Color Centers and Hyperbolic Phonon Polaritons in Hexagonal Boron Nitride: A New Platform for Quantum Optics

TL;DR

The paper presents a cavity QED framework that couples a single hBN color center to hyperbolic phonon polaritons in a thin hBN slab, enabling the color center to act as a quantum source of HPPs. It analyzes two generation pathways: spontaneous emission into a phonon sideband and a stimulated Raman process, the latter offering spectral selectivity and directional, ray-like propagation. The approach demonstrates how HPPs can mediate long-range interactions between spatially separated emitters on a chip, while the quantum emitter provides nonclassical polariton states and potential for entanglement protocols in the mid-IR. Together, these results fuse quantum emitter physics with hyperbolic polaritonics, outlining a versatile platform for strong light–matter coupling, spectral control, and on-chip quantum photonics in the mid-infrared.

Abstract

Hyperbolic phonon polaritons (HPPs) in hexagonal boron nitride (hBN) confine mid-infrared light to deep-subwavelength scales and may offer a powerful route to strong light-matter interactions. Generation and control of HPPs are typically accessed using classical near-field probes, which limits experiments at the quantum level.A complementary frontier in hBN research focuses on color centers: bright, stable, atomically localized emitters that have rapidly emerged as a promising platform for solid-state quantum optics. Here we establish a key connection between these two directions by developing a cavity-QED framework in which a single hBN color center serves as a quantum source of HPPs. We quantify the emitter-HPP interaction and analyze two generation schemes. The first is spontaneous emission into the phonon sideband, which can produce single-HPP events and, in ultrathin slabs, becomes single-mode with an enhanced decay rate. The second is a stimulated Raman process that provides frequency selectivity, tunable conversion rate, and narrowband excitation. This drive launches spatially confined, ray-like HPPs that propagate over micrometer distances. We also outline a two-emitter correlation measurement that can directly test the single-polariton character of these emissions. By connecting color-center quantum optics with hyperbolic polaritonics, our approach enables quantum emitters to act as on-chip quantum sources and controls for HPPs, while HPPs provide long-range channels that couple spatially separated emitters. Together, these capabilities point to a new direction for mid-infrared photonic experiments that unite strong coupling, spectral selectivity, and spatial reach within a single material system.

Figures (13)

• Figure 1: Schematic of the HPP cavity considered in this work. Photons and phonons in an hBN slab (yellow) hybridize with coupling strength $g_{ph}$ forming HPPs that propagate inside the slab and decay evanescently outside. HPPs can also interact with a localized color center (emitter) embedded in the hBN, with coupling strength $g$. The color center is modeled as a two-level system in our description. The slab, of thickness $d$, is assumed to be surrounded by air.
• Figure 2: Dielectric function of hBN. The blue and orange lines denote the in-plane and out-of-plane components, respectively. The red shaded areas indicate the two Reststrahlen bands, where one component of the dielectric function is negative and the material becomes hyperbolic.
• Figure 3: The dispersion and vacuum field strength of HPPs (of the second Reststrahlen band) in an hBN slab. From top to bottom, the solid curves correspond to the mode indices $n=0,1,2,3,4$, respectively. (a) Dispersion of HPPs in an hBN slab surrounded by air. The black dashed lines indicate the in-plane LO and TO phonon frequencies. (b) The in-plane vacuum electric field strength of HPPs in an hBN slab, normalized by $E_0(d) = \sqrt{\frac{\hbar\omega}{2\epsilon_0\epsilon_{x\infty}d A_{\text{eff}}}}$.
• Figure 4: Schematic of the two mechanisms for generating HPPs from a single color center in an hBN slab. (a) Spontaneous phonon sideband emission: an optical excitation at frequency $\omega_{eg}$ (purple) relaxes by emitting one HPP at $\omega_{\rm HPP}$ (red) together with a Stokes photon at $\omega_{eg}-\omega_{\rm HPP}$ (blue). (b) Stimulated Raman process: two drives at $\omega_{eg}$ and $\omega_{eg}-\omega_{\rm HPP}$ stimulates the transition, leading to narrowband, coherent HPP emission at $\omega_{\rm HPP}$.
• Figure 5: Calculated intensity ratio between the phonon sideband (PSB) and the zero-phonon line (ZPL) as a function of slab thickness. We use a momentum cutoff $\Lambda = 1/(2\,\text{nm})$ and dipole moment $\mu_d = e_0 \cdot (2\,\text{nm})$ for illustration. Solid curves correspond to HPP branches with mode indices $n = 0, 1, 2, 3, 4$ (from top to bottom). The dotted curve sums the contributions of the branches $n=0$ up to $n\approx\lfloor \frac{\Lambda d}{\pi} \rfloor$, so fewer branches enter for thinner hBN. As $d$ decreases, the coupling per branches first grows while higher-order branches gradually drop out due to the momentum cutoff. In the ultrathin hBN, the response is dominated by the $n=0$ branch, i.e., a single-mode HPP cavity.