Stability of the Quantum Coherent Superradiant States in Relation to Exciton-Phonon Interactions and the Fundamental Soliton in Hybrid Perovskites

TL;DR

This work develops a coordinate-space description of a quasi-2D Wannier exciton in hybrid perovskites interacting with phonons, leading to a 2D nonlocal nonlinear Schrödinger equation for the lowest exciton state. A linear stability analysis of plane-wave (superradiant) solutions reveals a modulational-instability threshold set by the exciton-LO phonon coupling, with a critical intensity $ ho_{cr}$ that can be made independent of the wave number in the small-$k$ limit. Extending to include acoustic phonons, the model acquires a local nonlinear term that reduces the stability window, while numerical results validate the analytical MI criteria and confirm the existence and stability of a fundamental 2D soliton in polar coordinates. The results illuminate how exciton-phonon interactions shape the stability and localization of superradiant states in hybrid perovskites, suggesting a route to robust room-temperature coherent states and soliton-based SF regimes.

Abstract

The use of macroscopic coherent quantum states at room temperature is crucial in modern quantum technologies. In light of recent experiments demonstrating high-temperature superfluorescence in hybrid perovskite thin films, in this work we investigate the stability of the superradiant state concerning exciton-phonon interactions. We focused on a quasi-2D Wannier exciton interacting with longitudinal optical (LO) phonons in polar crystals, as well as with acoustic phonons. Our study leads to the derivation of nonlinear equations in the coordinate space that govern the exciton wavefunction's coefficient in the single-exciton basis for the lowest exciton state, which translates to the complex-valued polarization. The resulting equations take the form of a 2D nonlocal nonlinear Schrodinger (NLS) equation. We perform a linear stability analysis of the plane wave solutions for the equations in question, which allows us to establish stability criteria. This analysis is particularly important for evaluating the stability of the superradiant state in the considered quasi-2D structures, as the superradiant state represents a specific case of the plane wave solution. Our findings indicate that, when the exciton interacts with LO phonons, a plane wave solution is modulationally stable, provided that the square of its amplitude does not exceed a critical intensity value defined by the exciton-LO phonon interaction parameters. Furthermore, interactions between the exciton and acoustic phonons reduce the intensity of modulationally stable waves compared to the case without such interactions. Our analytical results are corroborated by numerical calculations. We also numerically solve the 2D nonlocal NLS equation in the polar coordinates and obtain its fundamental soliton solution, which is stable.

Figures (14)

• Figure 1: The parameter of the exciton-phonon interaction $\omega _{0}(R_{m^{\prime}m})$ (in arbitrary units) as a function of $y=R_{m^{\prime }m}/a_{0}$ for $p_{e}\equiv m_{r}/m_{e}^{\ast}=2/3$ and $p_{h}\equiv m_{r}/m_{h}^{\ast}=1/3$, where $1/m_{r}=1/m_{e}^{\ast}+1/m_{h}^{\ast}$ is the inverse reduced mass.
• Figure 2: Modulus of $\tilde{C}_{0}(\tilde{x},\tilde{y},t)$ at $t=0$, $\tilde{C}_{0}(\tilde{x},\tilde{y},0)=\sqrt{\rho_{0}}\left[ 1+0.01\cdot noise\left( \tilde{x},\tilde{y}\right) \right]$, (a); $t=1.48\cdot 10^{\mathbf{-}15}s$ (b), $t=3.69\cdot10^{\mathbf{-}14}s$ (c), $t=7.39\cdot 10^{\mathbf{-}14}s$ (d) and $t=1.11\cdot10^{\mathbf{-}13}s$ (e) for subcritical case ($\rho_{0}=0.5\rho_{cr,0}$) in dimensionless coordinates.
• Figure 3: Square of dimensionless increment $(\lambda\tau)^{2}$, Eq.(\ref{['eq:lambda^2']}), as a function of wave intensity $\rho_{0}$ and $kD$. Calculations using exact formula Eq.(\ref{['eq:rho_cr']}) (a,c), and the long-wave limit (small $k$) Eq.(\ref{['eq:(rho_0)_cr2']}) (b). The green line is drawn at the level $\rho_{0}=0.5\rho_{cr,0}$, the yellow line - at the level $\rho _{0}=\rho_{cr,0}$, and the red line - at the level $\rho_{0}=10\rho_{cr,0}$ (a,c). The blue line is drawn at the level $(\lambda\tau)^{2}=0$ (c).
• Figure 4: Modulus of $\tilde{C}_{0}(\tilde{x},\tilde{y},t)$ at $t=0$, $\tilde{C}_{0}(\tilde{x},\tilde{y},0)=\sqrt{\rho_{0}}\left[ 1+0.01\cdot noise\left( \tilde{x},\tilde{y}\right) \right]$, (a); $t=1.48\cdot 10^{\mathbf{-}13}s$ (b), $t=\tau_{0}/2$ (c), $t=\tau_{0}$ (d) and $t=2\tau _{0}$ (e) for supercritical case ($\rho_{0}=10\rho_{cr}$) in dimensionless coordinates.
• Figure 5: Function $r^{3}\omega_{0}(r)$ (in arbitrary units) as a function of $y=r/a_{0}$ for $p_{e}=2/3$ and $p_{h}=1/3$.