Exciton-Exciton and Exciton-Photon Annihilation in Polaritonic Systems

Abstract

Strong light--matter interactions forming hybrid quasiparticles termed polaritons can specifically tailor molecular photophysics. In this spirit, enhancing energy transport has recently been of special interest. Exciton--exciton annihilation is commonly used to quantify energy transfer in excitonic systems, and has been recently applied to investigate transport dynamics in polaritonic systems. However, the interpretation of experimental findings is challenging without a microscopic theory that accounts for the various nonradiative relaxation channels determining the quasiparticle diffusion length. In this work, we develop a microscopic model for polariton annihilation based on exciton--exciton annihilation and propose an exciton--photon annihilation as the decisive process that competes with exciton--exciton annihilation. The interplay between exciton--exciton and exciton--photon annihilation ultimately governs the annihilation dynamics and sets the fundamental limit to the transport efficiency. Our model explains recent experimental results and demonstrates that increased annihilation rates might serve as an explicit fingerprint to differentiate between the response of polaritons and other untargeted effects.

Figures (4)

• Figure 1: Microscopic representations of exciton--exciton and exciton--photon annihilation in polaritonic systems. Either two singly excited molecules couple resonantly through Coulomb interactions with coupling strength $K$ or a singly excited molecule and a cavity photon couple resonantly through light--matter interactions with coupling strength $g_f$ such that a highly excited molecular state is formed by both processes. Subsequently, the resulting excited molecular state undergoes fast internal conversion with rate $1/\tau_\mathrm{nr}$ into the first excited molecular state.
• Figure 2: Exciton--exciton and exciton--photon annihilation rates as functions of molecular number and collective light–matter coupling strength. (a) Exciton--exciton $\Gamma_\text{ex-ex}$ and exciton--photon $\Gamma_\text{ex-ph}$ annihilation rates depending on the inverse number of coupled molecules for typical parameters of a system in the strong light--matter coupling regime. The inset shows the dependence of the ratio of both annihilation rates on the number of coupled molecules. (b) Ratio of exciton--photon and exciton--exciton annihilation rates depending on the number of coupled molecules for various values of the collective light--matter coupling strength. For a given number of molecules $N$, the resonance energy of the cavity is always tuned to the first eigenstate of the molecular Hamiltonian $H_m$.
• Figure 3: Ratio of exciton--photon and exciton--exciton annihilation rates depending on the system parameters, i.e., the magnitude of the effective transition dipole moment from the ground to the first excited state $\mu_{eg}$ of the molecules and the effective vacuum electric field strength of the quantized field $\epsilon$. Three cases are considered, where the resonance energy of the cavity is (a) tuned to the first eigenstate of the molecular Hamiltonian $H_m$, (b) negatively detuned, or (c) positively detuned.
• Figure 4: Effect of detuning between the cavity and the molecular subsystem. (a) Dependence of the exciton--photon and exciton--exciton annihilation rates on the detuning between the cavity and the molecular subsystem with system parameters $\mu_{eg}=\sqrt{0.1\ \mathrm{eV}}$ and $\epsilon=\sqrt{0.1\ \mathrm{eV}}$. (b) Dependence of the Boltzmann averaged state character on the detuning between the cavity and the molecular subsystem with the same system parameters as in (a). The Boltzmann averaged state character is defined by $P_I = \sum_\alpha \frac{1}{Z}e^{-\frac{\omega_{\alpha}}{k_BT}} \sum_{i\in I} |c^{(\alpha)}_i|^2$, where $I$ is an index set indexing either purely photonic ($|2,0\rangle$), exciton--photon ($|1,e_i\rangle$), or purely molecular ($|0,e_ie_j\rangle$) basis states.