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arXiv:2405.14263 · Physical Review A

Optimizing four-wave mixing in Rydberg atoms for microwave-optical conversion

Ning Ji, Yanzhao Liang, Wanrang Yu, Qiuyu Yin, Thibault Vogt

Published Nov 18, 2024• 3 citations
arXivHTMLPDF

Abstract

We perform a numerical and analytical investigation of microwave-to-optical conversion based on four-wave mixing in Rydberg atoms. Our work demonstrates that both all-resonant and off-resonant frequency-mixing configurations achieve near-unit photon conversion efficiencies. We review the conditions that can lead to the presence of two possible dark states. We find that for both configurations, one of the dark states can be detrimental at high microwave powers, and show that an additional limitation to all-resonant frequency mixing is microwave-induced fluorescence. Finally, we confirm that the off-resonant configuration is more appropriate as it allows for efficient photon conversion on a wider range of input microwave intensities with reduced total power of the auxiliary fields.

DOI
10.1103/physreva.110.052608

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We perform a numerical and analytical investigation of microwave-to-optical conversion based on four-wave mixing in Rydberg atoms. Our work demonstrates that both all-resonant and off-resonant frequency-mixing configurations achieve near-unit photon conversion efficiencies. We review the conditions that can lead to the presence of two possible dark states. We find that for both configurations, one of the dark states can be detrimental at high microwave powers, and show that an additional limitation to all-resonant frequency mixing is microwave-induced fluorescence. Finally, we confirm that the off-resonant configuration is more appropriate as it allows for efficient photon conversion on a wider range of input microwave intensities with reduced total power of the auxiliary fields.
We present an experimental demonstration of converting a microwave field to an optical field via frequency mixing in a cloud of cold ^{87}Rb atoms, where the microwave field strongly couples to an electric dipole transition between Rydberg states. We show that the conversion allows the phase information of the microwave field to be coherently transferred to the optical field. With the current energy level scheme and experimental geometry, we achieve a photon-conversion efficiency of ∼0.3% at low microwave intensities and a broad conversion bandwidth of more than 4 MHz. Theoretical simulations agree well with the experimental data, and they indicate that near-unit efficiency is possible in future experiments.
We demonstrate microwave-to-optical conversion using six-wave mixing in cold 87Rb^{87}\mathrm{Rb}87Rb atoms where the microwave field couples to two Rydberg states and propagates collinearly with the converted optical field. Our experiment is performed with a free-space microwave field, and we achieve a conversion efficiency of about 55%5 for the microwave photons entering the conversion medium. In addition, we theoretically investigate all-resonant six-wave mixing and outline a realistic experimental scheme for reaching an efficiency close to 70%.
Abstract We propose an efficient scheme for microwave-to-optical quantum frequency conversion mediated by a single atom simultaneously coupled to a superconducting microwave resonator and an optical cavity. The atom mediates efficient interactions between the two electromagnetic modes via non-linear frequency mixing owing to the presence of huge microwave transition dipole moments between nearby Rydberg states as well as suitable optical transitions between low-lying states. In the regime of four-wave mixing with off-resonant fields, the excited states can be adiabatically eliminated, leading to an effective Hamiltonian that directly describes the two-mode interaction responsible for the frequency conversion. However, in this regime, the converter is slow, hence sensitive to losses due to cavity decays. To enhance the performance of the conversion process, we employ pulse engineering to tailor the atom-field couplings. The resulting protocol exhibits high robustness against decoherence and parameter fluctuations, making it well suited for realistic experimental implementations. Our scheme provides a promising route toward high-fidelity and scalable hybrid quantum interfaces connecting superconducting and optical quantum networks.
Rydberg EIT-based microwave sensing has limited microwave-to-optical conversion bandwidth due to fundamental limitation in the optical pumping rate to its dark state. We demonstrate a parametric six-wave mixing of optical probe and coupling fields driving the atoms to a Rydberg state via two-photon excitation and two microwave fields with frequency offset of δδδ driving the Rydberg-Rydberg transition in thermal atomic vapor. Microwave-to-optical conversion bandwidth of 171717 MHz is achieved in the present experiment which is limited by the available coupling power. Further theoretical investigation of the system presents higher modulation bandwidth with larger coupling Rabi frequency.
Microwave-to-optics conversion is a core technology for hybrid quantum networks, enabling the integration of microwave and optical frequency domains essential for quantum communication and quantum information processing. However, the Doppler broadening effect in thermal atomic ensembles often severely limits the conversion efficiency. This study aims to propose a novel mechanism for microwave-to-optics conversion using four-wave mixing (FWM) in room-temperature Rydberg atoms, addressing the challenges posed by Doppler broadening and providing a theoretical framework for practical applications. We develop a theoretical model based on the coupled Maxwell-Bloch equations to describe the FWM process in a symmetric double-ladder four-level system. The density matrix method and perturbation method combined with Maxwell’s equations are used to derive an analytical expression for the coherence coefficient between the microwave field and the optical field. This coherence coefficient characterizes the energy transfer between the microwave and optical fields and is used to obtain an analytical expression for the FWM conversion efficiency. We use cesium vapor as a medium to analyze the propagation characteristics of the FWM efficiency and explore the effects of laser field intensity and the Doppler effect on the conversion efficiency. Our analysis reveals that the detuning effect caused by the thermal motion of atoms significantly reduces the resonance coupling efficiency. Specifically, when the Doppler frequency is lower than the natural linewidth, the conversion efficiency can be notably improved. In a Doppler-free environment, the conversion efficiency approaches unity at an optimal propagation distance. In contrast, in room-temperature cesium vapor (300 K), the conversion efficiency is significantly reduced due to Doppler broadening. However, by cooling the atoms to microkelvin temperatures, the Doppler broadening can be minimized, leading to a substantial increase in conversion efficiency. This study provides new theoretical guidance and experimental schemes for microwave-to-optics conversion at room temperature. The proposed mechanism based on Rydberg atoms provides a promising approach to overcoming the limitations imposed by Doppler broadening. Our findings are of great significance for advancing quantum information technology, especially in the context of developing efficient quantum networks.
Microwave-to-optical frequency conversion is a key enabling technology for quantum sensing of microwave fields and for hybrid quantum networks connecting superconducting processors with optical channels. Here, we demonstrate coherent microwave-to-optical conversion using four-wave mixing in a room-temperature cesium vapor. The system achieves an internal photon conversion efficiency close to 0.003 , a dynamic range exceeding 17 dB, and a wide bandwidth of 25 MHz despite using reduced powers of the auxiliary fields. Experimental results are qualitatively reproduced by a Maxwell–Bloch model incorporating Doppler averaging. Numerical analysis indicates that the conversion efficiency can potentially reach several percent by increasing the powers of the auxiliary lasers. These findings establish an experimental and theoretical framework for developing efficient, coherent, and broadband frequency conversion with cesium vapors.