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Entropy

Electromagnetically Induced Transparency in Media with Rydberg Excitons 2: Cross-Kerr Modulation

David Ziemkiewicz, Sylwia Zielińska‐Raczyńska

Published Jan 30, 2020• 6 citations
Publisher

Abstract

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.

DOI
10.3390/e22020160

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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.
In third order nonlinear mediums, the intensity of one optical field can modify the phase of another optical field. This is known as cross-phase modulation (XPM) and is important for Quantum Information Processing (QIP) as phase shifts of single-photons that exceed π rad can be used to implement two-qubit quantum logic gates. For a conventional XPM scheme, the Kerr nonlinearity responsible for XPM is too small for appreciable phase shifts to be achieved with low intensity optical fields. However, Electromagnetically Induced Transparency (EIT) can increase this nonlinearity by several orders of magnitude. This thesis discusses the experimental construction of a laser-atomic system capable of EIT modulated XPM. This includes construction of a rubidium magneto-optical trap (RbMOT), characterization of this RbMOT, demonstration of EIT in the RbMOT, and a system capable of detecting optical phase shifts produced by EIT. The talk will conclude with an outlook on further implementations to the experiment that will increase this nonlinearity such that phase shifts at the single-photon level are possible. | 76 pages
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.
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.
A four-level inverted-Y scheme with an electromagnetically induced transparency (EIT) core is investigated for the enhancement of cross-Kerr effect in rubidium atoms. When detunings of the coupling and control fields are appropriately set, an enhanced EIT window is observed, and the induced phase shift of the probe field due to cross-phase modulation (XPM) is obtained by measuring the dispersive property of the probe transition. The maximal XPM phase shift is about 12° under the current experimental conditions. The experimental measurements agree well with the theoretical calculations. The enhanced XPM phase shift in such an atomic system has applications in quantum nonlinear optics and quantum information science.