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Acta Physica Sinica

Microwave-to-optics conversion characteristics based on four-wave mixing of Rydberg atoms at room temperature

Fang Li

Published Jan 1, 2025• 0 citations
Publisher

Abstract

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.

DOI
10.7498/aps.74.20250706

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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.
Abstract The coupling of microwave and optical systems presents an immense challenge due to the natural incompatibility of energies, but potential applications range from optical interconnects for quantum computers to next-generation quantum microwave sensors, detectors and coherent imagers. Several of the engineered platforms that have emerged are constrained by specific conditions, such as cryogenic environments, impulse protocols or narrowband fields. Here we employ Rydberg atoms that allow the wideband coupling of optical and microwave photons at room temperature with the use of a modest set-up. We present continuous-wave conversion of a 13.9 GHz field to a near-infrared optical signal using an ensemble of Rydberg atoms via a free-space six-wave mixing process designed to minimize noise interference from any nearby frequencies. The Rydberg photonic converter exhibits a conversion dynamic range of 57 dB and a wide conversion bandwidth of 16 MHz. Using photon counting, we demonstrate the readout of photons of free-space 300 K thermal background radiation at 1.59 nV cm −1 rad −1/2 s −1/2 (3.98 nV cm −1 Hz −1/2 ) with a sensitivity down to 3.8 K of noise-equivalent temperature, allowing us to observe Hanbury Brown and Twiss interference of microwave photons.
The transient dynamics of electromagnetically induced transparency (EIT) are fundamental to understanding coherent light–atom interactions and the advancement of quantum technologies such as optical switching and quantum memory. However, in room-temperature atomic vapors, Doppler broadening significantly alters these dynamics, yet a comprehensive understanding of its impact on the transient EIT response remains lacking. In this study, we combine analytical and numerical methods to investigate the absorption dynamics of a weak probe field in a three-level Λ-type system driven by a strong coupling field, based on the optical Bloch equations and Laplace transform techniques. Our results show that the transient response is highly sensitive to both the atomic spontaneous emission rate and the Rabi frequency of the coupling field. Increasing the coupling field intensity not only accelerates the approach to steady state but also induces oscillatory dynamics and negative absorption. Under Doppler broadening, the time required to reach steady state increases by approximately three orders of magnitude compared to the Doppler-free case—an effect that is surprisingly insensitive to temperature variations across the 100–400 K range. Moreover, restoring a short steady-state time under broadened conditions necessitates increasing the coupling laser intensity by two orders of magnitude. These findings provide key insights into the influence of Doppler broadening on coherent transient processes and offer practical guidelines for the design of room-temperature atomic devices, including quantum memories and optical modulators.
Abstract Coherent microwave-to-optical conversion is crucial for transferring quantum information generated in the microwave domain to optical frequencies, where propagation losses can be minimized. Coherent, atom-based transducers have shown rapid progress in recent years. This paper reports an experimental demonstration of coherent microwave-to-optical conversion that maps a microwave signal to a large, tunable 550(30) MHz range of optical frequencies using room-temperature 87Rb atoms. The inhomogeneous Doppler broadening of the atomic vapor advantageously supports the tunability of an input microwave channel to any optical frequency channel within the Doppler width, along with the simultaneous conversion of a multi-channel input microwave field to corresponding optical channels. In addition, we demonstrate phase-correlated amplitude control of select channels, providing an analog to a frequency domain beam splitter across five orders of magnitude in frequency. With these capabilities, neutral atomic systems may also be effective quantum processors for quantum information encoded in frequency-bin qubits.
Efficient microwave-to-optical frequency conversion (MOC) is crucial for applications such as radiometry, electrometry, quantum microwave illumination and quantum networks. Rydberg atoms provide a unique platform for realizing free-space MOC, promising wide-bandwidth, scalable, and flexible quantum interfaces. Here, we develop a theoretical framework to evaluate the system conversion efficiency, accounting for the mismatch between microwave and optical wavelengths comparing with the atomic ensemble size. Our analysis reveals that the conversion efficiency is fundamentally limited by the focusing of the free-space microwave field, with an upper bound of about 3/16 for diffraction-limited focusing. We propose using a microwave near-field antenna to overcome this limit. Our work provides a foundation for assessing and optimizing free-space MOC, paving the way for a variety of applications based on free-space MOC.
Quantum information encoded in optical photons can be transmitted over long distances with very high information density, and suffers from negligible thermal noise at room temperature. On the other hand, microwave photons at cryogenic temperatures can be confined in high quality resonators and strongly coupled to solid-state qubits, providing a quantum bus to connect qubits and a route to deterministic photonic non-linearities. The coherent interconversion of microwave and optical photons has therefore recently emerged as a highly desirable capability that would enable freely-scalable networks of optically-linked qubits, or large-scale photonic information processing with multi-photon interactions mediated by microwaves. Here, we propose a route to efficient and coherent microwave-optical conversion based on frequency mixing in Rydberg atoms. The interaction requires no microfabricated components or cavities, and is tunable, broadband, and both spatially and spectrally multimode.