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Optical Properties of Rydberg Excitons

Sylwia Zielińska‐Raczyńska, G. Czajkowski, David Ziemkiewicz

Published Nov 27, 2015• 0 citations
OpenAlex

Abstract

We show how to compute the optical functions when Rydberg Excitons appear, including the effect of the coherence between the electron-hole pair and the electromagnetic field. We use the Real Density Matrix Approach (RDMA), which, combined with Green's function method, enables one to derive analytical expressions for the optical functions. Choosing the susceptibility, we performed numerical calculations appropriate to a Cu$_2$0 crystal. The effect of the coherence is displayed in the line shape. We also examine in details and explain the dependence of the oscillator strength and the resonance placement on the state number. We report a good agreement with recently published experimental data.

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We show how to compute the optical functions when Rydberg Excitons appear, including the effect of the coherence between the electron-hole pair and the electromagnetic field. We use the Real Density Matrix Approach (RDMA), which, combined with Green's function method, enables one to derive analytical expressions for the optical functions. Choosing the susceptibility, we performed numerical calculations appropriate to a Cu2_22​0 crystal. The effect of the coherence is displayed in the line shape. We also examine in details and explain the dependence of the oscillator strength and the resonance placement on the state number. We report a good agreement with recently published experimental data.
We show how to compute the nonlinear optical functions (absorption, reflection, and transmission) for a medium with Rydberg excitons (REs), including the effect of the coherence between the electron-hole pair and the electromagnetic field. Using the real density-matrix approach the analytical expressions for nonlinear optical functions are obtained and numerical calculations are performed for Cu2O{\mathrm{Cu}}_{2}\mathrm{O}Cu2​O crystal where REs have been observed. We report a good agreement with recently published experimental data. Propagation of the electromagnetic waves in Rydberg exciton media with nonlinear effect is also discussed and the possibility of obtaining self-phase modulation due to Kerr nonlinearity is investigated.
Dynamics of Cu2_22​O Rydberg excitons -- real density matrix approach
Basing on recent reliable measurements of the life- and coherence time of Cu2_22​O Rydberg excitons, we present an analytical method which enables to describe the experimental results. The real-density matrix approach (RDMA) is applied to describe two-photon absorption in Cu2_22​O through the excitonic response to the exciting fields. This approach produces an analytical expression for the emission intensity time evolution, and can be used to explain trends in reported experimental data. Our approach takes into account the effect of the coherence between the electron-hole pair and the electromagnetic fields, the quantum beats and the life- and coherence time dependence on the applied laser power. Adding a separation of slow- and rapid dynamics components we find excellent agreement with the experimental data.
The quantum confinement of Rydberg excitons (REs) in quantum structures opens the way towards considering nonlinear interactions in such systems. We present a theoretical calculation of optical functions in the case of a nonlinear coupling between REs in a quantum well with an electromagnetic wave. Using the real density matrix approach (RDMA), the analytical expressions for a linear and nonlinear absorption are derived and numerical calculations for Cu2O{\mathrm{Cu}}_{2}\mathrm{O}Cu2​O quantum wells are performed. The results indicate the conditions in which quantum well confinement states can be observed in linear and nonlinear optical spectra. The Kerr nonlinearity and self-phase modulation in such a system are studied. The effect of the Rydberg blockade and the associated optical bleaching are also discussed and confronted with available experimental data.
We theoretically investigate the nonlinear optical transmission through a cuprous oxide crystal for wavelengths that cover the series of highly excited excitons, observed in recent experiments. Since such Rydberg excitons have strong van der Waals interactions, they can dynamically break the conditions for resonant exciton creation and dramatically modify the refractive index of the material in a nonlinear manner. We explore this mechanism theoretically and determine its effects on the optical properties of a semiconductor for the case of degenerate pair-state asymptotes of Rydberg excitons in Cu_{2}O. Upon analyzing the additional effects of a dilute residual electron-hole plasma, we find quantitative agreement with previous transmission measurements, which provides strong indications for the enhancement of Rydberg-induced nonlinearities by surrounding free charges.
The theory of the coherent pairing of excitons in the presence of a resonant electromagnetic field is generalized to describe the biexciton spectra of molecular crystals, which contain several molecules (atoms) in the unit cell. The excitation spectrum for crystals like anthracene having two molecules per unit cell is discussed in detail. It is found that, at high exciton densities and under resonance of near-resonance conditions and at temperatures below some value T c , the formation of four biexciton states is feasible provided that the dielectric gaps induced by the electromagnetic field are less than those of the corresponding biexciton states. Expressions for the absorption coefficient describing optical transitions to the biexciton states are derived.