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solve the nonlinear +Schrödinger equation + + + + Tangui + Aladjidi + https://orcid.org/0000-0002-3109-9723 + + + Clara + Piekarski + https://orcid.org/0000-0001-6871-6003 + + + Quentin + Glorieux + https://orcid.org/0000-0003-0903-0233 + + + + 07 + 23 + 2024 + + + 6607 + + + 10.21105/joss.06607 + + + http://creativecommons.org/licenses/by/4.0/ + http://creativecommons.org/licenses/by/4.0/ + http://creativecommons.org/licenses/by/4.0/ + + + + Software archive + 10.5281/zenodo.12795395 + + + GitHub review issue + https://github.com/openjournals/joss-reviews/issues/6607 + + + + 10.21105/joss.06607 + https://joss.theoj.org/papers/10.21105/joss.06607 + + + https://joss.theoj.org/papers/10.21105/joss.06607.pdf + + + + + + Bose-Einstein condensation and +superfluidity + Pitaevskij + 10.1017/cbo9780511524240.005 + 978-0-19-875888-4 + 2016 + Pitaevskij, L. P., & Stringari, +S. (2016). Bose-Einstein condensation and superfluidity. Oxford +University Press. +https://doi.org/10.1017/cbo9780511524240.005 + + + GPUE: Graphics Processing Unit +Gross-Pitaevskii Equation solver + Schloss + Journal of Open Source +Software + 32 + 3 + 10.21105/joss.01037 + 2018 + Schloss, J. R., & O’Riordan, L. +J. (2018). GPUE: Graphics Processing Unit Gross-Pitaevskii Equation +solver. Journal of Open Source Software, 3(32), 1037. +https://doi.org/10.21105/joss.01037 + + + Superfluid motion and drag-force cancellation +in a fluid of light + Michel + Nat. Comm. + 1 + 9 + 10.1038/s41467-018-04534-9 + 2018 + Michel, C., Boughdad, O., Albert, M., +Larré, P.-É., & Bellec, M. (2018). Superfluid motion and drag-force +cancellation in a fluid of light. Nat. Comm., 9(1), 2108. +https://doi.org/10.1038/s41467-018-04534-9 + + + Quantum fluids of light + Carusotto + Rev. Mod. Phys. + 1 + 85 + 10.1103/RevModPhys.85.299 + 0034-6861 + 2013 + Carusotto, I., & Ciuti, C. +(2013). Quantum fluids of light. Rev. Mod. Phys., 85(1), 299–366. +https://doi.org/10.1103/RevModPhys.85.299 + + + Full optical control of quantum fluids of +light in hot atomic vapors + Aladjidi + 10.5281/zenodo.12698001 + 2023 + Aladjidi, T. (2023). Full optical +control of quantum fluids of light in hot atomic vapors (Theses No. +2023SORUS406, Sorbonne Université). +https://doi.org/10.5281/zenodo.12698001 + + + Hot atomic vapors for nonlinear and quantum +optics + Glorieux + New Journal of Physics + 5 + 25 + 10.1088/1367-2630/acce5a + 2023 + Glorieux, Q., Aladjidi, T., Lett, P. +D., & Kaiser, R. (2023). Hot atomic vapors for nonlinear and quantum +optics. New Journal of Physics, 25(5), 051201. +https://doi.org/10.1088/1367-2630/acce5a + + + Turbulent dynamics in a two-dimensional +paraxial fluid of light + Baker-Rasooli + Physical Review A + 6 + 108 + 10.1103/PhysRevA.108.063512 + 2023 + Baker-Rasooli, M., Liu, W., Aladjidi, +T., Bramati, A., & Glorieux, Q. (2023). Turbulent dynamics in a +two-dimensional paraxial fluid of light. Physical Review A, 108(6), +063512. +https://doi.org/10.1103/PhysRevA.108.063512 + + + Array programming with NumPy + Harris + Nature + 7825 + 585 + 10.1038/s41586-020-2649-2 + 2020 + Harris, C. R., Millman, K. J., Walt, +S. J. van der, Gommers, R., Virtanen, P., Cournapeau, D., Wieser, E., +Taylor, J., Berg, S., Smith, N. J., Kern, R., Picus, M., Hoyer, S., +Kerkwijk, M. H. van, Brett, M., Haldane, A., Río, J. F. del, Wiebe, M., +Peterson, P., … Oliphant, T. E. (2020). Array programming with NumPy. +Nature, 585(7825), 357–362. +https://doi.org/10.1038/s41586-020-2649-2 + + + CuPy: A NumPy-compatible library for NVIDIA +GPU calculations + Okuta + Proceedings of workshop on machine learning +systems (LearningSys) in the thirty-first annual conference on neural +information processing systems (NIPS) + 2017 + Okuta, R., Unno, Y., Nishino, D., +Hido, S., & Loomis, C. (2017). CuPy: A NumPy-compatible library for +NVIDIA GPU calculations. Proceedings of Workshop on Machine Learning +Systems (LearningSys) in the Thirty-First Annual Conference on Neural +Information Processing Systems (NIPS). +http://learningsys.org/nips17/assets/papers/paper_16.pdf + + + Numba: A LLVM-based python JIT +compiler + Lam + Proceedings of the second workshop on the +LLVM compiler infrastructure in HPC + 10.1145/2833157.2833162 + 2015 + Lam, S. K., Pitrou, A., & +Seibert, S. (2015). Numba: A LLVM-based python JIT compiler. 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    + + + + +Journal of Open Source Software +JOSS + +2475-9066 + +Open Journals + + + +6607 +10.21105/joss.06607 + +NLSE: A Python package to solve the nonlinear Schrödinger +equation + + + +https://orcid.org/0000-0002-3109-9723 + +Aladjidi +Tangui + + +* + + +https://orcid.org/0000-0001-6871-6003 + +Piekarski +Clara + + + + +https://orcid.org/0000-0003-0903-0233 + +Glorieux +Quentin + + + + + +Laboratoire Kastler Brossel, Sorbonne University, CNRS, +ENS-PSL University, Collège de France; 4 Place Jussieu, 75005 Paris, +France + + + + +* E-mail: + + +15 +3 +2024 + +9 +99 +6607 + +Authors of papers retain copyright and release the +work under a Creative Commons Attribution 4.0 International License (CC +BY 4.0) +2022 +The article authors + +Authors of papers retain copyright and release the work under +a Creative Commons Attribution 4.0 International License (CC BY +4.0) + + + +Python +NLSE +Evolution +Nonlinear optics +Quantum fluids + + + + + + Summary +

    The nonlinear Schrödinger equation (NLSE) is a general nonlinear + equation used to model the propagation of light in nonlinear media. + This equation is mathematically isomorphic to the Gross-Pitaevskii + equation (GPE) + (Pitaevskij + & Stringari, 2016) describing the evolution of cold atomic + ensembles. Recently, the growing field of quantum fluids of light + (Carusotto + & Ciuti, 2013) has proven a fruitful testbed for several + fundamental quantum and classical phenomena such as superfluidity + (Michel + et al., 2018) or turbulence + (Baker-Rasooli + et al., 2023). Providing a flexible, modern and performant + framework to solve these equations is crucial to model realistic + experimental scenarios.

    +
    + + Statement of need +

    NumPy + (Harris + et al., 2020) is the default package for array operations in + Python, which is the language of choice for most physicists. However, + the performance of NumPy for large arrays and + Fourier transforms quickly bottlenecks homemade implementations of + popular solvers like the split-step spectral scheme.

    +

    Over the years, there have been several packages striving to + provide performant split-step solvers for NLSE type equations. Here + are a few examples:

    + + +

    FourierGPE.jl + for 1D to 3D Gross-Pitavskii equations in the context of cold + atoms in Julia.

    +
    + +

    GPUE + (Schloss + & O’Riordan, 2018) for 1D to 3D Gross-Pitaevskii + equations accelerated on GPU, in C++ (currently unmaintained).

    +
    + +

    py-fmas + for 1D NLSE in optical fibers, with a split-step method (currently + unmaintained).

    +
    +
    +

    With our project, we bring similar performance to C++ and Julia + implementations, while striving for accessibility and maintainability + by using Python. Using easy to extend object-oriented classes, users + can readily input experimental parameters to quickly model real + setups.

    +
    + + Functionality +

    NLSE harnesses the power of pseudo-spectral + schemes to solve efficiently the following general type of + equation:

    +

    + + itψ=12m2ψ+Vψ+g|ψ|2ψ.

    +

    To take advantage of the computing power of modern Graphics + Processing Units (GPUs) for Fast Fourier Transforms (FFTs), the main + workhorse of this code is the + CuPy + (Okuta + et al., 2017) package that maps + NumPy + functionalities onto the GPU using NVIDIA’s + CUDA + API. It also heavily uses just-in-time compilation using + Numba + (Lam + et al., 2015) to optimize performance while having an easily + maintainable Python codebase. Compared to naive NumPy-based CPU + implementations, this package provides a 100 to 10000 times speedup + for typical sizes + [fig:bench]. While + optimized for the use with GPU, NLSE also provides a performant CPU + fallback layer.

    +

    The goal of this package is to provide a natural framework to model + the propagation of light in nonlinear media or the temporal evolution + of Bose gases. It can also be used to model the propagation of light + in general. It supports lossy, nonlinear and nonlocal media.

    +

    It provides several classes to model 1D, 2D or 3D propagation, and + leverages the array functionalities of NumPy + like broadcasting to allow scans of physical parameters to most + faithfully replicate experimental setups. The typical output of a + simulation run is presented in + [fig:output].

    +

    This code was initially developed in Aladjidi + (2023) + and used as the main simulation tool for several publications like + Glorieux et al. + (2023) + and Baker-Rasooli et al. + (2023).

    + +

    Left: CPU vs GPU vs NumPy benchmark for 1 cm of + propagation (200 evolution steps). Right: Comparison versus the + JuliaGPE.jl package on the study of vortex + precession. +

    + +
    + +

    Example of an output of the solver. A shearing layer is + observed nucleating vortices, that are attracted towards the center + due to an attractive potential. The density and phase of the field + are represented as well as the momentum distribution get a quick + overview of the state of the + field.

    + +
    +
    + + Reproducibility +

    The code used to generate the figures can be found in the + examples + folder of the repository with the + fig2_turbulence.py + and + fig1_benchmarks.py + scripts. Note that you will need Julia installed to run the + JuliaGPE.jl script.

    +
    + + Acknowledgements +

    We acknowledge contributions from Myrann Baker-Rasooli as our most + faithful beta tester.

    +
    + + Authors contribution +

    TA wrote the original code and is the main maintainer, CP extended + the functionalities to include coupled systems. QG supervised the + project.

    +
    + + + + + + + + PitaevskijLev P. + StringariSandro + + Bose-Einstein condensation and superfluidity + Oxford University Press + Oxford + 2016 + 978-0-19-875888-4 + 10.1017/cbo9780511524240.005 + + + + + + SchlossJames R. + O’RiordanLee J. + + GPUE: Graphics Processing Unit Gross-Pitaevskii Equation solver + Journal of Open Source Software + The Open Journal + 2018 + 3 + 32 + https://doi.org/10.21105/joss.01037 + 10.21105/joss.01037 + 1037 + + + + + + + MichelClaire + BoughdadOmar + AlbertMathias + LarréPierre-Élie + BellecMatthieu + + Superfluid motion and drag-force cancellation in a fluid of light + Nat. Comm. + 2018 + 9 + 1 + 10.1038/s41467-018-04534-9 + 2108 + + + + + + + CarusottoIacopo + CiutiCristiano + + Quantum fluids of light + Rev. Mod. Phys. + 2013 + 20200326 + 85 + 1 + 0034-6861 + http://arxiv.org/abs/1205.6500 + 10.1103/RevModPhys.85.299 + 299 + 366 + + + + + + AladjidiTangui + + Full optical control of quantum fluids of light in hot atomic vapors + Sorbonne Université + 202310 + https://theses.hal.science/tel-04391272 + 10.5281/zenodo.12698001 + + + + + + GlorieuxQuentin + AladjidiTangui + LettPaul D. + KaiserRobin + + Hot atomic vapors for nonlinear and quantum optics + New Journal of Physics + 2023 + 25 + 5 + https://dx.doi.org/10.1088/1367-2630/acce5a + 10.1088/1367-2630/acce5a + 051201 + + + + + + + Baker-RasooliMyrann + LiuWei + AladjidiTangui + BramatiAlberto + GlorieuxQuentin + + Turbulent dynamics in a two-dimensional paraxial fluid of light + Physical Review A + 2023 + 108 + 6 + 10.1103/PhysRevA.108.063512 + 063512 + + + + + + + HarrisCharles R. + MillmanK. Jarrod + WaltStéfan J. van der + GommersRalf + VirtanenPauli + CournapeauDavid + WieserEric + TaylorJulian + BergSebastian + SmithNathaniel J. + KernRobert + PicusMatti + HoyerStephan + KerkwijkMarten H. van + BrettMatthew + HaldaneAllan + RíoJaime Fernández del + WiebeMark + PetersonPearu + Gérard-MarchantPierre + SheppardKevin + ReddyTyler + WeckesserWarren + AbbasiHameer + GohlkeChristoph + OliphantTravis E. + + Array programming with NumPy + Nature + Springer Science; Business Media LLC + 202009 + 585 + 7825 + https://doi.org/10.1038/s41586-020-2649-2 + 10.1038/s41586-020-2649-2 + 357 + 362 + + + + + + OkutaRyosuke + UnnoYuya + NishinoDaisuke + HidoShohei + LoomisCrissman + + CuPy: A NumPy-compatible library for NVIDIA GPU calculations + Proceedings of workshop on machine learning systems (LearningSys) in the thirty-first annual conference on neural information processing systems (NIPS) + 2017 + http://learningsys.org/nips17/assets/papers/paper_16.pdf + + + + + + LamSiu Kwan + PitrouAntoine + SeibertStanley + + Numba: A LLVM-based python JIT compiler + Proceedings of the second workshop on the LLVM compiler infrastructure in HPC + 2015 + 10.1145/2833157.2833162 + 1 + 6 + + + + +

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