IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v80y2009i4p732-740.html
   My bibliography  Save this article

Ultracold atoms in 1D optical lattices: mean field, quantum field, computation, and soliton formation

Author

Listed:
  • Mishmash, R.V.
  • Carr, L.D.

Abstract

In this work, we highlight the correspondence between two descriptions of a system of ultracold bosons in a one-dimensional optical lattice potential: (1) the discrete nonlinear Schrödinger equation, a discrete mean-field theory, and (2) the Bose–Hubbard Hamiltonian, a discrete quantum-field theory. The former is recovered from the latter in the limit of a product of local coherent states. Using a truncated form of these mean-field states as initial conditions, we build quantum analogs to the dark soliton solutions of the discrete nonlinear Schrödinger equation and investigate their dynamical properties in the Bose–Hubbard Hamiltonian. We also discuss specifics of the numerical methods employed for both our mean-field and quantum calculations, where in the latter case we use the time-evolving block decimation algorithm due to Vidal.

Suggested Citation

  • Mishmash, R.V. & Carr, L.D., 2009. "Ultracold atoms in 1D optical lattices: mean field, quantum field, computation, and soliton formation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(4), pages 732-740.
    • Handle: RePEc:eee:matcom:v:80:y:2009:i:4:p:732-740
    DOI: 10.1016/j.matcom.2009.08.025
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475409002754
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2009.08.025?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matcom:v:80:y:2009:i:4:p:732-740. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.