Symmetry-Controlled Ultrastrong Phonon-Photon Coupling in a Terahertz Cavity

TL;DR

This work addresses in situ tunability of ultrastrong light–matter coupling, i.e., $g$, across a symmetry-changing phase transition in MAPbI3. The authors use MAPbI3 in nanoslot terahertz cavities and THz spectroscopy, analyzed with a multimode Hopfield model that includes the $A^2$ diamagnetic term to describe coupled cavity-phonon spectra. They observe three polariton branches above $T_c$ and a fourth branch below $T_c$ owing to the activation of a third phonon, with normalized couplings $g_1/
=6$, $g_2/=4$ above $T_c$ and $g_1/
=8$, $g_2/=6$, $g_3/=5$ below $T_c$. The results demonstrate symmetry-controlled USC and offer a route to phonon-engineered functional materials in perovskites and related systems.

Abstract

Optical cavities provide a powerful means to engineer light-matter hybrid states by coupling confined electromagnetic fields with matter excitations. Achieving in situ control of the coupling strength is essential for investigating how such hybridization evolves with the coupling strength. In this work, we use a symmetry-changing structural phase transition in lead halide perovskites to reversibly tune the phonon-photon coupling strength, leveraging the fact that their phonon frequencies and oscillator strengths are dictated by lattice symmetry. Terahertz time-domain spectroscopy of MAPbI3 embedded in nanoslot cavities reveals three polariton branches above the critical temperature Tc = 162.5 K, and the emergence of an additional branch below Tc, activated by a new phonon mode in the low-temperature phase. The full dispersion is accurately reproduced using a multimode Hopfield model, confirming that all normalized coupling strengths remain in the ultrastrong coupling regime. These results demonstrate symmetry-controlled tuning of ultrastrong coupling via phonon engineering in optical cavities.

Figures (5)

• Figure 1: Temperature-dependent terahertz transmission spectra of MAPbI$_3$. Upper: Bare MAPbI$_3$ film showing two phonon modes at around 0.95 THz and 1.78 THz in the tetragonal phase (165 K) and three modes in the orthorhombic phase (below $T_\text{c}$ = 162.5 K) due to structural splitting of Pb--I vibrations. Lower: Transmission of a nanoslot cavity ($l =$ 60 $\upmu$m) exhibiting a resonance at 1.52 THz.
• Figure 2: THz transmission maps of MAPbI$_3$--nanoslot hybrid systems. (a) Schematic illustration of the hybrid structure. (b) The dependence of the cavity resonance frequency on nanoslot length $l$. (c) Normalized transmittance color maps at 165 K (tetragonal) and 151 K (orthorhombic), respectively. Three polaritonic branches, lower (LP), middle (MP), and upper (UP), arise from the ultrastrong coupling of the cavity mode with phonon modes TO$_1$ and TO$_2$; below $T_\text{c}$ a new branch appears near 0.83 THz, indicating coupling with the emergent third phonon mode.
• Figure 3: Polaritonic dispersion as a function of the cavity frequency for $T =\unit[165]{K} > T_\textrm{c}$, calculated by numerical diagonalization of Eq. \ref{['eq:hamiltonian']}, and compared with the experimental data (black markers). (a) The colour scale encodes the photonic (yellow) and phononic (green) content of each polaritonic eigenmode $\alpha$, quantified by the fractions $\sum_\lambda \mathcal{F}^\mathrm{ph}_{\lambda,\alpha}$ and $\mathcal{F}^\mathrm{pt}_{\alpha}$, respectively. In (b), the colours scale represents the phononic contribution from the $\textrm{TO}_1$ mode to each polariton branch $\mathcal{F}^\mathrm{ph}_{\lambda=1,\alpha}$. (a, b) Dashed lines indicate the uncoupled cavity and bare phonon-mode frequencies. The transverse--optical phonons are located at $\omega_1=\unit[0.95]{THz}$ and $\omega_2=\unit[1.78]{THz}$. The coupling strengths $g_\lambda$ reported in the main text are then obtained by fitting the calculated dispersion to these experimental data.
• Figure 4: Polaritonic dispersion as a function of the cavity frequency, calculated by numerical diagonalization of Eq. \ref{['eq:hamiltonian']}, and compared with the experimental data (black markers), simirally as Fig. \ref{['fig:fitting_data_hopfield_high_t']}, but for $T =\unit[151]{K} < T_\textrm{c}$. The colours scale represents the phononic contribution from the $\textrm{TO}_1$ (a) and $\textrm{TO}_3$ (b) modes to each polariton branch. Here, the transverse--optical phonons are located at $\omega_1=\unit[0.98]{THz}$, $\omega_2=\unit[1.7]{THz}$ and $\omega_3=\unit[0.77]{THz}$.
• Figure 5: Temperature-dependent THz transmission spectra of hybrid systems with cavity frequencies $\omega_\text{c}=1.2$ THz and 2.2 THz. Each color map shows the evolution of polariton branches as the sample is heated through the tetragonal–orthorhombic transition near $T_\text{c}\simeq$ 162.5 K, indicated by vertical dashed lines. Some of the polariton branches gradually disappear or saturate above $T_\text{c}$. Despite the markedly different light--matter hybridization conditions, the transition occurs at approximately the same temperature within the 2 K experimental uncertainty.