomenon to inter-atomic interactions. The inclusion of a repulsive non-linear term, corresponding to positive scattering lengths in the GP equation, induces a shift from localized to delocalized states. The findings align with outcomes derived from the paper of the discrete non-linear Schrödinger equation (DNLSE) with random potentials.
4. Numerical Results: Detailed accounts of localization patterns as functions of optical lattice parameters and non-linearity strength reveal that even minimal repulsive interactions can disrupt localization. Numerical results depicting density distributions and momentum profiles confirm theoretical predictions and past experimental results.
5. Dynamical Behavior: The paper further explores the dynamics when a harmonically trapped BEC is released into a quasi-periodic potential. This mirrors experimental setups where the transition from harmonic confinement to potential landscapes is probed, resulting in breathing modes and non-equilibrium dynamics.

Implications and Future Directions

The implications of this research are significant for understanding the underlying physics of disordered systems and quantum localization phenomena. The interplay between disorder and interactions provides crucial insights into phenomena such as Anderson localization and BEC dynamics in complex environments.

Future studies may focus on extending the dimensionality of the lattice, exploring higher-order interactions, or integrating additional controls such as time-dependent potentials to further explore localized states. Considering the results' qualitative agreement with previous theoretical models, continued experimental validations could refine our understanding and utilization of BECs in optical lattices for quantum simulations. The research serves as a foundational step towards more comprehensive studies on localization in complex quantum systems, paving the way for potential applications in quantum computing and information processing.