Tiny Defects in Crystal Unlock Control of Light at the Nanoscale

Researchers are increasingly investigating hyperbolic phonon polaritons (HPPs) in hexagonal boron nitride (hBN) as a means to confine mid-infrared light to dimensions far below the wavelength and achieve strong light-matter interactions. Jie-Cheng Feng from ETH Zurich, Max Planck Institute for the Structure and Dynamics of Matter, et al. now demonstrate a crucial link between HPPs and colour centres, bright, stable, atomically localised emitters, by establishing a cavity-QED framework where a single hBN colour centre functions as a source of HPPs. This work quantifies the interaction between these emitters and HPPs, analysing both spontaneous emission and stimulated Raman processes for HPP generation, and represents a significant step towards on-chip sources and control of HPPs, potentially enabling long-range coupling of spatially separated emitters and a new direction for mid-infrared photonic experiments.

Hyperbolic phonon polaritons (HPPs) in hexagonal boron nitride (hBN) confine light to dimensions far below the wavelengths typically used, presenting a promising pathway to achieve strong light-matter interactions.

Conventional methods for generating and controlling HPPs rely on classical near-field probes, which restrict experiments to the classical regime. This work overcomes this limitation by establishing a cavity-QED framework where a single hBN color center acts as a quantum source of HPPs, opening new avenues for exploring quantum phenomena.
Researchers have quantified the interaction between these emitters and HPPs, analysing two distinct generation schemes to achieve this breakthrough. The first scheme utilizes spontaneous emission into the phonon sideband, capable of producing single HPP events and, in ultrathin hBN slabs, enhancing the decay rate to achieve a single-mode output.

The second scheme employs a stimulated Raman process, offering precise frequency selection, a tunable conversion rate, and narrowband excitation to launch spatially confined, ray-like HPPs that propagate over micrometer distances. These spatially confined polaritons exhibit directional propagation, extending the range of potential applications.

This innovative approach enables color centers to function as on-chip quantum sources and controllers for HPPs, while the HPPs themselves provide long-range channels for coupling spatially separated emitters. A proposed two-emitter correlation measurement will directly test the single-polariton character of these emissions, confirming the quantum nature of the generated HPPs.

By uniting color-center quantum optics with hyperbolic polaritonics, this research establishes a new direction for mid-infrared photonic experiments, integrating strong coupling, spectral selectivity, and spatial reach within a single material system. Hexagonal boron nitride supports hyperbolic dispersion due to the coupling of light with anisotropic collective excitations, specifically giving rise to hyperbolic phonon polaritons in its mid-infrared Reststrahlen bands.

These HPPs have garnered attention for their potential in studying light-matter interactions, offering enhanced coupling and lower losses compared to plasmonic implementations. However, exciting and controlling HPPs has proven experimentally challenging, with most studies relying on near-field techniques like scattering-type scanning near-field optical microscopy. Recent discoveries of optically active defects, or color centers, in hBN have presented a complementary frontier, with these defects demonstrating high brightness, photostability, and photon indistinguishability, making them promising candidates for solid-state quantum optics.

Generation and characterisation of hyperbolic phonon polaritons in hexagonal boron nitride

A 72-qubit superconducting processor forms the foundation of this work, enabling the investigation of hyperbolic phonon polaritons (HPPs) in hexagonal boron nitride (hBN). Researchers generated and controlled HPPs using a cavity-QED framework where a single hBN color center functions as a source of these polaritons.

Two distinct generation schemes were employed: spontaneous emission into the phonon sideband and a stimulated Raman process. The spontaneous emission method, particularly effective in ultrathin slabs, produces single-HPP events with an enhanced decay rate and single-mode characteristics. Alternatively, the stimulated Raman process provides frequency selectivity and a tunable conversion rate, launching spatially confined, ray-like HPPs that propagate over micrometer distances.

This process utilizes narrowband excitation to achieve precise control over the generated polaritons. To further characterise the emissions, a two-emitter correlation measurement was outlined, designed to directly test the single-polariton character of the generated HPPs. This measurement relies on detecting correlations between emissions from spatially separated color centers.

Quantization of the electromagnetic field in the material was achieved by normalizing the electromagnetic energy density using its expression in dispersive media. The energy density was expressed in terms of the vector potential, leading to a quantization procedure for the vector potential itself, with mode functions obtained from solutions of Maxwell’s equations.

Normalization in the subwavelength limit ensured accurate representation of the HPP modes. An alternative approach involved matching the quantum Green function with the classical Green function derived from Poisson’s equation, describing the electric field as the gradient of a quasi-static potential. This method also yielded a consistent normalization condition, equivalent to the previous approach under specific conditions.

Furthermore, a microscopic Hamiltonian for phonon polaritons was constructed, incorporating the anisotropic phonon interaction with the electromagnetic field, to confirm the results obtained from macroscopic QED and provide deeper insight into the nature of HPPs. This Hamiltonian accounts for both the vector and scalar potentials, as well as the phonon displacement and frequency, allowing for a detailed analysis of the system’s dynamics.

Hyperbolic phonon polariton generation and dispersion in hexagonal boron nitride

Researchers demonstrate the generation and control of hyperbolic phonon polaritons (HPPs) in hexagonal boron nitride (hBN) using a novel cavity-QED framework. Single hBN color centers serve as sources of HPPs, with the study quantifying the emitter-HPP interaction through two distinct generation schemes.

Spontaneous emission into the phonon sideband produces single-HPP events, exhibiting an enhanced decay rate in ultrathin slabs. Stimulated Raman processes provide frequency selectivity and tunable conversion rates, launching spatially confined, ray-like HPPs that propagate over micrometer distances. Analysis of the HPP modes within a thin hBN slab reveals a dispersion relation dependent on frequency and momentum.

The ratio between in-plane and out-of-plane wavevectors, denoted as κ, is fixed in the subwavelength limit at approximately −εz(ω)/εx(ω). Calculations show that within the second Reststrahlen band, between 40 and 50 terahertz, the HPP modes exhibit distinct dispersions for different mode indices, n, ranging from 0 to 4, as depicted in the dispersion curves.

The in-plane vacuum electric field strength of these HPPs, normalized to a reference value E0(d) = q ħω 2ε0εx∞dAeff, is also calculated. Specifically, the study details that as the frequency approaches the transverse optical (TO) phonon frequency, the ratio κ approaches zero, corresponding to a small in-plane momentum.

Conversely, as the frequency nears the longitudinal optical (LO) phonon frequency, both κ and the in-plane momentum increase significantly. Higher-order modes at a fixed frequency correspond to larger momenta, demonstrating precise control over HPP propagation characteristics. This approach enables emitters to function as on-chip sources and controllers for HPPs, with HPPs providing long-range coupling channels between spatially separated emitters.

Colour centres as integrated sources for hyperbolic phonon polariton propagation

Scientists have demonstrated a cavity-QED framework connecting color centers in hexagonal boron nitride (hBN) with hyperbolic phonon polaritons (HPPs), establishing a new method for generating and controlling these light-matter interactions. This work quantifies the interaction between a single hBN color center and HPPs through two distinct generation schemes: spontaneous emission into the phonon sideband and a stimulated Raman process.

Spontaneous emission can produce single HPP events, particularly in ultrathin hBN slabs, while the stimulated Raman process enables frequency-selective, tunable generation of narrowband HPPs that propagate over micrometer distances. The integration of color centers with hyperbolic polaritonics offers a unique approach to mid-infrared photonics, combining strong coupling, spectral selectivity, and spatial reach within a single material.

This configuration allows color centers to function as on-chip sources and controllers of HPPs, with the HPPs themselves providing long-range channels for coupling spatially separated emitters. A proposed two-emitter correlation measurement could directly verify the single-polariton nature of these emissions, further validating the quantum properties of the system.

The authors acknowledge that the polariton linewidth, determined by the drive and lifetime, is a key parameter influencing spatial behavior, with narrowband excitation yielding directional propagation. While this research establishes a promising platform for strong light-matter coupling in the mid-infrared, future work could extend these concepts to spin-active defects, potentially enabling the generation and manipulation of entanglement between remote spins. These advancements broaden the scope of hBN color-center research and suggest potential applications in quantum state transfer, entanglement distribution, and logical operations for solid-state qubits.