@article{60298,
  abstract     = {{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.}},
  author       = {{Wingenbach, Jan and Bauch, David and Ma, Xuekai and Schade, Robert and Plessl, Christian and Schumacher, Stefan}},
  issn         = {{0010-4655}},
  journal      = {{Computer Physics Communications}},
  publisher    = {{Elsevier BV}},
  title        = {{{PHOENIX – Paderborn highly optimized and energy efficient solver for two-dimensional nonlinear Schrödinger equations with integrated extensions}}},
  doi          = {{10.1016/j.cpc.2025.109689}},
  volume       = {{315}},
  year         = {{2025}},
}

@article{61249,
  author       = {{Ai, Qiang and Wingenbach, Jan and Yang, Xinmiao and Wei, Jing and Hatzopoulos, Zaharias and Savvidis, Pavlos G. and Schumacher, Stefan and Ma, Xuekai and Gao, Tingge}},
  issn         = {{2331-7019}},
  journal      = {{Physical Review Applied}},
  number       = {{2}},
  publisher    = {{American Physical Society (APS)}},
  title        = {{{Optically and remotely controlling localization of exciton-polariton condensates in a potential lattice}}},
  doi          = {{10.1103/physrevapplied.23.024029}},
  volume       = {{23}},
  year         = {{2025}},
}

@article{62867,
  abstract     = {{<jats:title>ABSTRACT</jats:title>
                  <jats:p>Effective manipulation of photonic spin–orbit coupling (SOC) in microcavities is of fundamental importance within topological photonics and applications. Anisotropic organic single‐crystalline materials can induce abundant SOC phenomenon due to their flexible tunability of molecular geometries, however, the intrinsic relationship between molecular geometries/orientations in 3D space and photonic SOC is lacking. In this study, we design two kinds of 2D organic polymorphs for the construction of organic microcavities to investigate the structure‐performance relationships. In two polymorphic microcavities, two distinctive photonic SOC phenomena are observed regardless of the in‐plane anisotropy of organic polymorphs. Theoretical analysis indicates that the photonic SOC strength is strongly influenced by the synergies between the crystal anisotropy and the tilted collective molecular transition dipole moment. Our results uncover the correlation mechanism between the structure of molecules and photonic SOC and open an avenue to engineer complex photonic SOC by use of organic microstructures towards the development of diverse integrated photonic devices.</jats:p>}},
  author       = {{Ji, Ying and Ma, Xuekai and Huang, Han and Deng, Yibo and Wang, Pingyang and Long, Teng and Li, Yuan and Zhao, Ruiyang and Li, Yunfei and An, Cunbin and Schumacher, Stefan and Gu, Chunling and Liao, Bo and Fu, Hongbing and Liao, Qing}},
  issn         = {{1863-8880}},
  journal      = {{Laser &amp; Photonics Reviews}},
  publisher    = {{Wiley}},
  title        = {{{Molecular Orientation‐Dependent Photonic Spin–Orbit Coupling in Organic Microcavities Filled with 2D Polymorphic Crystals}}},
  doi          = {{10.1002/lpor.202501874}},
  year         = {{2025}},
}

@article{62862,
  abstract     = {{<jats:p>Exciton polariton condensates are macroscopic coherent states in which topological excitations can be observed. In this work, we observe the excitation of the vortices and realize tuning the topological charge by manipulating the pumping configurations. Using a digital micromirror device, we constructed an annular pumping pattern where the inner and outer rings can be easily tuned. Both the number and the topological charge of the vortices can be changed by slightly tuning the inner ring position against the outer ring. The experimental results can be reproduced in theory by the Gross–Pitaevskii equation. Our work offers to generate and manipulate vortices in exciton polariton condensates using a straightforward optical method.</jats:p>}},
  author       = {{Ai, Qiang and Ma, Xuekai and Barkhausen, Franziska and Zhai, Xiaokun and Xing, Chunzi and Yang, Xinmiao and Wang, Peilin and Liu, Tianyu and Zhang, Yong and Gu, Yazhou and Li, Peigang and Li, Zhitong and Hatzopoulos, Zacharias and Savvidis, Pavlos G. and Schumacher, Stefan and Gao, Tingge}},
  issn         = {{0003-6951}},
  journal      = {{Applied Physics Letters}},
  number       = {{12}},
  publisher    = {{AIP Publishing}},
  title        = {{{Tuning polariton vortices in an asymmetric ring potential}}},
  doi          = {{10.1063/5.0287076}},
  volume       = {{127}},
  year         = {{2025}},
}

@article{62865,
  author       = {{Sun, Jinming and Chen, Manna and Schumacher, Stefan and Hu, Wei and Ma, Xuekai}},
  issn         = {{2469-9950}},
  journal      = {{Physical Review B}},
  number       = {{11}},
  publisher    = {{American Physical Society (APS)}},
  title        = {{{Higher-order dark solitons and control dynamics in microcavity polariton condensates}}},
  doi          = {{10.1103/p357-vyq8}},
  volume       = {{112}},
  year         = {{2025}},
}

@article{60992,
  abstract     = {{Non-Hermitian systems hosting exceptional points (EPs) exhibit enhanced sensitivity and unconventional mode dynamics. Going beyond isolated EPs, here we report on the existence of exceptional rings (ERs) in planar optical resonators with specific form of circular dichroism and TE-TM splitting. Such exceptional rings possess intriguing topologies as discussed earlier for condensed matter systems, but they remain virtually unexplored in presence of nonlinearity, for which our photonic platform is ideal. We find that when Kerr-type nonlinearity (or saturable gain) is introduced, the linear ER splits into two concentric ERs, with the larger-radius ring being a ring of third-order EPs. Transitioning from linear to nonlinear regime, we present a rigorous analysis of spectral topology and report enhanced and adjustable perturbation response in the nonlinear regime. Whereas certain features are specific to our system, the results on non-Hermitian spectral topology and nonlinearity-enhanced perturbation response are generic and equally relevant to a broad class of other nonlinear non-Hermitian systems, providing a universal framework for engineering ERs and EPs in nonlinear non-Hermitian systems.}},
  author       = {{Wingenbach, Jan and Ares Santos, Laura  and Ma, Xuekai and Sperling, Jan and Schumacher, Stefan}},
  journal      = {{Arxiv}},
  publisher    = {{Arxiv}},
  title        = {{{Sensitivity and Topology of Exceptional Rings in Nonlinear Non-Hermitian Planar Optical Microcavities}}},
  doi          = {{10.48550/ARXIV.2507.07099}},
  year         = {{2025}},
}

@article{51105,
  author       = {{Wingenbach, Jan and Schumacher, Stefan and Ma, Xuekai}},
  journal      = {{Physical Review Research, in press}},
  title        = {{{Manipulating spectral topology and exceptional points by nonlinearity in non-Hermitian polariton systems}}},
  year         = {{2024}},
}

@article{51104,
  author       = {{Liang, Qian and Ma, Xuekai and Gu, Chunling and Ren, Jiahuan and An, Cunbin and Fu, Hongbing and Schumacher, Stefan and Liao, Qing}},
  journal      = {{Journal of the American Chemical Society (JACS)}},
  title        = {{{Photochemical Reaction Enabling the Engineering of Photonic Spin−Orbit Coupling in Organic-Crystal Optical Microcavities}}},
  doi          = {{10.1021/jacs.3c11373}},
  year         = {{2024}},
}

@article{61250,
  author       = {{Bennenhei, Christoph and Shan, Hangyong and Struve, Marti and Kunte, Nils and Eilenberger, Falk and Ohmer, Jürgen and Fischer, Utz and Schumacher, Stefan and Ma, Xuekai and Schneider, Christian and Esmann, Martin}},
  issn         = {{2330-4022}},
  journal      = {{ACS Photonics}},
  number       = {{8}},
  pages        = {{3046--3054}},
  publisher    = {{American Chemical Society (ACS)}},
  title        = {{{Organic Room-Temperature Polariton Condensate in a Higher-Order Topological Lattice}}},
  doi          = {{10.1021/acsphotonics.4c00268}},
  volume       = {{11}},
  year         = {{2024}},
}

@article{61255,
  abstract     = {{<jats:title>Abstract</jats:title>
               <jats:p>Topological states have been widely investigated in different types of systems and lattices. In the present work, we report on topological edge states in double-wave (DW) chains, which can be described by a generalized Aubry-André-Harper (AAH) model. For the specific system of a driven-dissipative exciton polariton system we show that in such potential chains, different types of edge states can form. For resonant optical excitation, we further find that the optical nonlinearity leads to a multistability of different edge states. This includes topologically protected edge states evolved directly from individual linear eigenstates as well as additional edge states that originate from nonlinearity-induced localization of bulk states. Extending the system into two dimensions (2D) by stacking horizontal DW chains in the vertical direction, we also create 2D multi-wave lattices. In such 2D lattices multiple Su–Schrieffer–Heeger (SSH) chains appear along the vertical direction. The combination of DW chains in the horizonal and SSH chains in the vertical direction then results in the formation of higher-order topological insulator corner states. Multistable corner states emerge in the nonlinear regime.</jats:p>}},
  author       = {{Schneider, Tobias and Gao, Wenlong and Zentgraf, Thomas and Schumacher, Stefan and Ma, Xuekai}},
  issn         = {{2192-8614}},
  journal      = {{Nanophotonics}},
  number       = {{4}},
  pages        = {{509--518}},
  publisher    = {{Walter de Gruyter GmbH}},
  title        = {{{Topological edge and corner states in coupled wave lattices in nonlinear polariton condensates}}},
  doi          = {{10.1515/nanoph-2023-0556}},
  volume       = {{13}},
  year         = {{2024}},
}

@article{61257,
  abstract     = {{<jats:p>Exceptional points (EPs), with their intriguing spectral topology, have attracted considerable attention in a broad range of physical systems, with potential sensing applications driving much of the present research in this field. Here, we investigate spectral topology and EPs in systems with significant nonlinearity, exemplified by a nonequilibrium exciton-polariton condensate. With the possibility to control loss and gain and nonlinearity by optical means, this system allows for a comprehensive analysis of the interplay of nonlinearities (Kerr type and saturable gain) and non-Hermiticity. Not only do we find that EPs can be intentionally shifted in parameter space by the saturable gain, but we also observe intriguing rotations and intersections of Riemann surfaces and find nonlinearity-enhanced sensing capabilities. With this, our results illustrate the potential of tailoring spectral topology and related phenomena in non-Hermitian systems by nonlinearity.</jats:p>
          <jats:sec>
            <jats:title/>
            <jats:supplementary-material>
              <jats:permissions>
                <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement>
                <jats:copyright-year>2024</jats:copyright-year>
              </jats:permissions>
            </jats:supplementary-material>
          </jats:sec>}},
  author       = {{Wingenbach, Jan and Schumacher, Stefan and Ma, Xuekai}},
  issn         = {{2643-1564}},
  journal      = {{Physical Review Research}},
  number       = {{1}},
  publisher    = {{American Physical Society (APS)}},
  title        = {{{Manipulating spectral topology and exceptional points by nonlinearity in non-Hermitian polariton systems}}},
  doi          = {{10.1103/physrevresearch.6.013148}},
  volume       = {{6}},
  year         = {{2024}},
}

@article{61261,
  author       = {{Liang, Qian and Ma, Xuekai and Gu, Chunling and Ren, Jiahuan and An, Cunbin and Fu, Hongbing and Schumacher, Stefan and Liao, Qing}},
  issn         = {{0002-7863}},
  journal      = {{Journal of the American Chemical Society}},
  number       = {{7}},
  pages        = {{4542--4548}},
  publisher    = {{American Chemical Society (ACS)}},
  title        = {{{Photochemical Reaction Enabling the Engineering of Photonic Spin–Orbit Coupling in Organic-Crystal Optical Microcavities}}},
  doi          = {{10.1021/jacs.3c11373}},
  volume       = {{146}},
  year         = {{2024}},
}

@article{48774,
  author       = {{Gao, Ying and Ma, Xuekai and Zhai, Xiaokun and Xing, Chunzi and Gao, Meini and Dai, Haitao and Wu, Hao and Liu, Tong and Ren, Yuan and Wang, Xiao and Pan, Anlian and Hu, Wei and Schumacher, Stefan and Gao, Tingge}},
  issn         = {{2469-9950}},
  journal      = {{Physical Review B}},
  number       = {{20}},
  pages        = {{205303}},
  publisher    = {{American Physical Society (APS)}},
  title        = {{{Single-shot spatial instability and electric control of polariton condensates at room temperature}}},
  doi          = {{10.1103/physrevb.108.205303}},
  volume       = {{108}},
  year         = {{2023}},
}

@article{35160,
  author       = {{Jia, Jichao and Cao, Xue and Ma, Xuekai and De, Jianbo and Yao, Jiannian and Schumacher, Stefan and Liao, Qing and Fu, Hongbing}},
  issn         = {{2041-1723}},
  journal      = {{Nature Communications}},
  keywords     = {{General Physics and Astronomy, General Biochemistry, Genetics and Molecular Biology, General Chemistry, Multidisciplinary}},
  number       = {{1}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Circularly polarized electroluminescence from a single-crystal organic microcavity light-emitting diode based on photonic spin-orbit interactions}}},
  doi          = {{10.1038/s41467-022-35745-w}},
  volume       = {{14}},
  year         = {{2023}},
}

@article{61269,
  author       = {{Gao, Ying and Ma, Xuekai and Zhai, Xiaokun and Xing, Chunzi and Gao, Meini and Dai, Haitao and Wu, Hao and Liu, Tong and Ren, Yuan and Wang, Xiao and Pan, Anlian and Hu, Wei and Schumacher, Stefan and Gao, Tingge}},
  issn         = {{2469-9950}},
  journal      = {{Physical Review B}},
  number       = {{20}},
  publisher    = {{American Physical Society (APS)}},
  title        = {{{Single-shot spatial instability and electric control of polariton condensates at room temperature}}},
  doi          = {{10.1103/physrevb.108.205303}},
  volume       = {{108}},
  year         = {{2023}},
}

@article{40274,
  author       = {{Zhai, Xiaokun and Ma, Xuekai and Gao, Ying and Xing, Chunzi and Gao, Meini and Dai, Haitao and Wang, Xiao and Pan, Anlian and Schumacher, Stefan and Gao, Tingge}},
  journal      = {{Physical Review Letters}},
  number       = {{13}},
  pages        = {{136901}},
  title        = {{{Electrically controlling vortices in a neutral exciton polariton condensate at room temperature}}},
  doi          = {{10.1103/PhysRevLett.131.136901}},
  volume       = {{131}},
  year         = {{2023}},
}

@article{36416,
  author       = {{De, Jianbo and Ma, Xuekai and Yin, Fan and Ren, Jiahuan and Yao, Jiannian and Schumacher, Stefan and Liao, Qing and Fu, Hongbing and Malpuech, Guillaume and Solnyshkov, Dmitry}},
  issn         = {{0002-7863}},
  journal      = {{Journal of the American Chemical Society (JACS)}},
  keywords     = {{Colloid and Surface Chemistry, Biochemistry, General Chemistry, Catalysis}},
  number       = {{3}},
  pages        = {{1557--1563}},
  publisher    = {{American Chemical Society (ACS)}},
  title        = {{{Room-Temperature Electrical Field-Enhanced Ultrafast Switch in Organic Microcavity Polariton Condensates}}},
  doi          = {{10.1021/jacs.2c07557}},
  volume       = {{145}},
  year         = {{2023}},
}

@article{35077,
  author       = {{Liang, Qian and Ma, Xuekai and Long, Teng and Yao, Jiannian and Liao, Qing and Fu, Hongbing}},
  issn         = {{1433-7851}},
  journal      = {{Angewandte Chemie International Edition}},
  keywords     = {{General Chemistry, Catalysis}},
  number       = {{9}},
  publisher    = {{Wiley}},
  title        = {{{Circularly Polarized Lasing from a Microcavity Filled with Achiral Single‐Crystalline Microribbons}}},
  doi          = {{10.1002/anie.202213229}},
  volume       = {{62}},
  year         = {{2023}},
}

@article{30966,
  author       = {{Ren, Jiahuan and Liao, Qing and Ma, Xuekai and Schumacher, Stefan and Yao, Jiannian and Fu, Hongbing}},
  issn         = {{1863-8880}},
  journal      = {{Laser & Photonics Reviews}},
  number       = {{1}},
  publisher    = {{Wiley}},
  title        = {{{Realization of Exciton‐Mediated Optical Spin‐Orbit Interaction in Organic Microcrystalline Resonators}}},
  doi          = {{10.1002/lpor.202100252}},
  volume       = {{16}},
  year         = {{2022}},
}

@article{30967,
  author       = {{Zhang, Xiu and Chen, Zhenshi and Liu, Dong and Wan, Lei and Ma, Xuekai and Gao, Tingge}},
  issn         = {{1882-0778}},
  journal      = {{Applied Physics Express}},
  number       = {{2}},
  publisher    = {{IOP Publishing}},
  title        = {{{Controlling exciton distribution in WS2 monolayer on a photonic crystal}}},
  doi          = {{10.35848/1882-0786/ac48d8}},
  volume       = {{15}},
  year         = {{2022}},
}