---
_id: '60298'
abstract:
- lang: eng
  text: In this work, we introduce PHOENIX, a highly optimized explicit open-source
    solver for two-dimensional nonlinear Schrödinger equations with extensions. The
    nonlinear Schrödinger equation and its extensions (Gross-Pitaevskii equation)
    are widely studied to model and analyze complex phenomena in fields such as optics,
    condensed matter physics, fluid dynamics, and plasma physics. It serves as a powerful
    tool for understanding nonlinear wave dynamics, soliton formation, and the interplay
    between nonlinearity, dispersion, and diffraction. By extending the nonlinear
    Schrödinger equation, various physical effects such as non-Hermiticity, spin-orbit
    interaction, and quantum optical aspects can be incorporated. PHOENIX is designed
    to accommodate a wide range of applications by a straightforward extendability
    without the need for user knowledge of computing architectures or performance
    optimization. The high performance and power efficiency of PHOENIX are demonstrated
    on a wide range of entry-class to high-end consumer and high-performance computing
    GPUs and CPUs. Compared to a more conventional MATLAB implementation, a speedup
    of up to three orders of magnitude and energy savings of up to 99.8% are achieved.
    The performance is compared to a performance model showing that PHOENIX performs
    close to the relevant performance bounds in many situations. The possibilities
    of PHOENIX are demonstrated with a range of practical examples from the realm
    of nonlinear (quantum) photonics in planar microresonators with active media including
    exciton-polariton condensates. Examples range from solutions on very large grids,
    the use of local optimization algorithms, to Monte Carlo ensemble evolutions with
    quantum noise enabling the tomography of the system's quantum state.
article_number: '109689'
article_type: original
author:
- first_name: Jan
  full_name: Wingenbach, Jan
  id: '69187'
  last_name: Wingenbach
- first_name: David
  full_name: Bauch, David
  id: '44172'
  last_name: Bauch
- first_name: Xuekai
  full_name: Ma, Xuekai
  id: '59416'
  last_name: Ma
- first_name: Robert
  full_name: Schade, Robert
  id: '75963'
  last_name: Schade
  orcid: 0000-0002-6268-5397
- first_name: Christian
  full_name: Plessl, Christian
  id: '16153'
  last_name: Plessl
  orcid: 0000-0001-5728-9982
- first_name: Stefan
  full_name: Schumacher, Stefan
  id: '27271'
  last_name: Schumacher
  orcid: 0000-0003-4042-4951
citation:
  ama: Wingenbach J, Bauch D, Ma X, Schade R, Plessl C, Schumacher S. PHOENIX – Paderborn
    highly optimized and energy efficient solver for two-dimensional nonlinear Schrödinger
    equations with integrated extensions. <i>Computer Physics Communications</i>.
    2025;315. doi:<a href="https://doi.org/10.1016/j.cpc.2025.109689">10.1016/j.cpc.2025.109689</a>
  apa: Wingenbach, J., Bauch, D., Ma, X., Schade, R., Plessl, C., &#38; Schumacher,
    S. (2025). PHOENIX – Paderborn highly optimized and energy efficient solver for
    two-dimensional nonlinear Schrödinger equations with integrated extensions. <i>Computer
    Physics Communications</i>, <i>315</i>, Article 109689. <a href="https://doi.org/10.1016/j.cpc.2025.109689">https://doi.org/10.1016/j.cpc.2025.109689</a>
  bibtex: '@article{Wingenbach_Bauch_Ma_Schade_Plessl_Schumacher_2025, title={PHOENIX
    – Paderborn highly optimized and energy efficient solver for two-dimensional nonlinear
    Schrödinger equations with integrated extensions}, volume={315}, DOI={<a href="https://doi.org/10.1016/j.cpc.2025.109689">10.1016/j.cpc.2025.109689</a>},
    number={109689}, journal={Computer Physics Communications}, publisher={Elsevier
    BV}, author={Wingenbach, Jan and Bauch, David and Ma, Xuekai and Schade, Robert
    and Plessl, Christian and Schumacher, Stefan}, year={2025} }'
  chicago: Wingenbach, Jan, David Bauch, Xuekai Ma, Robert Schade, Christian Plessl,
    and Stefan Schumacher. “PHOENIX – Paderborn Highly Optimized and Energy Efficient
    Solver for Two-Dimensional Nonlinear Schrödinger Equations with Integrated Extensions.”
    <i>Computer Physics Communications</i> 315 (2025). <a href="https://doi.org/10.1016/j.cpc.2025.109689">https://doi.org/10.1016/j.cpc.2025.109689</a>.
  ieee: 'J. Wingenbach, D. Bauch, X. Ma, R. Schade, C. Plessl, and S. Schumacher,
    “PHOENIX – Paderborn highly optimized and energy efficient solver for two-dimensional
    nonlinear Schrödinger equations with integrated extensions,” <i>Computer Physics
    Communications</i>, vol. 315, Art. no. 109689, 2025, doi: <a href="https://doi.org/10.1016/j.cpc.2025.109689">10.1016/j.cpc.2025.109689</a>.'
  mla: Wingenbach, Jan, et al. “PHOENIX – Paderborn Highly Optimized and Energy Efficient
    Solver for Two-Dimensional Nonlinear Schrödinger Equations with Integrated Extensions.”
    <i>Computer Physics Communications</i>, vol. 315, 109689, Elsevier BV, 2025, doi:<a
    href="https://doi.org/10.1016/j.cpc.2025.109689">10.1016/j.cpc.2025.109689</a>.
  short: J. Wingenbach, D. Bauch, X. Ma, R. Schade, C. Plessl, S. Schumacher, Computer
    Physics Communications 315 (2025).
date_created: 2025-06-23T07:38:52Z
date_updated: 2025-06-29T12:00:36Z
department:
- _id: '27'
doi: 10.1016/j.cpc.2025.109689
intvolume: '       315'
language:
- iso: eng
project:
- _id: '52'
  name: 'PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing'
publication: Computer Physics Communications
publication_identifier:
  issn:
  - 0010-4655
publication_status: published
publisher: Elsevier BV
status: public
title: PHOENIX – Paderborn highly optimized and energy efficient solver for two-dimensional
  nonlinear Schrödinger equations with integrated extensions
type: journal_article
user_id: '75963'
volume: 315
year: '2025'
...
---
_id: '50829'
article_number: L012017
author:
- first_name: Nils
  full_name: Heinisch, Nils
  id: '90283'
  last_name: Heinisch
- first_name: Nikolas
  full_name: Köcher, Nikolas
  id: '79191'
  last_name: Köcher
- first_name: David
  full_name: Bauch, David
  id: '44172'
  last_name: Bauch
- first_name: Stefan
  full_name: Schumacher, Stefan
  id: '27271'
  last_name: Schumacher
  orcid: 0000-0003-4042-4951
citation:
  ama: 'Heinisch N, Köcher N, Bauch D, Schumacher S. Swing-up dynamics in quantum
    emitter cavity systems: Near ideal single photons and entangled photon pairs.
    <i>Physical Review Research</i>. 2024;6(1). doi:<a href="https://doi.org/10.1103/PhysRevResearch.6.L012017">10.1103/PhysRevResearch.6.L012017</a>'
  apa: 'Heinisch, N., Köcher, N., Bauch, D., &#38; Schumacher, S. (2024). Swing-up
    dynamics in quantum emitter cavity systems: Near ideal single photons and entangled
    photon pairs. <i>Physical Review Research</i>, <i>6</i>(1), Article L012017. <a
    href="https://doi.org/10.1103/PhysRevResearch.6.L012017">https://doi.org/10.1103/PhysRevResearch.6.L012017</a>'
  bibtex: '@article{Heinisch_Köcher_Bauch_Schumacher_2024, title={Swing-up dynamics
    in quantum emitter cavity systems: Near ideal single photons and entangled photon
    pairs}, volume={6}, DOI={<a href="https://doi.org/10.1103/PhysRevResearch.6.L012017">10.1103/PhysRevResearch.6.L012017</a>},
    number={1L012017}, journal={Physical Review Research}, publisher={American Physical
    Society (APS)}, author={Heinisch, Nils and Köcher, Nikolas and Bauch, David and
    Schumacher, Stefan}, year={2024} }'
  chicago: 'Heinisch, Nils, Nikolas Köcher, David Bauch, and Stefan Schumacher. “Swing-up
    Dynamics in Quantum Emitter Cavity Systems: Near Ideal Single Photons and Entangled
    Photon Pairs.” <i>Physical Review Research</i> 6, no. 1 (2024). <a href="https://doi.org/10.1103/PhysRevResearch.6.L012017">https://doi.org/10.1103/PhysRevResearch.6.L012017</a>.'
  ieee: 'N. Heinisch, N. Köcher, D. Bauch, and S. Schumacher, “Swing-up dynamics in
    quantum emitter cavity systems: Near ideal single photons and entangled photon
    pairs,” <i>Physical Review Research</i>, vol. 6, no. 1, Art. no. L012017, 2024,
    doi: <a href="https://doi.org/10.1103/PhysRevResearch.6.L012017">10.1103/PhysRevResearch.6.L012017</a>.'
  mla: 'Heinisch, Nils, et al. “Swing-up Dynamics in Quantum Emitter Cavity Systems:
    Near Ideal Single Photons and Entangled Photon Pairs.” <i>Physical Review Research</i>,
    vol. 6, no. 1, L012017, American Physical Society (APS), 2024, doi:<a href="https://doi.org/10.1103/PhysRevResearch.6.L012017">10.1103/PhysRevResearch.6.L012017</a>.'
  short: N. Heinisch, N. Köcher, D. Bauch, S. Schumacher, Physical Review Research
    6 (2024).
date_created: 2024-01-24T15:17:37Z
date_updated: 2024-01-24T16:07:57Z
department:
- _id: '230'
- _id: '623'
- _id: '15'
- _id: '170'
- _id: '297'
doi: 10.1103/PhysRevResearch.6.L012017
intvolume: '         6'
issue: '1'
language:
- iso: eng
project:
- _id: '173'
  grant_number: '231447078'
  name: 'TRR 142 - C09: TRR 142 - Ideale Erzeugung von Photonenpaaren für Verschränkungsaustausch
    bei Telekom Wellenlängen (C09*)'
- _id: '52'
  name: 'PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing'
publication: Physical Review Research
publication_identifier:
  issn:
  - 2643-1564
publication_status: published
publisher: American Physical Society (APS)
status: public
title: 'Swing-up dynamics in quantum emitter cavity systems: Near ideal single photons
  and entangled photon pairs'
type: journal_article
user_id: '90283'
volume: 6
year: '2024'
...
---
_id: '62858'
abstract:
- lang: eng
  text: Phonons in solid-state quantum emitters play a crucial role in their performance
    as photon sources in quantum technology. For resonant driving, phonons dampen
    the Rabi oscillations resulting in reduced preparation fidelities. The phonon
    spectral density, which quantifies the strength of the carrier-phonon interaction,
    is non-monotonous as a function of energy. As one of the most prominent consequences,
    this leads to the reappearance of Rabi rotations for increasing pulse power, which
    was theoretically predicted in Phys. Rev. Lett. 98, 227403 (2007). In this paper
    we present the experimental demonstration of the reappearance of Rabi rotations.
author:
- first_name: L.
  full_name: Hanschke, L.
  last_name: Hanschke
- first_name: T. K.
  full_name: Bracht, T. K.
  last_name: Bracht
- first_name: E.
  full_name: Schöll, E.
  last_name: Schöll
- first_name: David
  full_name: Bauch, David
  id: '44172'
  last_name: Bauch
- first_name: Eva
  full_name: Berger, Eva
  last_name: Berger
- first_name: Patricia
  full_name: Kallert, Patricia
  last_name: Kallert
- first_name: M.
  full_name: Peter, M.
  last_name: Peter
- first_name: A. J.
  full_name: Garcia, A. J.
  last_name: Garcia
- first_name: S. F. Covre da
  full_name: Silva, S. F. Covre da
  last_name: Silva
- first_name: S.
  full_name: Manna, S.
  last_name: Manna
- first_name: A.
  full_name: Rastelli, A.
  last_name: Rastelli
- first_name: Stefan
  full_name: Schumacher, Stefan
  id: '27271'
  last_name: Schumacher
  orcid: 0000-0003-4042-4951
- first_name: D. E.
  full_name: Reiter, D. E.
  last_name: Reiter
- first_name: Klaus
  full_name: Jöns, Klaus
  id: '85353'
  last_name: Jöns
citation:
  ama: Hanschke L, Bracht TK, Schöll E, et al. Experimental measurement of the reappearance
    of Rabi rotations in semiconductor quantum dots. <i>arXiv:240919167</i>. Published
    online 2024.
  apa: Hanschke, L., Bracht, T. K., Schöll, E., Bauch, D., Berger, E., Kallert, P.,
    Peter, M., Garcia, A. J., Silva, S. F. C. da, Manna, S., Rastelli, A., Schumacher,
    S., Reiter, D. E., &#38; Jöns, K. (2024). Experimental measurement of the reappearance
    of Rabi rotations in semiconductor quantum dots. In <i>arXiv:2409.19167</i>.
  bibtex: '@article{Hanschke_Bracht_Schöll_Bauch_Berger_Kallert_Peter_Garcia_Silva_Manna_et
    al._2024, title={Experimental measurement of the reappearance of Rabi rotations
    in semiconductor quantum dots}, journal={arXiv:2409.19167}, author={Hanschke,
    L. and Bracht, T. K. and Schöll, E. and Bauch, David and Berger, Eva and Kallert,
    Patricia and Peter, M. and Garcia, A. J. and Silva, S. F. Covre da and Manna,
    S. and et al.}, year={2024} }'
  chicago: Hanschke, L., T. K. Bracht, E. Schöll, David Bauch, Eva Berger, Patricia
    Kallert, M. Peter, et al. “Experimental Measurement of the Reappearance of Rabi
    Rotations in Semiconductor Quantum Dots.” <i>ArXiv:2409.19167</i>, 2024.
  ieee: L. Hanschke <i>et al.</i>, “Experimental measurement of the reappearance of
    Rabi rotations in semiconductor quantum dots,” <i>arXiv:2409.19167</i>. 2024.
  mla: Hanschke, L., et al. “Experimental Measurement of the Reappearance of Rabi
    Rotations in Semiconductor Quantum Dots.” <i>ArXiv:2409.19167</i>, 2024.
  short: L. Hanschke, T.K. Bracht, E. Schöll, D. Bauch, E. Berger, P. Kallert, M.
    Peter, A.J. Garcia, S.F.C. da Silva, S. Manna, A. Rastelli, S. Schumacher, D.E.
    Reiter, K. Jöns, ArXiv:2409.19167 (2024).
date_created: 2025-12-04T12:16:58Z
date_updated: 2025-12-11T12:54:41Z
department:
- _id: '623'
- _id: '15'
- _id: '429'
- _id: '642'
external_id:
  arxiv:
  - '2409.19167'
language:
- iso: eng
publication: arXiv:2409.19167
status: public
title: Experimental measurement of the reappearance of Rabi rotations in semiconductor
  quantum dots
type: preprint
user_id: '48188'
year: '2024'
...