The ambition of this Sapere Aude Starting Grant was to leverage the intense optical field confinement endowed by polaritons — quasiparticles formed when light hybridizes with matter excitations such as plasmons, excitons, and phonons — in two-dimensional (2D) atomically thin materials, to enhance nonlinear light-matter interactions at the nanoscale. In the 2D limit, the electronic properties of these materials are more readily controlled by external stimuli than their bulk counterparts, making them uniquely suited as active and tunable platforms for nonlinear photonics. The central hypothesis of the project was that polaritons in atomically thin materials can provide unprecedented control over nonlinear optical phenomena, both with respect to active tunability and reduced optical power thresholds, potentially enabling the control of light using light itself at the level of individual photons.
The research was divided into two main themes: the first focused on simulating the intrinsic polariton-driven nonlinear optical response of nanostructured 2D materials using atomistic quantum mechanical methods, while the second explored strategies to leverage the optical nonlinearity endowed in 2D materials by nearby fermionic quantum light emitters, such as atoms and molecules. The project also pursued, in collaboration with leading international groups, the ambitious goal of exploring polariton-driven nonlinear optics at the level of individual light quanta — investigating whether graphene plasmon polaritons could serve as a platform for quantum logic operations.
More information about the project
The work performed in this project was organized around the following key research directions:
- Development of a "second-principles" atomistic simulation framework for nonlinear nanophotonics in 2D materials. Motivated by the computational infeasibility of rigorous first-principles simulations of nonlinear optical excitations in mesoscopic 2D nanostructures, the project developed a powerful and versatile "second-principles" atomistic simulation framework. This approach uses electronic states obtained from first-principles calculations as the basis for self-consistent optical response simulations, and proved capable of describing nanoscale light-matter interactions in nanostructures comprising thousands of atoms — well beyond the reach of state-of-the-art density functional theory. The framework was applied to study the plasmon-driven nonlinear optical response of electrically doped phosphorene nanoribbons [ACS Nano 17, 20043 (2023)] and photothermally excited graphene nanoribbons [Nano Lett. 24, 13755 (2024)], demonstrating that the light intensity thresholds required to trigger nonlinear optical phenomena can be significantly reduced by plasmons — corroborating a key hypothesis of the proposal.
- Macroscopic quantum electrodynamic (QED) formalism for quantum light sources near tunable 2D materials. A detailed macroscopic QED formalism was developed and reported across several publications to predict the temporal and spectral changes in quantum light generation near actively tunable 2D materials or thin metallic films. The formalism incorporates both the enhancement in spontaneous emission (Purcell effect) and the renormalization of quantum emitter transition energies (Lamb shift) due to the modification of electromagnetic vacuum modes by the tunable 2D material. A key result was the discovery of a large intrinsic optical nonlinearity associated with the self-interaction of a two-level emitter mediated by an extended graphene sheet. The active optoelectronic tuning of the graphene sheet was shown to enable electrical control over the quantum state of the optically driven emitter, leading to optoelectronic bistability — the switching between two metastable optical states — a mechanism for storing and retrieving quantum information [Phys. Rev. Lett. 129, 253602 (2022)]. The formalism was subsequently extended to study chiral light-matter interactions of emitters with magnetoplasmons in graphene nanostructures [Nano Lett. 25, 313 (2025)].
- Theoretical investigation of polariton-driven quantum nonlinear optics. In collaboration with groups at the ICFO and the University of Vienna, the project explored polariton-driven nonlinear optical phenomena at the level of individual light quanta. The interaction of counter-propagating graphene plasmon polaritons was theoretically predicted to enable unity-order reflection of one guided polariton by another, a mechanism for realizing quantum logic operations in integrated graphene-based nanophotonic devices [Phys. Rev. Research 5, 013188 (2023)]. The project also investigated the nonlinear generation of entangled guided photon pairs produced by energetic free electrons interacting with plasmons in 2D material waveguides [Sci. Adv. 10, eadn6312 (2024)], and large ponderomotive optical nonlinearities in atomic chains triggered by individual free electrons [Phys. Rev. Research 5, L022015 (2023)].
- Training and career development of early-career researchers. The project supported the PhD research of Mikkel Have Eriksen, who successfully defended his thesis entitled "Quantum nonlinear nano-optics in hybrid polaritonic systems" in January 2025. The thesis was evaluated by an international committee as being "of outstanding international standard — among the very best within the field." The project also recruited postdoctoral researcher Dr. Line Jelver, whose expertise in ab initio descriptions of electronic states in 2D materials and their heterostructures brought crucial insights from condensed matter physics to nonlinear nanophotonics. Dr. Jelver played a central role in the development and application of the “second-principles” atomistic simulation framework, driving some of the project’s most significant results.
Key scientific results advancing the state of the art include:
- The development of a "second-principles" atomistic simulation framework capable of describing the nonlinear optical response of 2D nanostructures comprising thousands of atoms, demonstrating that plasmons can significantly reduce the optical power thresholds required to trigger nonlinear optical phenomena in phosphorene and graphene — and providing a powerful tool now applicable across a wide range of atomically thin and ultrathin systems.
- The prediction of optoelectronic bistability in atom-graphene hybrid systems, arising from the large intrinsic optical nonlinearity of a quantum emitter self-interacting via an extended graphene sheet, and enabling active optoelectronic control over quantum optical switching and information storage at the nanoscale.
- The theoretical prediction that counter-propagating graphene plasmon polaritons can achieve unity-order mutual reflection, opening a pathway to quantum logic gates in integrated graphene-based nanophotonic devices and demonstrating that 2D materials can support the nonlinear interactions required for quantum information processing.
The success of this project, beyond its scientific achievements, was the establishment of productive international collaborations with the Institute of Photonic Sciences (ICFO, Spain), the University of Vienna (Austria), and the Instituto de Química Física Blas Cabrera (IQF, Spain). The project brought together experts in quantum optics, condensed matter theory, and nanophotonics, advancing fundamental knowledge of nonlinear light-matter interactions in 2D materials and facilitating the transfer of knowledge between international collaborators and colleagues at the host institution. The results open pathways toward more efficient integrated photonic devices based on 2D materials, addressing the pressing global challenge of energy consumption in information and communication technologies, while advancing nonlinear optics towards the ultimate limit of single-photon nonlinearity — a paradigm with enormous potential for emerging quantum technologies.
Publications (selected)
1. Optoelectronic control of atomic bistability with graphene, Mikkel Have Eriksen, Jakob E. Olsen, Christian Wolff, and Joel D. Cox, Physical Review Letters 129, 253602 (2022)
2. Nonlinear quantum logic with colliding graphene plasmons, Giuseppe Calajò, Philipp K. Jenke, Lee A. Rozema, Philip Walther, Darrick E. Chang, and Joel D. Cox, Physical Review Research 5, 013188 (2023)
3. Nonlocal and cascaded effects in nonlinear graphene nanoplasmonics, Theis P. Rasmussen, Álvaro Rodríguez Echarri, F. Javier García de Abajo, and Joel D. Cox, Nanoscale 15, 3150 (2023)
4. Nonlinear plasmonics in nanostructured phosphorene, Line Jelver and Joel D. Cox, ACS Nano 17, 20043 (2023)
5. Electron-induced nonlinear dynamics in atomic chains, Line Jelver and Joel D. Cox, Physical Review Research 5, L022015 (2023)
6. Generation of entangled waveguided photon pairs by free electrons, Theis P. Rasmussen, Álvaro Rodríguez Echarri, Joel D. Cox, and F. Javier García de Abajo, Science Advances 10, eadn6312 (2024)
7. Nonlocal effects in plasmon-emitter interactions, Mikkel Have Eriksen, Christos Tserkezis, N. Asger Mortensen, and Joel D. Cox, Nanophotonics 13, 2741 (2024)
8. Nonlinear thermoplasmonics in graphene nanostructures, Line Jelver and Joel D. Cox, Nano Letters 24, 13775 (2024)
9. Chiral light-matter interactions with thermal magnetoplasmons in graphene nanodisks, Mikkel Have Eriksen, Juan R. Deop-Ruano, Joel D. Cox, and Alejandro Manjavacas, Nano Letters 25, 313 (2025)
10. Nonreciprocal plasmons in one-dimensional carbon nanostructures, Álvaro Rodríguez Echarri, F. Javier García de Abajo, and Joel D. Cox, Nature Communications 17, 1114 (2026)
Grant holder Joel D. Cox
The project 'Towards single-photon nonlinear optics in atomically-thin materials' is supported with a grant from Independent Research Fund Denmark (Grant 2025.0165-00051B) part of the Sapere Aude Programme.
