Quantum beats of exciton-polarons in CsPbI3 perovskite nanocrystals

TL;DR

This work demonstrates long-lived coherent exciton–polaron dynamics in CsPbI$_3$ perovskite nanocrystals, manifested as quantum beats between polaron states in two-pulse photon echoes at 2 K. A four-level polaron model with two discrete low-energy optical phonons (3.2 and 5.1 meV) quantitatively captures the observed oscillations, yielding Huang–Rhys factors of order 10$^{-2}$–10$^{-1}$ and phonon lifetimes of a few to ~10 ps. The experiments reveal a strong size dependence of exciton–phonon coupling and phonon lifetimes (scaling roughly as $S_{ m HR}\propto a^{-3}$), enabling tunability of polaronic transitions and coherent optical dynamics. These findings highlight the role of polaron physics in resonant, ultrafast excitations and suggest routes to on-demand coherent control and phonon generation in lead halide perovskite nanocrystals for solid-state quantum technologies.

Abstract

Exciton-phonon interactions govern the energy level spectrum and thus the optical response in semiconductors. In this respect, lead-halide perovskite nanocrystals represent a unique system, for which the interaction with optical phonons is particularly strong, giving rise to a ladder of multiple exciton states which can be optically excited with femtosecond pulses. We establish a new regime of coherent exciton-polaron dynamics with exceptionally long coherence times (T2 ~300 ps) in an ensemble of CsPbI3 nanocrystals embedded in a glass matrix. Using transient two-pulse photon echo at 2 K temperature, we observe quantum beats between the exciton-polaron states. Within a four-level model, we directly quantify the exciton-phonon coupling strength through the Huang-Rhys factors of 0.05-0.1 and 0.02-0.04 for low-energy optical phonons with energies of 3.2 and 5.1 meV, respectively. The pronounced size dependence of both coupling strengths and phonon lifetimes offers a path to tune the optical transitions between polaron states and to tailor the coherent optical dynamics in perovskite semiconductors for solid-state quantum technologies.

Figures (4)

• Figure 1: Photon echoes in CsPbI$_3$ nanocrystals. (a) Typical photoluminescence (PL) spectrum for excitation with photon energy of 2.33 eV. Vertical dashed line indicates the highest photon energy used in the four-wave mixing FWM experiment. The scale on top corresponds to the NC diameter. (b) Schematic representation of the experimental geometry, where the laser pulses hit the sample with wave vectors ${\bf k}_1$, ${\bf k}_2$. The photon echo is detected along the direction $2{\bf k}_2 - {\bf k}_1$ using a heterodyning technique by overlapping it with a reference pulse. Inset shows schematically a CsPbI$_3$ perovskite nanocrystal. (c) Two-dimensional plot of the FWM electric field amplitude $\mathcal{E}^*_{\rm FWM}$ as function of delay between the two pulses $\tau_{12}$ and the reference time $\tau_{\rm ref}$. The photon echo (PE) signal forms at the time $\tau_{\rm ref}=2\tau_{12}$. The amplitude of the PE shows oscillations during the initial evolution when $\tau_{12}$ is scanned. The signal is recorded in linearly co-polarized configuration. Photon energy $h\nu=1.736$eV. (d) Decay of two-pulse photon echo amplitudes for excitation with different photon energies. Black dashed lines are fits with exponential functions, from which the labeld exciton coherence times $T_2$ are extracted. Temperature $T=2$ K.
• Figure 2: Quantum beats of exciton-polarons. (a) Initial range of the PE dynamics in the co-linear ($\|$) and cross-linear ($\times$) polarization configurations shown with blue and red lines, respectively. Photon energy $h\nu=1.746$ eV. The amplitude of the $\times$ signal is multiplied by two for clarity. (b) Dynamics of $\rho$ (black) and $\Sigma$ (green) as defined by Eqs. \ref{['eq:rho']} and \ref{['eq:Sigma']}, respectively. The dashed red curve is a fit using the polaron model with Eq. \ref{['eq:PhononEqs']} with the following parameters for two phonon modes: $\hbar\Omega_1 = 3.2$ meV, $S_{\mathrm{HR1}}=0.097$, $\tau_{\mathrm{ph1}}=5.1$ ps; $\hbar\Omega_2 = 5.1$ meV, $S_{\mathrm{HR2}}=0.032$, $\tau_{\mathrm{ph2}}=10$ ps. (c) Fast Fourier transform (FFT) amplitude spectra of $\rho$ (black), $\Sigma$ (green), and the fit curves in panel (b). Vertical dashed lines mark the peaks corresponding to optical phonons. (d) Raman spectrum measured at photon energy $h\nu=1.734$ eV. Vertical dashed lines indicate the positions of peaks corresponding to the optically active optical phonon modes that couple most strongly to the exciton.
• Figure 3: Level schemes. (a) Energy levels of the bright exciton fine structure. (b) Energy level structure of the excitons interacting with optical phonons. We assume this level structure for each phonon mode, independent of the exciton polarization. The probability of the diagonal transitions is proportional to the Huang-Rhys factor $S_{\rm HR}$. $\gamma_{ph}$ is the phonon decay rate and $\gamma_0$ is the exciton decay rate, mostly determined by its oscillator strength. (c) Sketch of adiabatic potential of an exciton interacting with a particular phonon mode. The solid parabolas represent the potential for phonons for the ground state of the crystal (no exciton, bottom) and the excited state (with one exciton, top). The solid parabolas are separated by the energy difference $E_X$ corresponding to the energy of zero-phonon exciton transition. $\hbar \Omega$ denotes the energy of the optical phonon.
• Figure 4: NC size dependence. Dependence of (a) the Huang-Rhys factor, $S_{\rm{HR}}$, and (b) the phonon lifetime, $\tau_{ph}$, for the two phonon modes with energies $\hbar\Omega_1=3.2$ meV (blue dots) and $\hbar\Omega_2=5.1$ meV (red dots) on NC diameter $a$. Dashed lines in (a) are fits proportional to $a^{-3}$. Dashed lines in (b) are guides to the eye.