Formation of Cavity-Polaritons via High-Order Van Hove Singularities

Cavity polaritons are hybrid light–matter states that emerge in systems where a material’s excitations are strongly coupled to the electromagnetic modes of a cavity [1]. They can mediate effective interactions between photons of an external light field incident on the system. If sufficiently strong, these interactions allow one incident photon to appreciably affect the transmission of others, potentially enabling all-optical switching of classical signals with few photons and photonic quantum information processing—key goals of quantum nonlinear optics [2].

The matter excitations most commonly considered for cavity-polariton formation appear as discrete resonances in the optical response of the uncoupled material, with Coulomb-bound excitons providing a familiar example [3]. A pre-existing discrete material resonance is not, however, essential: coupling a cavity mode to a continuum of matter excitations can generate a discrete polariton state below the continuum threshold [4].

In our work [5], we investigate whether shaping an insulator’s interband particle–hole continuum can enhance its hybridization with a cavity mode below the gap. This continuum is characterized by the joint density of states (JDOS), which counts available transitions from the valence to the conduction band per unit energy and exhibits a nonanalytic feature at the gap: a Van Hove singularity (VHS). We show that a stronger VHS enhances hybridization and therefore propose engineering a nonparabolic band dispersion near the gap to realize a high-order Van Hove singularity (HOVHS) [6]. This can be achieved in insulating phases realized with ultracold fermions in optical lattices, as the laser interference pattern that generates the lattice offers precise control over the band dispersion.

Our findings identify HOVHS at the gap edge as a promising resource for quantum nonlinear optics.

References

• [1] D. N. Basov et al., “Polariton panorama”, Nanophotonics 10, 549–577 (2021).
• [2] D. E. Chang, V. Vuletić, and M. D. Lukin, “Quantum nonlinear optics — photon by photon”, Nature Photonics 8, 685–694 (2014).
• [3] A. Delteil et al., “Towards polariton blockade of confined exciton–polaritons”, Nature Materials 18, 219–222 (2019).
• [4] F. Helmrich et al., “Cavity-driven attractive interactions in quantum materials”, Nature 654, 361–368 (2026).
• [5] I. Gianardi, M. Pini, and F. Piazza, “Formation of Cavity-Polaritons via High-Order Van Hove Singularities”, arXiv:2509.15849 (2025).
• [6] A. Chandrasekaran, A. Shtyk, J. J. Betouras, and C. Chamon, “Catastrophe theory classification of Fermi surface topological transitions in two dimensions”, Physical Review Research 2, 013355 (2020).

Short Bio

Igor Gianardi is a PhD student at the Max Planck Institute for the Physics of Complex Systems in Dresden, under the supervision of Prof. Francesco Piazza. He earned his bachelor’s and master’s degrees in theoretical physics at the University of Pisa. His research focuses on low-dimensional quantum materials coupled to electromagnetic cavity fields. He investigates how cavity vacuum fluctuations can be used to engineer material properties (cavity QED with quantum materials) and how these systems can control the quantum properties of an incident light beam by mediating effective interactions between its photons (quantum nonlinear optics).