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arXiv:2312.00757 · APL Photonics

Giant microwave–optical Kerr nonlinearity via Rydberg excitons in cuprous oxide

Jon D. Pritchett, Liam A. P. Gallagher, Alistair Brewin, Horatio Q. X. Wong, W. Langbein, Stephen A. Lynch, Charles S. Adams, M. P. A. Jones

Published Mar 1, 2024• 9 citations
arXivHTMLPDF

Abstract

Microwave–optical conversion is key to future networks of quantum devices, such as those based on superconducting technology. Conversion at the single quantum level requires strong nonlinearity, high bandwidth, and compatibility with a millikelvin environment. A large nonlinearity is observed in Rydberg atoms, but combining atomic gases with dilution refrigerators is technically challenging. Here, we demonstrate a strong microwave–optical nonlinearity in a cryogenic, solid-state system by exploiting Rydberg states of excitons in Cu2O. We measure a microwave–optical cross-Kerr coefficient of B0 = 0.022 ± 0.008 m V−2 at 4 K, which is several orders of magnitude larger than other solid-state systems. The results are in quantitative agreement with a nonlinear susceptibility model based on the giant microwave dipole moment between nearby excitonic states. Our results highlight the potential of Rydberg excitons for nonlinear optics and form the basis for a microwave–optical frequency converter based on Cu2O.

DOI
10.1063/5.0192710

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Microwave–optical conversion is key to future networks of quantum devices, such as those based on superconducting technology. Conversion at the single quantum level requires strong nonlinearity, high bandwidth, and compatibility with a millikelvin environment. A large nonlinearity is observed in Rydberg atoms, but combining atomic gases with dilution refrigerators is technically challenging. Here, we demonstrate a strong microwave–optical nonlinearity in a cryogenic, solid-state system by exploiting Rydberg states of excitons in Cu2O. We measure a microwave–optical cross-Kerr coefficient of B0 = 0.022 ± 0.008 m V−2 at 4 K, which is several orders of magnitude larger than other solid-state systems. The results are in quantitative agreement with a nonlinear susceptibility model based on the giant microwave dipole moment between nearby excitonic states. Our results highlight the potential of Rydberg excitons for nonlinear optics and form the basis for a microwave–optical frequency converter based on Cu2O.
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.
The primary objective of this thesis is to investigate the feasibility of cuprous oxide (cuprite) as a competitive platform for microwave-to-optical conversion utilising Rydberg excitons. While the ultimate goal is the simultaneous enhancement of both microwave and optical domains to reach the strong-coupling regime, this work focuses on characterising the two domains independently to establish the necessary foundational parameters. The approach follows a two-pronged strategy: increasing the optical field interaction by embedding cuprite within a Fabry-Pérot microcavity and, in parallel, enhancing the microwave field through integration of cuprite with superconducting microwave resonators. Within the microcavity, high-resolution spectroscopy enabled the resolution of Rydberg resonances as high as 17P. A coupled-oscillator model fitting confirmed the achievement of the strong-coupling regime for states n≤4n \leq 4n≤4. In the second-harmonic generation regime, the microcavity facilitated the identification of doubly resonant locations satisfying the quasi-phase matching conditions required to simultaneously enhance the pump field and the SHG output. This architecture permitted the observation of Rydberg states up to 10D, the highest reported to date in a microcavity sample and revealed significant cavity-induced splittings of the 3S and 3D excitonic resonances. Microwave field confinement was addressed through the development of superconducting lumped-element resonators. A nested split-ring resonator design achieved peak electric field intensities exceeding 1.2×1061.2 \times 10^61.2×106 V/m and a sub-wavelength mode volume of Vm≈2156V_m \approx 2156Vm​≈2156 $\upmu\mathrm{m}^3$, satisfying the high-confinement requirements for efficient microwave-to-optical coupling. Leveraging the multi-mode response of this platform, we provide the first reported measurement of cuprite's relative permittivity at microwave frequencies and sub-Kelvin temperatures of εr=6.66±0.08\varepsilon_r = 6.66 \pm 0.08εr​=6.66±0.08. Furthermore, the loss tangent of cuprite was constrained to the 10−510^{-5}10−5-10−410^{-4}10−4 range using a lumped-element interdigitated capacitor resonator architecture. The convergence of these optical and microwave architectures provides a definitive roadmap for a hybrid quantum system where Rydberg excitons couple concurrently to both domains. By accessing high-n states within a co-localized field geometry, this work establishes the engineering strategies necessary to realise scalable, cuprite-based quantum transduction devices for next-generation communication systems.
Rydberg excitons are, with their ultrastrong mutual interactions, giant optical nonlinearities, and very high sensitivity to external fields, promising for applications in quantum sensing and nonlinear optics at the single-photon level. To design quantum applications it is necessary to know how Rydberg excitons and other excited states relax to lower-lying exciton states. Here, we present photoluminescence excitation spectroscopy as a method to probe transition probabilities from various excitonic states in cuprous oxide. We show giant Rydberg excitons at T=38T=38T=38 mK with principal quantum numbers up to n=30n=30n=30, corresponding to a calculated diameter of $3\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{m}$.
We experimentally demonstrate an effective interaction between telecommunication-wavelength optical photons and microwave photons, mediated by Rydberg atoms. A microwave-induced giant cross-Kerr effect is observed in a 85Rb{}^{85}\mathrm{Rb}85Rb vapor cell by our probing higher excited atomic states at the optical telecommunication band, and the measured third-order cross-Kerr coefficient ${\ensuremath{\chi}}^{(3)}$ can reach approximately $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}\phantom{\rule{0.2em}{0ex}}{\mathrm{m}}^{2}/{\mathrm{V}}^{2}$. These results can be applied to information processing of the integration of wireless and fiber-optic networks in the classical regime or the quantum regime.
By mapping photons into the sample of cuprous oxide with Rydberg excitons, it is possible to obtain a significant optical phase shift due to third-order cross-Kerr nonlinearities realized under the conditions of electromagnetically induced transparency. The optimum conditions for observation of the phase shift over π in Rydberg excitons media are examined. A discussion of the application of the cross-phase modulations in the field of all-optical quantum information processing in solid-state systems is presented.