Multimode Phonon-Polaritons in Lead-Halide Perovskites in the Ultrastrong Coupling Regime

Abstract

Phonons play a central role in fundamental solid-state phenomena, including superconductivity, Raman scattering, and symmetry-breaking phases. Harnessing phonons to control these effects and enable quantum technologies is therefore of great interest. However, most existing phonon control strategies rely on external driving fields or anharmonic interactions, limiting their applicability. Here, we realize multimode ultrastrong light--matter coupling and theoretically show the modulation of phonon emission. This regime is realized by coupling two optical phonon modes in lead halide perovskites to a nanoslot array functioning as a single-mode cavity. The small mode volume of the nanoslots enables high coupling strengths in the phonon-polariton system. We show theoretically that the nanoslot resonator mediates an effective interaction between phonon modes, leading to superthermal phonon bunching in thermal equilibrium between distinct modes. Our findings are well described by a multimode Hopfield model. This work establishes a pathway for engineering phononic properties for light-harvesting and light-emitting technologies.

Figures (3)

• Figure 1: Perovskite--nanoslot hybrid system in the ultrastrong coupling regime.a, Hybridization between a nanoslot-cavity mode, with frequency $\omega_\mathrm{c}$, and two transverse optical phonon modes in perovskite materials, with frequencies $\omega_{1}$ and $\omega_{2}$, in the far-detuned, low cavity frequency regime, $\omega_\mathrm{c}\ll \omega_{\lambda}$ ($\lambda=1,2$). The coupling strengths of these phonon modes are denoted as $g_1$ and $g_2$, respectively. Anomalous correlations between phonons are mediated by the cavity mode and governed by the coupling ratios $g_{\lambda}/\omega_{\lambda}$. b, Illustration of the perovskite--nanoslot hybrid system under illumination by terahertz light. Seven nanoslots of different lengths ($l=$ 30-160 $\upmu$m) were fabricated to tune the cavity resonance frequency. The inset shows a scanning electron microscope image showing a bare nanoslot (top view); Scale bar: 20 $\upmu$m. c, Numerical simulation (COMSOL) showing an enhancement of the $x$ component of the electric field ($E_x$) at resonance (0.77 THz) in a nanoslot filled with MAPbI$_3$ perovskite. Left: top view ($z=0$ plane); Right: cross-section ($y=0$ plane). The white dotted lines outline the area filled with MAPbI$_3$. The white solid lines outline the nanoslot area.
• Figure 2: Terahertz transmission spectra.a, Transmission spectra for bare cavities (nanoslots) with different lengths ($l$) (green curves) showing a single cavity mode. The green dashed line shows the simulated transmission through the nanoslot ($l=80\,\upmu$m). Transmission spectrum for a 200-nm-thick bare MAPbI$_3$ film (black curve) showing two transmission dips due to the two optical phonon modes ($\lambda=1$ and $\lambda=2$) with angular frequencies $\omega_{1}$ and $\omega_{2}$, respectively. b, Bare cavity resonance frequencies as a function of nanoslot length $l$ in the reciprocal axis (green circles). The linear fit (green dashed line) shows good agreement with the experimental data. The $\lambda=1$--cavity and $\lambda=2$--cavity resonances occur with an 80-$\upmu$m-long slot and with a 50-$\upmu$m-long slot, respectively, when the cavity mode frequency coincides with the phonon frequencies (red and blue dashed lines). c, Transmission spectra for the MAPbI$_3$--nanoslots hybrid system showing three polariton branches. UP: upper polariton, MP: middle polariton, and LP: lower polariton. The dashed lines indicate the two phonon frequencies. The spectra are vertically offset by 0.2 for clarity. d, Numerical simulation (COMSOL) of the transmission as a function of cavity frequency (color map). Each spectrum has been normalized by its maximum transmittance to clearly show the three polariton branches; the black solid circles are the experimental results.
• Figure 3: Phonon-polariton properties in perovskite--nanoslot hybrid systems. Top: MAPbI$_3$ films (3D perovskite). Bottom: (BA)$_2$(MA)Pb$_2$I$_7$ (2D perovskite) films. a,b, Crystal structures of MAPbI$_3$ and (BA)$_2$(MA)Pb$_2$I$_7$. BA: CH$_3$(CH$_2$)$_3$NH$_3^+$, MA: CH$_3$NH$_3^+$. c,f, Polariton dispersion as a function of cavity frequency; UP: upper polariton, MP: middle polariton, LP: lower polariton. Solid circles: Peak frequencies extracted from the experimental transmission spectra. Solid lines: Fit of the extracted peak frequencies using the microscopic Hopfield model. The dashed lines indicate the $\lambda=1$ and $\lambda=2$ phonon modes and the cavity resonance. The two polariton gaps (see text) are denoted as $\Delta_{1}$ and $\Delta_{2}$. d,g, Phonon Hopfield coefficients (H.C.) of the LP as a function of cavity frequency, showing a divergence in the low cavity frequency limit. e,h, Theoretical predictions: Equal-time second-order phonon--phonon correlation functions $g^{(2)}_{\lambda,\lambda'} (\tau=0)$ for a polariton thermal state at room temperature as a function of cavity frequency. The inset in (e) shows $g^{(2)}_{\lambda,\lambda'} (0)$ as a function of temperature $T$ for a cavity frequency of 0.1 THz.