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Physical Review Letters

Self-Kerr Effect across the Yellow Rydberg Series of Excitons in Cu2O

Corentin Morin, J. Tignon, Juliette Mangeney, Sukhdeep S. Dhillon, G. Czajkowski, Karol Karpiński, Sylwia Zielińska‐Raczyńska, David Ziemkiewicz, Thomas Boulier

Published Sep 19, 2022• 23 citations
Publisher

Abstract

We investigate the nonlinear refraction induced by Rydberg excitons in Cu_{2}O. Using a high-precision interferometry imaging technique that spatially resolves the nonlinear phase shift, we observe significant shifts at extremely low laser intensity near each exciton resonance. From this, we derive the nonlinear index n_{2}, present the n_{2} spectrum for principal quantum numbers n≥5, and report large n_{2} values of order 10^{-3} mm^{2}/mW. Moreover, we observe a rapid saturation of the Kerr nonlinearity and find that the saturation intensity I_{sat} decreases as n^{-7}. We explain this with the Rydberg blockade mechanism, whereby giant Rydberg interactions limit the exciton density, resulting in a maximum phase shift of 0.5 rad in our setup.

DOI
10.1103/physrevlett.129.137401

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We investigate the nonlinear refraction induced by Rydberg excitons in Cu_{2}O. Using a high-precision interferometry imaging technique that spatially resolves the nonlinear phase shift, we observe significant shifts at extremely low laser intensity near each exciton resonance. From this, we derive the nonlinear index n_{2}, present the n_{2} spectrum for principal quantum numbers n≥5, and report large n_{2} values of order 10^{-3} mm^{2}/mW. Moreover, we observe a rapid saturation of the Kerr nonlinearity and find that the saturation intensity I_{sat} decreases as n^{-7}. We explain this with the Rydberg blockade mechanism, whereby giant Rydberg interactions limit the exciton density, resulting in a maximum phase shift of 0.5 rad in our setup.
Self-Kerr effect across the yellow Cu2O\mathrm{Cu_2O}Cu2​O Rydberg series
We investigate the nonlinear refraction induced by Rydberg excitons in Cu2O\mathrm{Cu_2O}Cu2​O. Using a high-precision interferometry imaging technique that spatially resolves the nonlinear phase shift, we observe significant shifts at extremely low laser intensity near each exciton resonance. From this, we derive the nonlinear index n2\mathrm{n_2}n2​, present the n2\mathrm{n_2}n2​ spectrum for n≥5n\geq 5n≥5 and report large n2\mathrm{n_2}n2​ values of order 10−310^{-3}10−3 mm2^22/mW. Moreover, we observe a rapid saturation of the Kerr nonlinearity and find that the saturation intensity Isat\mathrm{I_{sat}}Isat​ decreases as n−7n^{-7}n−7. We explain this with the Rydberg blockade mechanism, whereby giant Rydberg interactions limit the exciton density, resulting in a maximum phase shift of 0.5 rad in our setup.
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.
Abstract Rydberg excitons (analogues of Rydberg atoms in condensed matter systems) are highly excited bound electron-hole states with large Bohr radii. The interaction between them as well as exciton coupling to light may lead to strong optical nonlinearity, with applications in sensing and quantum information processing. Here, we achieve strong effective photon–photon interactions (Kerr-like optical nonlinearity) via the Rydberg blockade phenomenon and the hybridisation of excitons and photons forming polaritons in a Cu2O-filled microresonator. Under pulsed resonant excitation polariton resonance frequencies are renormalised due to the reduction of the photon-exciton coupling with increasing exciton density. Theoretical analysis shows that the Rydberg blockade plays a major role in the experimentally observed scaling of the polariton nonlinearity coefficient as ∝ n4.4±1.8 for principal quantum numbers up to n = 7. Such high principal quantum numbers studied in a polariton system for the first time are essential for realisation of high Rydberg optical nonlinearities, which paves the way towards quantum optical applications and fundamental studies of strongly correlated photonic (polaritonic) states in a solid state system.
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.
We report experimental and theoretical investigations of interacting excitons of the yellow series in cuprous oxide (Cu2_22​O) with principal quantum numbers up to by means of second harmonic generation (SHG). Using picosecond pulsed laser excitation up to 10 GW/cm2^22 peak intensity we observe a pronounced change of the spectra with increasing pump laser intensity: an energetic shift to lower absolute energies and a spectral broadening. The absolute intensities of the spectral lines scale for low powers with the square of the pump power, but saturates at higher powers. At still higher powers the SHG intensity is actually reduced. To explain these results quantitively, we developed a semi-classical theory of resonant SHG where the process of SHG is fully coherent. The excitons are assumed to be bosons interacting by a distance dependent potential giving rise to both the changes in spectral line shape and the saturation by a Rydberg\it{Rydberg}Rydberg blockade. The concomitant measurement of two-photon absorption allows to derive quantitative values for the exciton-exciton interaction. While the results agree in order of magnitude with those calculated by state-of-the art atomic-like van der Waals interaction theory, the scaling with principle quantum number is quite different. As a possible screening by an electron-hole plasma created by three-photon absorption into blue and violet band states could be ruled out, our results point toward fundamental differences between excitons and atoms.