Unified Effective Field Theory Models Nonlinear and Quantum Optics across Terahertz to Near-Visible Frequencies

The challenge of accurately modelling both the subtle effects of individual photons and the powerful behaviour of intense light has long required scientists to employ separate theoretical approaches, limiting predictive power. Now, Xiaochen Liu and Ken-Tye Yong, both from The University of Sydney, present a unified theoretical framework that bridges this gap, offering a single, consistent method for describing light-matter interactions across a broad range of intensities. This new effective field theory successfully predicts the behaviour of materials from terahertz to near-visible frequencies, achieving two to four percent agreement with existing experimental data for diverse systems including semiconductor cavities, transparent conductors and superconducting circuits. By resolving the inconsistencies between different theoretical regimes, this work represents a significant step towards a more complete understanding of nonlinear and quantum optical phenomena and promises to accelerate the development of advanced photonic technologies.

This work constructs a comprehensive field theory treating electromagnetic and polarization fields equally, ensuring both local gauge and BRST symmetry are preserved. The team introduced effective polarization fields representing material modes, coupling them to the gauge potential in a manner that guarantees gauge invariance and allows for topological interactions. A general potential was included to generate nonlinear susceptibilities of any order, providing a versatile platform for modeling material responses.

Through a rigorous application of the Keldysh formalism and BRST quantization, researchers derived closed one-loop renormalization-group equations for the third-order susceptibility, χ3. Measurements confirm that these equations accurately reproduce experimentally measured dispersion of χ3 from terahertz to near-visible frequencies, after matching a single datum per material. This demonstrates the accuracy of the theoretical predictions across different materials. Real-time dynamics, solved using a matrix-product-operator engine, yield agreement of 2 to 4 percent with published results obtained from GaAs polariton cavities, epsilon-near-zero indium-tin-oxide films, and superconducting “quarton” circuits, demonstrating the predictive power of the new theoretical framework across diverse material systems. The current formulation is limited to one-dimensional geometries and frequencies below a material-dependent cutoff, but the researchers anticipate that extending the framework to higher dimensions and above-cutoff frequencies will require incorporating additional degrees of freedom or employing numerical methods. This research successfully bridges a gap between theoretical descriptions of few-photon and strong-field nonlinear phenomena, offering a framework valid across a broad frequency range. A key achievement is the development of a covariant Dirac, BRST quantisation method which eliminates gauge redundancy while preserving causality and positivity, alongside a finite one-loop renormalisation group flow ensuring well-behaved nonlinear coefficients from terahertz to petahertz frequencies. The resulting model demonstrates predictive power across diverse physical scenarios, quantitatively explaining photon correlations in GaAs microcavities, humidity-tuned terahertz filamentation, transitions in silicon photonic lattices, and energy-flow reversal in epsilon-near-zero films using a consistent set of parameters.

This coherence across vastly different physical scales suggests the framework captures essential physics beyond existing phenomenological models, and importantly, provides a direct route to deterministic photonic quantum logic at room temperature. The research demonstrates that the same third-order Kerr nonlinearity emerging from the unified action can serve as a controlled-phase interaction between single photons. Future research directions include embedding the framework on two-dimensional manifolds to describe ultrafast nonlinearities in materials like graphene, and extending the model to ultra-strong-coupling cavities where light and matter strongly interact. The coexistence of strong Kerr nonlinearities and quantum entanglement also presents opportunities for further investigation.