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arXiv:2505.10240

Frequency conversion between optical and microwave photons in non-Markovian environments

Jia Tang, H. Z. Shen

Published May 15, 2025• 0 citations
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Abstract

In this paper, we propose a scheme for frequency conversion between optical photons and microwave photons in non-Markovian environments using both magnetic and mechanical excitations as intermediate media. When the frequencies of optical photons, magnons, phonons, and microwave photons resonance, the conversion efficiency can be made close to reach 98.76$\%$ by adjusting the defined complex cooperativities, while in the case of Markovian, the conversion efficiency is 90.44$\%$. By controlling the environmental spectral widths, the efficiency of frequency conversion exhibits a transition from Markovian regimes to non-Markovian regimes. This transformation simultaneously improves frequency conversion efficiency and conversion bandwidth, which is due to the excitation backflow generated by the interaction between the system and the non-Markovian environments. In the case, when the optical pump power in the non-Markovian regimes are of a large order of magnitude, the conversion bandwidth can be increased, but at the cost of reduced conversion efficiency. Our scheme improves the frequency conversion efficiency and bandwidth between optical photons and microwave photons, breaking the limitations of frequency conversion in Markovian environments and providing a new approach for long-distance quantum communication research of other non-Markovian quantum systems in quantum optics.

DOI
10.48550/arxiv.2505.10240

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In this paper, we propose a scheme for frequency conversion between optical photons and microwave photons in non-Markovian environments using both magnetic and mechanical excitations as intermediate media. When the frequencies of optical photons, magnons, phonons, and microwave photons resonance, the conversion efficiency can be made close to reach 98.76%\%% by adjusting the defined complex cooperativities, while in the case of Markovian, the conversion efficiency is 90.44%\%%. By controlling the environmental spectral widths, the efficiency of frequency conversion exhibits a transition from Markovian regimes to non-Markovian regimes. This transformation simultaneously improves frequency conversion efficiency and conversion bandwidth, which is due to the excitation backflow generated by the interaction between the system and the non-Markovian environments. In the case, when the optical pump power in the non-Markovian regimes are of a large order of magnitude, the conversion bandwidth can be increased, but at the cost of reduced conversion efficiency. Our scheme improves the frequency conversion efficiency and bandwidth between optical photons and microwave photons, breaking the limitations of frequency conversion in Markovian environments and providing a new approach for long-distance quantum communication research of other non-Markovian quantum systems in quantum optics.
As the main medium of quantum information, the frequency difference between optical and microwave photons is five orders of magnitude. Therefore, we generally improve the transmission efficiency of optical and microwave photons through coherent and bidirectional measures. The studies of the frequency conversion of optical and microwave photons in recent decades are all limited to Markovian approximations. In this paper we propose a scheme to achieve a two-stage frequency conversion between optical and microwave photons based on a hybrid of magnetic and mechanical excitations in non-Markovian environments. We estimate the interacting strengths under the optimal conditions of yttrium iron garnet and derive the conversion efficiency of optical and microwave photons through the scattering matrix. In all resonance modes, adjusting the defined complex cooperativities can get the conversion efficiency close to unity. The frequency conversion efficiency demonstrates a transition from Markovian to non-Markovian regimes by controlling the environmental spectral widths. This transition leads to enhancements of both the frequency conversion efficiency and conversion bandwidths, which originates from the excitation backflow obtained through the interaction between the systems and non-Markovian environments. In non-Markovian regimes, we predict that in areas with a large order of magnitude of optical pump power, the conversion bandwidths can be increased, but at the cost of a decrease in conversion efficiency, while decreasing the spectral widths can also achieve the same maximum conversion efficiency as in Markovian environments without requiring such a large optical pump power in non-Markovian regimes. Our scheme may provide an opportunity for the investigation of long-distance quantum communication for other non-Markovian quantum systems in quantum optics.
Developing schemes for efficient and broadband frequency conversion of quantum signals is an ongoing challenge in the field of modern quantum information. The coherent conversion between microwave and optical signals is an especially important milestone towards long-distance quantum communication. In this work, we propose a two-stage conversion protocol, employing a resonant interaction between magnetic and mechanical excitations as a mediator between microwave and optical photons. Based on estimates for the coupling strengths under optimized conditions for yttrium iron garnet, we predict close to unity conversion efficiency without the requirement of matching cooperativities. We predict a conversion bandwidth in the regions of largest efficiency of the order of magnitude of the coupling strengths that can be further increased at the expense of reduced conversion efficiency.
Quantum conversion or interface is one of the most prominent protocols in quantum information processing and quantum state engineering. We propose a photon-phonon conversion protocol in a hybrid magnomechanical system comprising a microwave optical mode, a driven magnon mode, and a mechanical-vibrating mode, which has attracted much interest and is expected to become a building block of the future quantum information network due to its controllability in coupling strengths. The microwave photons in the optical cavity are coupled to the magnons by the Zeeman interaction, and the latter are coupled to the mechanical phonons by the magnetostrictive interaction. With a strong photon-magnon interaction and a strong driving on the magnon, an effective Hamiltonian is constructed to describe the conversion between photons and phonons near their resonant point. The cavity-magnon system can then play the role of quantum memory. Moreover, the faithfulness of the photon-phonon conversion is estimated in terms of fidelities for state evolution and state-independent transfer. The former is discussed in the Lindblad master equation, taking account of the leakages of photons, phonons, and magnons into consideration. The latter is derived by the Heisenberg-Langevin equation considering the non-Markovian noise from the structured environments for both optical and mechanical modes. The state-evolution fidelity is found to be robust to the weak leakage. The transfer fidelity can be maintained by the Ohmic and sub-Ohmic environments of the photons and is insensitive to the 1/f1/f1/f noise of the phonons. Our work thus provides an interesting application for the magnon system as a photon-phonon converter in the microwave regime.
Coherent conversion of microwave and optical photons in the single quantum level can significantly expand our ability to process signals in various fields. Efficient up-conversion of a feeble signal in the microwave domain to the optical domain will lead to quantum-noise-limited microwave amplifiers. Coherent exchange between optical photons and microwave photons will also be a stepping stone to realize long-distance quantum communication. Here we demonstrate bidirectional and coherent conversion between microwave and light using collective spin excitations in a ferromagnet. The converter consists of two harmonic oscillator modes, a microwave cavity mode and a magnetostatic mode called the Kittel mode, where microwave photons and magnons in the respective modes are strongly coupled and hybridized. An itinerant microwave field and a traveling optical field can be coupled through the hybrid system, where the microwave field is coupled to the hybrid system through the cavity mode, while the optical field addresses the hybrid system through the Kittel mode via Faraday and inverse Faraday effects. The conversion efficiency is theoretically analyzed and experimentally evaluated. The possible schemes for improving the efficiency are also discussed.
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.
We propose a low-noise, triply resonant, electro-optic (EO) scheme for quantum microwave-to-optical conversion based on coupled nanophotonics resonators integrated with a superconducting qubit. Our optical system features a split resonance---a doublet---with a tunable frequency splitting that matches the microwave resonance frequency of the superconducting qubit. This is in contrast to conventional approaches, where large optical resonators with free-spectral range comparable to the qubit microwave frequency are used. In our system, EO mixing between the optical pump coupled into the low-frequency doublet mode and a resonance microwave photon results in an up-converted optical photon on resonance with high-frequency doublet mode. Importantly, the down-conversion process, which is the source of noise, is suppressed in our scheme as the coupled-resonator system does not support modes at that frequency. Our device has at least an order of magnitude smaller footprint than conventional devices, resulting in large overlap between optical and microwave fields and a large photon conversion rate ($g/2\ensuremath{\pi}$) in the range of $\ensuremath{\sim}5$--15 kHz. Owing to a large ggg factor and doubly resonant nature of our device, microwave-to-optical frequency conversion can be achieved with optical pump powers in the range of tens of microwatts, even with moderate values for optical Q\mathit{Q}Q ($\ensuremath{\sim}{10}^{6}$) and microwave QQQ ($\ensuremath{\sim}{10}^{4}$). The performance metrics of our device, with substantial improvement over the previous EO-based approaches, promise a scalable quantum microwave-to-optical conversion and networking of superconducting processors via optical fiber communication.