IDEAS home Printed from https://ideas.repec.org/a/nat/natcom/v14y2023i1d10.1038_s41467-023-35892-8.html
   My bibliography  Save this article

Experimental realisations of the fractional Schrödinger equation in the temporal domain

Author

Listed:
  • Shilong Liu

    (University of Ottawa
    Zhejiang University)

  • Yingwen Zhang

    (University of Ottawa
    National Research Council)

  • Boris A. Malomed

    (Tel Aviv University
    Universidad de Tarapacá)

  • Ebrahim Karimi

    (University of Ottawa
    National Research Council)

Abstract

The fractional Schrödinger equation (FSE)—a natural extension of the standard Schrödinger equation—is the basis of fractional quantum mechanics. It can be obtained by replacing the kinetic-energy operator with a fractional derivative. Here, we report the experimental realisation of an optical FSE for femtosecond laser pulses in the temporal domain. Programmable holograms and the single-shot measurement technique are respectively used to emulate a Lévy waveguide and to reconstruct the amplitude and phase of the pulses. Varying the Lévy index of the FSE and the initial pulse, the temporal dynamics is observed in diverse forms, including solitary, splitting and merging pulses, double Airy modes, and “rain-like” multi-pulse patterns. Furthermore, the transmission of input pulses carrying a fractional phase exhibits a “fractional-phase protection” effect through a regular (non-fractional) material. The experimentally generated fractional time-domain pulses offer the potential for designing optical signal-processing schemes.

Suggested Citation

  • Shilong Liu & Yingwen Zhang & Boris A. Malomed & Ebrahim Karimi, 2023. "Experimental realisations of the fractional Schrödinger equation in the temporal domain," Nature Communications, Nature, vol. 14(1), pages 1-9, December.
    • Handle: RePEc:nat:natcom:v:14:y:2023:i:1:d:10.1038_s41467-023-35892-8
    DOI: 10.1038/s41467-023-35892-8
    as

    Download full text from publisher

    File URL: https://www.nature.com/articles/s41467-023-35892-8
    File Function: Abstract
    Download Restriction: no
    File URL: https://libkey.io/10.1038/s41467-023-35892-8?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
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Raviola, Lisandro A. & De Leo, Mariano F., 2024. "Performance of affine-splitting pseudo-spectral methods for fractional complex Ginzburg-Landau equations," Applied Mathematics and Computation, Elsevier, vol. 466(C).
    2. dos Santos, Mateus C.P., 2024. "Orthogonal multi-peak solitons from the coupled fractional nonlinear Schrödinger equation," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    3. Chen, Zhiming & Liu, Xiuye & Xie, Hongqiang & Zeng, Jianhua, 2024. "Three-dimensional Bose–Einstein gap solitons in optical lattices with fractional diffraction," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).

    More about this item

    Statistics

    Access and download statistics

    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:nat:natcom:v:14:y:2023:i:1:d:10.1038_s41467-023-35892-8. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.nature.com .

    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.