Emitter–optomechanical interaction in ultrahigh-Q hBN nanocavities Open Access

Light–matter interaction between active quantum materials and photons confined in high-Q nanocavities is the central pillar in the study of cavity QED.1–4 Conventional electron–photon coupling is described by the Jaynes–Cummings model and exhibits a trivial symmetric feature with respect to the spectral detuning.5,6 Recently, cavity optomechanics has emerged, in which the coupling between photonic and mechanical modes allows coherent phonons to be controlled via photons or vice versa.7–10 This opens up new perspectives for applications in ultraprecise sensing and metrology,11,12 as well as building non-trivial optical devices with novel functionalities and asymmetric responses.13–16 In addition, the cavity mechanical modes enable new approaches to control active quantum material through the phononic degree of freedom, e.g., tuning the emission energy and linewidth as reported for quantum dots and 2D materials.17–21 The multi-modal coupling paves the way to quantum transduction between different degrees of freedom and opens new avenues in cavity QED.22–24 

Traditional quantum emitters are dominated by zero-phonon emission and can couple directly to local optical fields without the participation of phonons. As such, the native phononic effects are not pronounced, and investigations are usually subjected to the extrinsic mechanical driving.17–19 In contrast, the charged boron vacancy $VB−$ in hexagonal boron nitride (hBN) is a recently explored quantum emitter25–29 that has a weak zero-phonon line, with emission instead being dominated by phonon-induced processes.30–33 This is indicative of robust electron–phonon polarons that arise from local phonon modes and couple to the optical field. As such, by creating $VB−$ centers in an hBN nanobeam cavity,³³ we realize a novel multi-modal interaction involving the coupling in both the photonic and phononic degrees of freedom between the spin defects and the nanocavity.

We investigate the multi-modal interaction system using spatially resolved photoluminescence (PL) and Raman spectroscopy. A spectral anomaly with pronounced asymmetry is observed in the line shape of PL from the cavity photonic mode only when the Q-factor is above a threshold of $∼104$⁠. We construct a numerical model that accounts well for the experiment, based on the fact that the light–matter interaction of $VB−$ is induced by local phonon modes,30–33 which differs from the traditional Jaynes–Cummings coupling. Moreover, compared to the standard Lorentzian emission for cavities without $VB−$ centers, the spectral anomaly with $VB−$ reveals that the local phonon modes in such systems are not isolated but rather arise from the coupling between $VB−$ lattice phonons and cavity mechanical modes. This coupling is further supported by spatially correlating the luminescence of $VB−$ in freely suspended structures³⁴ and resonantly exciting the cavity photonic mode.⁹ These results indicate the great potential of hBN nanocavities for applications in non-trivial optical devices.

The structure of our hBN/Si₃N₄ nanobeam cavity is schematically depicted in Fig. 1(a). The confinement for nanophotonic modes is achieved by locally chirping the photonic crystal periodicity around the cavity center. The cavity photonic mode exhibits a high Q-factor of $∼105$⁠, limited only by the spectral resolution of our detection system.35,36 In addition to the nanophotonic mode, the cavity also hosts nanomechanical modes since the hBN/Si₃N₄ nanobeam is freely suspended but clamped at both ends.²¹ We use a 30 keV N⁺ ion beam of 10¹³ ions/cm² fluence (dose) to create $VB−$ centers within the volume of the photonic mode. Fabrication procedures are presented in Sec. I A of the supplementary material. Recent works have reported that the zero-phonon line of $VB−$ is at $∼773$ nm and exhibits very weak emission intensity, while its phonon-induced emission gives rise to a broad spectrum centered at $∼800$ nm and coupling of local phonon modes to the optical transitions of the $VB−$ center.30–33 As such, the system involves coupling between electronic transitions, $VB−$ lattice phonons, cavity photons, and cavity nanomechanical modes, as a multi-modal emitter–optomechanical interaction depicted schematically in Fig. 1(b).

We begin by comparing the emission spectral line shape observed from the cavities with and without irradiation. All cavities are excited using a 532 nm cw-laser having a spot size of $∼1μm$ and a power of $∼120μW$⁠. The cavity photonic mode is hence excited by the emission of $VB−$ centers in hBN (irradiated) and/or filtered light arising from other native luminescent defects in the hBN and underlying Si₃N₄ (non-irradiated). Typical spectra recorded from four representative cavities with and without irradiation are presented in the upper and lower panels of Fig. 1(a), respectively. The emission of vacancies in hBN is very broad, with an FWHM over 150 nm,³³ and thereby features as a plane background in the spectra in Fig. 1(a), for which the wavelength range is smaller than 1 nm. The peaks in Fig. 1(a) are from the photonic mode of the cavities. The photonic modes are at a wavelength of $∼800$ nm, which is within the broad phonon sideband emission of $VB−$⁠.33,37,38 

In addition, we use bi-peak fitting, including a major peak (red) and a minor replica (blue) at the shorter wavelength side, to quantify the asymmetry, as shown by the example in Fig. 1(d) inset. The Voigt peak (convolution of Lorentz and Gaussian peaks) is used for the fitting because the spectral broadening of our detection system results in a convolution of signals by a Gaussian window function with a width of 50 pm.³⁶ After deconvolution, we extract the real Lorentzian linewidth, e.g., with the values of 0.04–0.09 mm for the cavity modes shown in Fig. 1(a), corresponding to the Q-factors of 8 × 10⁴ to 2 × 10⁵. The high Q-factors are owing to the design of the hybrid nanobeam cavity that avoids etching rough photonic crystal nanoholes in hBN.³⁵ The asymmetry is quantified via the intensity ratio of the replica to the major peak, and the results of all measured cavities are presented in Fig. 1(d). By comparison, the solid line in Fig. 1(d) is the calculation result using Eq. (2), which well reproduces the experimental data. As shown, when the cavity Q-factor is smaller than 10⁴, the replica is suppressed, and the cavity emission is a standard Lorentz peak (after deconvolution). In contrast, when the Q-factor exceeds 10⁴, the spectral anomaly arises, and the cavity emission becomes non-Lorentzian. This threshold behavior indicates that the multi-modal light–matter interaction needs to exceed the system decay rate (1/Q) for the spectral anomaly. Despite the model in Eq. (2) being rather simple, it nicely captures the essential physics underpinning our experimental observations, e.g., the phonon-induced coupling as shown in Fig. 1(c) and the threshold for asymmetry as shown by the solid line in Fig. 1(d).

In the phonon-induced coupling model shown in Fig. 1(b), the local phonon modes arising from the coupling between $VB−$ lattice phonons and cavity mechanical modes play central roles. To further support this point, we next probe the local phonon modes in their coupling to the photons in cavity photonic mode or the electronic transition of $VB−$ individually. We first explore the phonon coupling for cavity photons using resonant Raman spectroscopy and present the results in Fig. 2. We tune a narrowband (⁠$≤1$ MHz) cw laser from 730.998 to 731.012 nm over the resonance of a cavity photonic mode, as depicted by the inset in Fig. 2(a). Color lines in Fig. 2(a) are the corresponding Raman spectra excited by the tunable laser. As denoted by the arrows, the sharp peak corresponding to the E_g mode from Si₃N₄⁴⁴ and the broad peak corresponding to the local vibrational mode from $VB−$⁴⁵ are observed. Details of the identification of Raman peaks can be found in Sec. II B of the supplementary material. We extract the intensity of Raman peaks and plot it as a function of drive laser detuning from the cavity mode in Fig. 2(c).

The steady state population of cavity photons is obviously enhanced around the resonance. Cavity photons then couple to the lattice phonons in Si₃N₄ or $VB−$ center, thereby enhancing the Raman signals.⁴⁶ For the Si₃N₄ phonon presented in the upper panel in Fig. 2(b), this enhancement is weak (10%) and nearly symmetric with respect to the detuning. The line shape reflects the real peak wavelength of the cavity mode, 731.007 nm, and the real linewidth, 3.5 ± 0.1 pm, corresponding to a Q-factor $>2×105$ in the ultrahigh regime.⁴⁷ The symmetry confirms that cavity photons directly couple to Si₃N₄ phonons, and the enhancement simply arises from a resonance in the optical density in the sample. In complete contrast, from the intensity of the $VB−$ phonon presented in the bottom panel of Fig. 2(b), we observe a much stronger enhancement $(>10×)$ around the resonance that exhibits a pronounced asymmetry with respect to the detuning. Notably, the intensity reduces rapidly at red detunings while being much slower for blue detunings. This observation reveals that the cavity mechanical modes induce coupling between cavity photons and $VB−$ phonons because the population of cavity mechanical phonons is reduced at red detunings (cooling) while enhanced at blue detunings (heating).⁹ As such, the correlation between $VB−$ lattice phonons and cavity mechanical phonons in the local phonon modes is demonstrated in the coupling to cavity photons.

Finally, we explore the coupling of local phonon modes to the electronic transition of $VB−$⁠. For this experiment, we fabricate a sample as depicted in Fig. 3(a). The sample is homogeneously irradiated by 30 keV N⁺ ions with an ion fluence (dose) of 10¹⁴ ions/cm² to create $VB−$ centers in the hBN flake.37,38 Such a sample does not support cavity phononic mode but hosts cavity mechanical modes such as the one shown in the top panel in Fig. 3(a). The local amplitude of the mechanical mode generally increases for positions away from the clamping point (orange dashed line). This enables us to probe the impact of the mechanical mode by performing position dependent spectroscopy of the $VB−$ centers.³⁴ 

$VB−$ emission is dominated by phonon sideband, i.e., the electronic transition couples to local phonon modes as a polaron and then emits a photon,30–33 and the photon wavelength is determined by the energy of local phonon modes. In Fig. 3(b), we present the broad phonon sideband emission of $VB−$ recorded from positions along the loop trace denoted in Fig. 3(a). The position dependence of $VB−$ emission, along with two anticrossings, is clearly observed as depicted by the dashed lines in Fig. 3(b). This is combined with the identity of spectra at the beginning and end of the loop. Similar anticrossings are also observed from the spatially resolved Raman spectra of $VB−$ (Sec. II C of the supplementary material), further supporting the generality of this conclusion. The anticrossings demonstrate the coherent correlation between $VB−$ lattice phonons and cavity mechanical modes with spatial dependence. This electron–phonon coupling in Fig. 3, combined with the photon–phonon coupling in Fig. 2, further strengthens the phononic coupling between the cavity mechanical modes and $VB−$ lattice phonons shown in the right part in Fig. 1(b), and thereby, greatly supports the non-Lorentzian cavity emission arising from the phonon-induced emitter–optomechanical interaction.

In summary, we report on the interaction between $VB−$ centers and optomechanical modes in a hBN nanocavity. Experimental results reveal that in both the phonon couplings to electrons and photons, the local phonon modes are not isolated but arise from the coupling between $VB−$ lattice phonons and cavity mechanical modes that are strongly correlated. This phonon-induced interaction between the electronic transition in $VB−$ and the cavity photonic mode results in the spectral anomaly in the emission from the hBN nanocavity. Such a multi-modal system provides exciting opportunities to interface fixed quantum degrees of freedom to photonic and phononic modes using 2D materials and opens up interesting perspectives for quantum sensing and quantum transduction.

The supplementary material includes the detailed methods and results of control experiments to support the conclusions.

All authors gratefully acknowledge the German Science Foundation (DFG) for the financial support via Grant Nos. FI 947/8-1, DI 2013/5-1, AS 310/9-1, and SPP-2244, as well as the clusters of excellence MCQST (EXS-2111) and e-conversion (EXS-2089). J. J. F. gratefully acknowledges the state of Bavaria via the One Munich Strategy and Munich Quantum Valley. C. Q. gratefully acknowledges the support from the Chinese Academy of Sciences Project for Young Scientists in Basic Research (Grant No. YSBR-112) and the National Natural Science Foundation of China (Grants Nos. 12474426, 12494601). C. Q. and V. V. gratefully acknowledge the Alexander v. Humboldt Foundation for the financial support in the framework of their fellowship program. The support from the Ion Beam Center (IBC) at HZDR is gratefully acknowledged.

The authors have no conflicts to disclose.

Chenjiang Qian: Conceptualization (lead); Data curation (lead); Formal analysis (lead); Funding acquisition (lead); Investigation (lead); Writing – original draft (lead); Writing – review & editing (equal). Viviana Villafañe: Data curation (equal); Investigation (equal); Writing – review & editing (equal). Martin Schalk: Data curation (equal); Investigation (equal); Writing – review & editing (equal). Georgy V. Astakhov: Data curation (equal); Investigation (equal); Writing – review & editing (equal). Ulrich Kentsch: Data curation (equal); Investigation (equal); Writing – review & editing (equal). Manfred Helm: Data curation (equal); Investigation (equal); Writing – review & editing (equal). Pedro Soubelet: Data curation (equal); Investigation (equal); Writing – review & editing (equal). Andreas V. Stier: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Writing – review & editing (equal). Jonathan J. Finley: Conceptualization (lead); Data curation (lead); Formal analysis (lead); Funding acquisition (lead); Investigation (lead); Writing – review & editing (equal).

The datasets generated and analyzed during the current study are available from the corresponding author upon reasonable request.

The hBN/Si₃N₄ hybrid nanobeam cavity is fabricated through e-beam lithography (EBL), inductively coupled plasma reactive ion etching (ICPRIE), the viscoelastic dry transfer method, and wet underetching. First, we prepare a Si substrate with 200 nm Si₃N₄ grown by low pressure chemical vapor deposition (LPCVD) on top. Then, we use EBL and ICPRIE to etch periodic nanotrenches in Si₃N₄. After removing the residual resist, we transfer the hBN flake with a thickness of $∼100nm$ on top of the nanotrenches. Finally, we use EBL and ICPRIE to etch the nanobeams, followed by a wet underetching to remove the bottom Si. Detailed fabrication procedures are presented in Sec. I A of the supplementary material.

The sample is excited using a 532 nm cw-laser for the spatially resolved spectroscopy or a tunable cw-laser for the resonant spectroscopy of the cavity photonic mode. The laser has a spot size $∼1μm$ and the excitation power $∼120μW$⁠. PL and Raman signals are recorded by a confocal micro-PL setup. The objective has a magnification of 100 and a NA of 0.75. The PL and Raman spectra of $VB−$ centers are collected by a matrix array Si CCD detector in a spectrometer, with a focal length of 0.55 m and a grating of 300 grooves per mm. The PL spectra of cavity photons are collected by the same detector and spectrometer but with a grating of 1200 grooves per mm.