Resolving exciton and polariton multi-particle correlations in an optical microcavity in the strong coupling regime

TL;DR

The paper investigates how multi-particle correlations among excitons, polaritons, and reservoir states govern ultrafast dynamics in strongly coupled microcavities based on 2D metal-halide perovskites. Using two-dimensional coherent spectroscopy (1Q and 2Q) and a dark-continuum scattering framework, it resolves interactions between lower polaritons, bright excitons, and reservoir states that drive polariton condensation. Key findings include ultrafast population transfer from higher-energy polaritons and reservoir populations to the lower polariton within ~100–150 fs, enhanced exciton-exciton annihilation in the cavity, and clear LP–X_A and LP–MP1 correlations indicating reservoir-mediated two-particle scattering. The results highlight the importance of beyond-mean-field fluctuations and scattering via a dark exciton continuum for polariton condensation and provide experimental signatures and rates to guide refined theories.

Abstract

Multi-particle correlations of exciton-polaritons and reservoir-excitons in the strong light-matter coupling regime dictate the quantum dynamics of optical microcavities. In this letter, we examine the many-body exciton-polariton dynamics in a Fabry-Pérot microcavity of a two-dimensional metal-halide semiconductor over timescales involving polariton ($\ll 1$\,ps) and exciton ($\gg 1$\,ps) scattering. We find enhanced exciton nonlinear dynamics in the microcavity versus the bare semiconductor, concomitant with ultrafast polariton scattering dynamics. We measure, by means of coherent spectroscopy, the coupling between exciton-polaritons, bright excitons, and reservoir-excitons that highlight the complex scattering landscape that fundamentally drives polariton condensation.

Figures (15)

• Figure 1: (a) Schematic representation of competing mechanisms populating and depopulating the lower-polariton $\vec{k}_\parallel=\vec{0}$ state (LP: lower polariton, UP: upper polariton). (b) Fabry-Pérot microcavity consisting of a distributed Bragg reflector (10.5 quarter-wave bilayers of TiO$_2$/SiO$_2$, central wavelength 520 nm), a 60-nm (PEA)$_2$PbI$_4$ film, a 125-nm poly(methylmethacrylate) spacer layer, and a 40-nm Ag film. (c) The reflectance energy dispersion at 5 K (right panel). The left panel includes the absorption (solid line) and photoluminescence (dashed line) spectra of (PEA)$_2$PbI$_4$.
• Figure 2: (a-c) Normalized photoluminescence energy dispersion at distinct incident excitation fluences. (d) Fluence dependence of the maximum PL intensity ($I_\text{PL,max}$) for various $\vec{k}_{\parallel}$. (e-f) Fraction of nonlinear PL ($\Delta$I$_\mathrm{PL}$/I$_\mathrm{PL}$), measured via ECPL, in a bare (PEA)$_2$PbI$_4$ film and the microcavity. The PL energy dispersion and the ECPL experiments share the same non-resonant excitation (2.638 eV, 200 fs) and collection conditions; however, for the ECPL measurements, we integrate the PL of the entire lower polariton branch.
• Figure 3: 1Q rephasing spectra at 10 K, where the absolute and real components at population times ($t_{\mathrm{pop}}$) of 20 fs and 140 fs are shown in (a-b) and (d-e), respectively. The dashed line corresponds to a cut along the emission energy axis at 2.342 eV. (c-f) Laser spectrum superposed with the normalized (1-R) of the microcavity at $\Vec{k}=\Vec{0}$. The population evolution of the absolute component is summarized by tracking the (g) contour of the LP, (h) the cut along the diagonal, and (i) the vertical cut marked in (a). (j) In the experimental setup, the pulses are arranged in a BoxCARS geometry (left) and time-ordered for phase-matching corresponding to the 1Q rephasing spectra (right). The pulses excite the sample at an angle of 2.3 $^\circ$, which corresponds to $|\vec{k}_\parallel | =0.92\,\mu\mathrm{m}^{-1}$.
• Figure 4: (a) Absolute, (b) real, and (c) imaginary components of the 2Q non-rephasing spectra measured at $t_\mathrm{1Q}=20$ fs. (d) A cut along the emission energy axis reveals two cross-peaks with energies 32 meV (green diamond) and 65 meV (purple diamond). (e) Schematic of a two-quantum non-rephasing spectrum of a system with LP--$X_\text{A}$ and LP--MP$_\mathrm{1}$ interactions, which manifest as cross-peaks with 2Q excitation energies of $E_\mathrm{LP}+E_{X_\mathrm{\text{A}}}$ and $E_\mathrm{LP}+E_\mathrm{MP}$, as indicated with green and purple diamonds respectively. (f) Schematic representation of the pulse sequence employed to measure the 2Q nonrephasing spectra, using the same phase matching of the BoxCARS geometry displayed in Fig. \ref{['fig:1Q']}(h).
• Figure S1: Hopfield coefficients of the polariton eigenstates. They were calculated by numerically diagonalizing the Hamiltonian (1) of the main text using the numerical package, Qutip. The simulation details are discussed in the text above.