Real-Time Formation of a Landau Polaron

Abstract

Polarons are electronic excitations dressed by a self-consistent lattice distortion, yet their formation has not been directly resolved in real time. We develop a microscopic lineshape framework that connects the growth of a collective lattice polarization to the population-time evolution of the anti-diagonal linewidth in coherent multidimensional spectroscopy. Within this formalism, the anti-diagonal linewidth directly tracks the decay of lattice frequency-frequency correlations. Underdamped phonon environments produce oscillatory linewidth modulation, whereas overdamped collective polarization dynamics generate monotonic exponential broadening. Applying this framework to multidimensional measurements on perovskite quantum dots, we show that the observed approximately 150 femtosecond exponential anti-diagonal broadening reflects the decay of a collective polarization order parameter. These results establish anti-diagonal linewidth dynamics as a direct real-time signature of Landau polaron formation.

Figures (3)

• Figure 1: Distinction between normal-mode phonons and collective polarization dynamics. (a) In crystalline semiconductors such as CdSe, lattice excitations are well-defined normal modes. (b) Time-domain Raman spectrum of CdSe quantum dots obtained by Fourier transforming transient absorption oscillations, showing sharp acoustic and optical phonons with negligible low-frequency spectral weight. (c) Displaced harmonic oscillator model illustrating coherent phonon dressing: excitation impulsively shifts a normal-mode coordinate, producing reversible oscillatory modulation of the transition energy. (d) In halide perovskites, lattice response is dominated by dynamically soft, anharmonic fluctuations rather than discrete modes. (e) Corresponding spectral density extracted from CMDS and transient absorption exhibits broad low-frequency weight extending to zero frequency, indicative of overdamped fluctuations. (f) Configuration coordinate for a collective polarization field: following excitation, the lattice evolves diffusively toward a self-consistent distortion rather than oscillating coherently. This overdamped regime enables Landau polaron formation.
• Figure 2: Stochastic dynamics of an overdamped lattice order parameter. (a) Representative time evolution of a normalized lattice order parameter following excitation, illustrating a characteristic reorganization time, following solution of Eq. (5). (b) Sample stochastic trajectories of transition-frequency fluctuations generated by an Ornstein–Uhlenbeck process with correlation time $\tau_{\mathrm{pol}}$. (c) Autocorrelation functions of the trajectories in (b), converging to exponential decay $C(t)=\exp(-t/\tau_{\mathrm{pol}})$. Exponential memory loss of the order parameter produces monotonic anti-diagonal linewidth growth within cumulant lineshape theory.
• Figure 3: Connection between correlation decay and multidimensional lineshape evolution. (a) CMDS pulse sequence consisting of three phase-resolved electric fields shown above the time axis. The first pulse creates a coherence, the second converts it to a population that evolves during waiting time $t_{2}$ under system–bath interactions, and the third converts the evolved state into a radiated third-order polarization. Frequency correlations accumulated during $t_{2}$ determine the anti-diagonal linewidth. (b) Calculated two-dimensional spectra at early and late $t_{2}$. Initially, excitation and emission frequencies are correlated, producing a diagonally elongated spectrum with narrow anti-diagonal width. As correlations decay, the spectrum becomes more circular and the anti-diagonal width increases, reflecting spectral diffusion governed by $C(t_{2})$. (c) Measured and modeled frequency–frequency correlation functions for perovskite and CdSe quantum dots. Perovskites exhibit monotonic exponential decay consistent with overdamped collective polarization dynamics, whereas CdSe shows weak decay with oscillatory structure characteristic of coherent LO phonons. (d) Population-time evolution of the anti-diagonal linewidth. The solid curves are calculated from Eq. (8) using the correlation functions in panel (c), and symbols represent experimental measurements. Perovskites exhibit monotonic linewidth growth governed by exponential correlation decay, whereas CdSe shows oscillatory modulation without cumulative broadening. The agreement demonstrates that the observed linewidth dynamics directly reflect the underlying correlation functions and constitute a real-time signature of Landau polaron formation.